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diff --git a/sourcecodes/bnt-master/nethelp3.3/CVS/Entries b/sourcecodes/bnt-master/nethelp3.3/CVS/Entries new file mode 100644 index 00000000..f617382b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/CVS/Entries @@ -0,0 +1,174 @@ +/conffig.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/confmat.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/conjgrad.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/consist.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/convertoldnet.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/datread.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/datwrite.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/dem2ddat.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/demard.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/demev1.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/demev2.htm/1.1.1.1/Wed Apr 27 17:58:54 2005// +/demev3.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgauss.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demglm1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demglm2.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgmm1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgmm2.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgmm3.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgmm4.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgmm5.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgp.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgpard.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgpot.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgtm1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demgtm2.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demhint.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demhmc1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demhmc2.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demhmc3.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demkmn1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demknn1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demmdn1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demmet1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demmlp1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demmlp2.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demnlab.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demns1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demolgd1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demopt1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/dempot.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demprgp.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demprior.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demrbf1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demsom1.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/demtrain.htm/1.1.1.1/Wed Apr 27 17:58:56 2005// +/dist2.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/eigdec.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/errbayes.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/evidence.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/fevbayes.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gauss.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gbayes.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glm.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmderiv.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmerr.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmevfwd.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmfwd.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmgrad.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmhess.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glminit.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmpak.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmtrain.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/glmunpak.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmm.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmactiv.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmem.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmminit.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmpak.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmpost.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmprob.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmsamp.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gmmunpak.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gp.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gpcovar.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gpcovarf.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gpcovarp.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gperr.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gpfwd.htm/1.1.1.1/Wed Apr 27 17:58:58 2005// +/gpgrad.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gpinit.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gppak.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gpunpak.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gradchek.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/graddesc.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gsamp.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtm.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmem.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmfwd.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtminit.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmlmean.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmlmode.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmmag.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmpost.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/gtmprob.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/hbayes.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/hesschek.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/hintmat.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/hinton.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/histp.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/hmc.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/index.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/kmeans.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/knn.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/knnfwd.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/linef.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/linemin.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/maxitmess.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/mdn.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/mdn2gmm.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/mdndist2.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/mdnerr.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/mdnfwd.htm/1.1.1.1/Wed Apr 27 17:59:00 2005// +/mdngrad.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mdninit.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mdnpak.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mdnpost.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mdnprob.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mdnunpak.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/metrop.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/minbrack.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlp.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpbkp.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpderiv.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlperr.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpevfwd.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpfwd.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpgrad.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlphdotv.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlphess.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlphint.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpinit.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlppak.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpprior.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlptrain.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/mlpunpak.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netderiv.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/neterr.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netevfwd.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netgrad.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/nethelp3.3.zip/1.1.1.1/Wed Apr 27 17:59:02 2005// +/nethess.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netinit.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netopt.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netpak.htm/1.1.1.1/Wed Apr 27 17:59:02 2005// +/netunpak.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/olgd.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/pca.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/plotmat.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/ppca.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/quasinew.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbf.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfbkp.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfderiv.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbferr.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfevfwd.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbffwd.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfgrad.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfhess.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfjacob.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfpak.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfprior.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfsetbf.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfsetfw.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbftrain.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rbfunpak.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rosegrad.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/rosen.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/scg.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/som.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/somfwd.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/sompak.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/somtrain.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +/somunpak.htm/1.1.1.1/Wed Apr 27 17:59:04 2005// +D diff --git a/sourcecodes/bnt-master/nethelp3.3/CVS/Repository b/sourcecodes/bnt-master/nethelp3.3/CVS/Repository new file mode 100644 index 00000000..d6658c37 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/CVS/Repository @@ -0,0 +1 @@ +FullBNT/nethelp3.3 diff --git a/sourcecodes/bnt-master/nethelp3.3/CVS/Root b/sourcecodes/bnt-master/nethelp3.3/CVS/Root new file mode 100644 index 00000000..f3bd14a6 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/CVS/Root @@ -0,0 +1 @@ +:ext:nsaunier@bnt.cvs.sourceforge.net:/cvsroot/bnt diff --git a/sourcecodes/bnt-master/nethelp3.3/conffig.htm b/sourcecodes/bnt-master/nethelp3.3/conffig.htm new file mode 100644 index 00000000..52aca7b9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/conffig.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual conffig +</title> +</head> +<body> +<H1> conffig +</H1> +<h2> +Purpose +</h2> +Display a confusion matrix. + +<p><h2> +Synopsis +</h2> +<PRE> +conffig(y, t) +fh = conffig(y, t)</PRE> + + +<p><h2> +Description +</h2> +<CODE>conffig(y, t)</CODE> displays the confusion matrix +and classification performance for the predictions mat{y} +compared with the targets <CODE>t</CODE>. The data is assumed to be in a +1-of-N encoding, unless there is just one column, when it is assumed to +be a 2 class problem with a 0-1 encoding. Each row of <CODE>y</CODE> and <CODE>t</CODE> +corresponds to a single example. + +<p>In the confusion matrix, the rows represent the true classes and the +columns the predicted classes. + +<p><CODE>fh = conffig(y, t)</CODE> also returns the figure handle <CODE>fh</CODE> which +can be used, for instance, to delete the figure when it is no longer needed. + +<p><h2> +See Also +</h2> +<CODE><a href="confmat.htm">confmat</a></CODE>, <CODE><a href="demtrain.htm">demtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/confmat.htm b/sourcecodes/bnt-master/nethelp3.3/confmat.htm new file mode 100644 index 00000000..2162293d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/confmat.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual confmat +</title> +</head> +<body> +<H1> confmat +</H1> +<h2> +Purpose +</h2> +Compute a confusion matrix. + +<p><h2> +Synopsis +</h2> +<PRE> +[C, rate] = confmat(y, t)</PRE> + + +<p><h2> +Description +</h2> +<CODE>[C, rate] = confmat(y, t)</CODE> computes the confusion matrix <CODE>C</CODE> +and classification performance <CODE>rate</CODE> for the predictions mat{y} +compared with the targets <CODE>t</CODE>. The data is assumed to be in a +1-of-N encoding, unless there is just one column, when it is assumed to +be a 2 class problem with a 0-1 encoding. Each row of <CODE>y</CODE> and <CODE>t</CODE> +corresponds to a single example. + +<p>In the confusion matrix, the rows represent the true classes and the +columns the predicted classes. The vector <CODE>rate</CODE> has two entries: +the percentage of correct classifications and the total number of +correct classifications. + +<p><h2> +See Also +</h2> +<CODE><a href="conffig.htm">conffig</a></CODE>, <CODE><a href="demtrain.htm">demtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/conjgrad.htm b/sourcecodes/bnt-master/nethelp3.3/conjgrad.htm new file mode 100644 index 00000000..4a70c330 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/conjgrad.htm @@ -0,0 +1,101 @@ +<html> +<head> +<title> +Netlab Reference Manual conjgrad +</title> +</head> +<body> +<H1> conjgrad +</H1> +<h2> +Purpose +</h2> +Conjugate gradients optimization. + +<p><h2> +Description +</h2> +<CODE>[x, options, flog, pointlog] = conjgrad(f, x, options, gradf)</CODE> uses a +conjugate gradients +algorithm to find the minimum of the function <CODE>f(x)</CODE> whose +gradient is given by <CODE>gradf(x)</CODE>. Here <CODE>x</CODE> is a row vector +and <CODE>f</CODE> returns a scalar value. +The point at which <CODE>f</CODE> has a local minimum +is returned as <CODE>x</CODE>. The function value at that point is returned +in <CODE>options(8)</CODE>. A log of the function values +after each cycle is (optionally) returned in <CODE>flog</CODE>, and a log +of the points visited is (optionally) returned in <CODE>pointlog</CODE>. + +<p><CODE>conjgrad(f, x, options, gradf, p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>, and the points visited +in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value +of <CODE>x</CODE> at the solution. If the absolute difference between +the values of <CODE>x</CODE> between two successive steps is less than +<CODE>options(2)</CODE>, then this condition is satisfied. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. If the absolute difference between the +objective function values between two successive steps is less than +<CODE>options(3)</CODE>, then this condition is satisfied. +Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function. + +<p><CODE>options(10)</CODE> returns the total number of function evaluations (including +those in any line searches). + +<p><CODE>options(11)</CODE> returns the total number of gradient evaluations. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p><CODE>options(15)</CODE> is the precision in parameter space of the line search; +default <CODE>1e-4</CODE>. + +<p><h2> +Examples +</h2> +An example of +the use of the additional arguments is the minimization of an error +function for a neural network: +<PRE> + +w = quasinew('neterr', w, options, 'netgrad', net, x, t); +</PRE> + + +<p><h2> +Algorithm +</h2> + +The conjugate gradients algorithm constructs search +directions <CODE>di</CODE> that are conjugate: i.e. <CODE>di*H*d(i-1) = 0</CODE>, +where <CODE>H</CODE> is the Hessian matrix. This means that minimising along +<CODE>di</CODE> does not undo the effect of minimising along the previous +direction. The Polak-Ribiere formula is used to calculate new search +directions. The Hessian is not calculated, so there is only an +<CODE>O(W)</CODE> storage requirement (where <CODE>W</CODE> is the number of +parameters). However, relatively accurate line searches must be used +(default is <CODE>1e-04</CODE>). + +<p><h2> +See Also +</h2> +<CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/consist.htm b/sourcecodes/bnt-master/nethelp3.3/consist.htm new file mode 100644 index 00000000..40bc374c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/consist.htm @@ -0,0 +1,78 @@ +<html> +<head> +<title> +Netlab Reference Manual consist +</title> +</head> +<body> +<H1> consist +</H1> +<h2> +Purpose +</h2> +Check that arguments are consistent. + +<p><h2> +Synopsis +</h2> +<PRE> +errstring = consist(net, type, inputs, outputs) +errstring = consist(net, type, inputs) +errstring = consist(net, type) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>errstring = consist(net, type, inputs)</CODE> takes a network +data structure <CODE>net</CODE> together with a string <CODE>type</CODE> containing +the correct network type, a matrix <CODE>inputs</CODE> of input vectors and checks +that the data structure is consistent with the other arguments. An empty +string is returned if there is no error, otherwise the string contains the +relevant error message. If the <CODE>type</CODE> string is empty, then any +type of network is allowed. + +<p><CODE>errstring = consist(net, type)</CODE> takes a network data structure +<CODE>net</CODE> together with a string <CODE>type</CODE> containing the correct +network type, and checks that the two types match. + +<p><CODE>errstring = consist(net, type, inputs, outputs)</CODE> also checks that the +network has the correct number of outputs, and that the number of patterns +in the <CODE>inputs</CODE> and <CODE>outputs</CODE> is the same. The fields in <CODE>net</CODE> +that are used are +<PRE> + type + nin + nout +</PRE> + + +<p><h2> +Example +</h2> + +<p><CODE>mlpfwd</CODE>, the function that propagates values forward through an MLP +network, has the following check at the head of the file: +<PRE> + +errstring = consist(net, 'mlp', x, t); +if ~isempty(errstring) + error(errstring) +end +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="mlpfwd.htm">mlpfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/convertoldnet.htm b/sourcecodes/bnt-master/nethelp3.3/convertoldnet.htm new file mode 100644 index 00000000..c3266367 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/convertoldnet.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual convertoldnet +</title> +</head> +<body> +<H1> convertoldnet +</H1> +<h2> +Purpose +</h2> +Convert pre-2.3 release MLP and MDN nets to new format + +<p><h2> +Synopsis +</h2> +<PRE> +net = convertoldnet(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = convertoldnet(net)</CODE> takes a network <CODE>net</CODE> and, if appropriate, +converts it from pre-2.3 to the current format. The difference is simply +that in MLPs and the MLP sub-net of MDNs the field <CODE>actfn</CODE> has been +renamed <CODE>outfn</CODE> to make it consistent with GLM and RBF networks. +If the network is not old-format or an MLP or MDN it is left unchanged. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mdn.htm">mdn</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/datread.htm b/sourcecodes/bnt-master/nethelp3.3/datread.htm new file mode 100644 index 00000000..78f087eb --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/datread.htm @@ -0,0 +1,57 @@ +<html> +<head> +<title> +Netlab Reference Manual datread +</title> +</head> +<body> +<H1> datread +</H1> +<h2> +Purpose +</h2> +Read data from an ascii file. + +<p><h2> +Synopsis +</h2> +<PRE> +[x, t, nin, nout, ndata] = datread(filename) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>[x, t, nin, nout, ndata] = datread(filename)</CODE> reads from +the file <CODE>filename</CODE> and returns a matrix <CODE>x</CODE> of input vectors, +a matrix <CODE>t</CODE> of target vectors, and integers <CODE>nin</CODE>, <CODE>nout</CODE> +and <CODE>ndata</CODE> specifying the number of inputs, the number of outputs +and the number of data points respectively. + +<p>The format of the data file is as follows: the first row contains the +string <CODE>nin</CODE> followed by the number of inputs, the second row +contains the string <CODE>nout</CODE> followed by the number of outputs, and +the third row contains the string <CODE>ndata</CODE> followed by the number +of data vectors. Subsequent lines each contain one input vector +followed by one output vector, with individual values separated by +spaces. + +<p><h2> +Example +</h2> +For the XOR data set we have + +<p><h2> +See Also +</h2> +<CODE><a href="nin2nout1ndata40.000000e+000.000000e+001.000000e+000.000000e+001.000000e+000.000000e+001.000000e+000.000000e+000.000000e+001.000000e+001.000000e+001.000000e+00SeeAlsodatwrite.htm">nin2nout1ndata40.000000e+000.000000e+001.000000e+000.000000e+001.000000e+000.000000e+001.000000e+000.000000e+000.000000e+001.000000e+001.000000e+001.000000e+00SeeAlsodatwrite</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/datwrite.htm b/sourcecodes/bnt-master/nethelp3.3/datwrite.htm new file mode 100644 index 00000000..1006b911 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/datwrite.htm @@ -0,0 +1,65 @@ +<html> +<head> +<title> +Netlab Reference Manual datwrite +</title> +</head> +<body> +<H1> datwrite +</H1> +<h2> +Purpose +</h2> +Write data to ascii file. + +<p><h2> +Synopsis +</h2> +<PRE> +datwrite(filename, x, t) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>datwrite(filename, x, t)</CODE> takes a matrix <CODE>x</CODE> of input vectors +and a matrix <CODE>t</CODE> of target vectors and writes them to an ascii +file named <CODE>filename</CODE>. The file format is as follows: the first +row contains the string <CODE>nin</CODE> followed by the number of inputs, +the second row contains the string <CODE>nout</CODE> followed by the number +of outputs, and the third row contains the string <CODE>ndata</CODE> followed +by the number of data vectors. Subsequent lines each contain one input +vector followed by one output vector, with individual values separated +by spaces. + +<p><h2> +Example +</h2> +For the XOR data set we have + +<p><PRE> + + nin 2 + nout 1 + ndata 4 + 0.000000e+00 0.000000e+00 1.000000e+00 + 0.000000e+00 1.000000e+00 0.000000e+00 + 1.000000e+00 0.000000e+00 0.000000e+00 + 1.000000e+00 1.000000e+00 1.000000e+00 +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="datread.htm">datread</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/dem2ddat.htm b/sourcecodes/bnt-master/nethelp3.3/dem2ddat.htm new file mode 100644 index 00000000..5dd49ba5 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/dem2ddat.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual dem2ddat +</title> +</head> +<body> +<H1> dem2ddat +</H1> +<h2> +Purpose +</h2> +Generates two dimensional data for demos. + +<p><h2> +Synopsis +</h2> +<PRE> +data = dem2ddat(ndata)</PRE> + +<PRE> +[data, c] = dem2ddat(ndata)</PRE> + + +<p><h2> +Description +</h2> +The data is +drawn from three spherical Gaussian distributions with priors 0.3, +0.5 and 0.2; centres (2, 3.5), (0, 0) and (0,2); and standard deviations +0.2, 0.5 and 1.0. <CODE>data = dem2ddat(ndata)</CODE> generates <CODE>ndata</CODE> +points. + +<p><CODE>[data, c] = dem2ddat(ndata)</CODE> also returns a matrix containing the +centres of the Gaussian distributions. + +<p><h2> +See Also +</h2> +<CODE><a href="demgmm1.htm">demgmm1</a></CODE>, <CODE><a href="demkmean.htm">demkmean</a></CODE>, <CODE><a href="demknn1.htm">demknn1</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demard.htm b/sourcecodes/bnt-master/nethelp3.3/demard.htm new file mode 100644 index 00000000..43923377 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demard.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual demard +</title> +</head> +<body> +<H1> demard +</H1> +<h2> +Purpose +</h2> +Automatic relevance determination using the MLP. + +<p><h2> +Synopsis +</h2> +<PRE> +demmlp1</PRE> + + +<p><h2> +Description +</h2> +This script demonstrates the technique of automatic relevance +determination (ARD) using a synthetic problem having three input +variables: <CODE>x1</CODE> is sampled uniformly from the range (0,1) and has +a low level of added Gaussian noise, <CODE>x2</CODE> is a copy of <CODE>x1</CODE> +with a higher level of added noise, and <CODE>x3</CODE> is sampled randomly +from a Gaussian distribution. The single target variable is determined +by <CODE>sin(2*pi*x1)</CODE> with additive Gaussian noise. Thus <CODE>x1</CODE> is +very relevant for determining the target value, <CODE>x2</CODE> is of some +relevance, while <CODE>x3</CODE> is irrelevant. The prior over weights is +given by the ARD Gaussian prior with a separate hyper-parameter for +the group of weights associated with each input. A multi-layer +perceptron is trained on this data, with re-estimation of the +hyper-parameters using <CODE>evidence</CODE>. The final values for the +hyper-parameters reflect the relative importance of the three inputs. + +<p><h2> +See Also +</h2> +<CODE><a href="demmlp1.htm">demmlp1</a></CODE>, <CODE><a href="demev1.htm">demev1</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demev1.htm b/sourcecodes/bnt-master/nethelp3.3/demev1.htm new file mode 100644 index 00000000..f7b05fbb --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demev1.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual demev1 +</title> +</head> +<body> +<H1> demev1 +</H1> +<h2> +Purpose +</h2> +Demonstrate Bayesian regression for the MLP. + +<p><h2> +Synopsis +</h2> +<PRE> +demev1</PRE> + + +<p><h2> +Description +</h2> +The problem consists an input variable <CODE>x</CODE> which sampled from a +Gaussian distribution, and a target variable <CODE>t</CODE> generated by +computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian noise. A 2-layer +network with linear outputs is trained by minimizing a sum-of-squares +error function with isotropic Gaussian regularizer, using the scaled +conjugate gradient optimizer. The hyperparameters <CODE>alpha</CODE> and +<CODE>beta</CODE> are re-estimated using the function <CODE>evidence</CODE>. A graph +is plotted of the original function, the training data, the trained +network function, and the error bars. + +<p><h2> +See Also +</h2> +<CODE><a href="evidence.htm">evidence</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE>, <CODE><a href="demard.htm">demard</a></CODE>, <CODE><a href="demmlp1.htm">demmlp1</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demev2.htm b/sourcecodes/bnt-master/nethelp3.3/demev2.htm new file mode 100644 index 00000000..c1db9e65 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demev2.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual demev2 +</title> +</head> +<body> +<H1> demev2 +</H1> +<h2> +Purpose +</h2> +Demonstrate Bayesian classification for the MLP. + +<p><h2> +Synopsis +</h2> +<PRE> +demev2</PRE> + + +<p><h2> +Description +</h2> +A synthetic two class two-dimensional dataset <CODE>x</CODE> is sampled +from a mixture of four Gaussians. Each class is +associated with two of the Gaussians so that the optimal decision +boundary is non-linear. +A 2-layer +network with logistic outputs is trained by minimizing the cross-entropy +error function with isotroipc Gaussian regularizer (one hyperparameter for +each of the four standard weight groups), using the scaled +conjugate gradient optimizer. The hyperparameter vectors <CODE>alpha</CODE> and +<CODE>beta</CODE> are re-estimated using the function <CODE>evidence</CODE>. A graph +is plotted of the optimal, regularised, and unregularised decision +boundaries. A further plot of the moderated versus unmoderated contours +is generated. + +<p><h2> +See Also +</h2> +<CODE><a href="evidence.htm">evidence</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE>, <CODE><a href="demard.htm">demard</a></CODE>, <CODE><a href="demmlp2.htm">demmlp2</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demev3.htm b/sourcecodes/bnt-master/nethelp3.3/demev3.htm new file mode 100644 index 00000000..55af4d64 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demev3.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual demev3 +</title> +</head> +<body> +<H1> demev3 +</H1> +<h2> +Purpose +</h2> +Demonstrate Bayesian regression for the RBF. + +<p><h2> +Synopsis +</h2> +<PRE> +demev3</PRE> + + +<p><h2> +Description +</h2> +The problem consists an input variable <CODE>x</CODE> which sampled from a +Gaussian distribution, and a target variable <CODE>t</CODE> generated by +computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian noise. An RBF +network with linear outputs is trained by minimizing a sum-of-squares +error function with isotropic Gaussian regularizer, using the scaled +conjugate gradient optimizer. The hyperparameters <CODE>alpha</CODE> and +<CODE>beta</CODE> are re-estimated using the function <CODE>evidence</CODE>. A graph +is plotted of the original function, the training data, the trained +network function, and the error bars. + +<p><h2> +See Also +</h2> +<CODE><a href="demev1.htm">demev1</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE>, <CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE>, <CODE><a href="netevfwd.htm">netevfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgauss.htm b/sourcecodes/bnt-master/nethelp3.3/demgauss.htm new file mode 100644 index 00000000..4ddc8059 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgauss.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual demgauss +</title> +</head> +<body> +<H1> demgauss +</H1> +<h2> +Purpose +</h2> +Demonstrate sampling from Gaussian distributions. + +<p><h2> +Synopsis +</h2> +<PRE> +demgauss +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>demgauss</CODE> provides a simple illustration of the generation of +data from Gaussian distributions. It first samples from a +one-dimensional distribution using <CODE>randn</CODE>, and then plots a +normalized histogram estimate of the distribution using <CODE>histp</CODE> +together with the true density calculated using <CODE>gauss</CODE>. + +<p><CODE>demgauss</CODE> then demonstrates sampling from a Gaussian distribution +in two dimensions. It creates a mean vector and a covariance matrix, +and then plots contours of constant density using the function +<CODE>gauss</CODE>. A sample of points drawn from this distribution, obtained +using the function <CODE>gsamp</CODE>, is then superimposed on the contours. + +<p><h2> +See Also +</h2> +<CODE><a href="gauss.htm">gauss</a></CODE>, <CODE><a href="gsamp.htm">gsamp</a></CODE>, <CODE><a href="histp.htm">histp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demglm1.htm b/sourcecodes/bnt-master/nethelp3.3/demglm1.htm new file mode 100644 index 00000000..7740b361 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demglm1.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demglm1 +</title> +</head> +<body> +<H1> demglm1 +</H1> +<h2> +Purpose +</h2> +Demonstrate simple classification using a generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +demglm1</PRE> + + +<p><h2> +Description +</h2> + +The problem consists of a two dimensional input +matrix <CODE>data</CODE> and a vector of classifications <CODE>t</CODE>. The data is +generated from two Gaussian clusters, and a generalized linear model +with logistic output is trained using iterative reweighted least squares. +A plot of the data together with the 0.1, 0.5 and 0.9 contour lines +of the conditional probability is generated. + +<p><h2> +See Also +</h2> +<CODE><a href="demglm2.htm">demglm2</a></CODE>, <CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demglm2.htm b/sourcecodes/bnt-master/nethelp3.3/demglm2.htm new file mode 100644 index 00000000..274d5b61 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demglm2.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demglm2 +</title> +</head> +<body> +<H1> demglm2 +</H1> +<h2> +Purpose +</h2> +Demonstrate simple classification using a generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +demglm1</PRE> + + +<p><h2> +Description +</h2> + +The problem consists of a two dimensional input +matrix <CODE>data</CODE> and a vector of classifications <CODE>t</CODE>. The data is +generated from three Gaussian clusters, and a generalized linear model +with softmax output is trained using iterative reweighted least squares. +A plot of the data together with regions shaded by the classification +given by the network is generated. + +<p><h2> +See Also +</h2> +<CODE><a href="demglm1.htm">demglm1</a></CODE>, <CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgmm1.htm b/sourcecodes/bnt-master/nethelp3.3/demgmm1.htm new file mode 100644 index 00000000..7476becb --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgmm1.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual demgmm1 +</title> +</head> +<body> +<H1> demgmm1 +</H1> +<h2> +Purpose +</h2> +Demonstrate EM for Gaussian mixtures. + +<p><h2> +Synopsis +</h2> +<PRE> +demgmm1</PRE> + + +<p><h2> +Description +</h2> +This script demonstrates the use of the EM algorithm to fit a mixture +of Gaussians to a set of data using maximum likelihood. A colour +coding scheme is used to illustrate the evaluation of the posterior +probabilities in the E-step of the EM algorithm. + +<p><h2> +See Also +</h2> +<CODE><a href="demgmm2.htm">demgmm2</a></CODE>, <CODE><a href="demgmm3.htm">demgmm3</a></CODE>, <CODE><a href="demgmm4.htm">demgmm4</a></CODE>, <CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmpost.htm">gmmpost</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgmm2.htm b/sourcecodes/bnt-master/nethelp3.3/demgmm2.htm new file mode 100644 index 00000000..f8a3f61d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgmm2.htm @@ -0,0 +1,52 @@ +<html> +<head> +<title> +Netlab Reference Manual demgmm1 +</title> +</head> +<body> +<H1> demgmm1 +</H1> +<h2> +Purpose +</h2> +Demonstrate density modelling with a Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> +demgmm1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of modelling data generated by a mixture of three +Gaussians in 2 dimensions. The priors are 0.3, +0.5 and 0.2; the centres are (2, 3.5), (0, 0) and (0,2); the variances +are 0.2, 0.5 and 1.0. The first figure contains a + scatter plot of the data. + +<p>A Gaussian mixture model with three components is trained using EM. The +parameter vector is printed before training and after training. The user +should press any key to continue at these points. The parameter vector +consists of priors (the column), centres (given as (x, y) pairs as +the next two columns), and variances (the last column). + +<p>The second figure is a 3 dimensional view of the density function, while +the third shows the 1-standard deviation circles for the three components of +the mixture model. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE>, <CODE><a href="gmmunpak.htm">gmmunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgmm3.htm b/sourcecodes/bnt-master/nethelp3.3/demgmm3.htm new file mode 100644 index 00000000..bbd7465c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgmm3.htm @@ -0,0 +1,55 @@ +<html> +<head> +<title> +Netlab Reference Manual demgmm3 +</title> +</head> +<body> +<H1> demgmm3 +</H1> +<h2> +Purpose +</h2> +Demonstrate density modelling with a Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> +demgmm3</PRE> + + +<p><h2> +Description +</h2> + +The problem consists of modelling data generated +by a mixture of three Gaussians in 2 dimensions with a mixture model +using diagonal covariance matrices. The priors are 0.3, 0.5 and 0.2; the +centres are (2, 3.5), (0, 0) and (0,2); the covariances are all axis aligned +(0.16, 0.64), (0.25, 1) and the identity +matrix. The first figure contains a scatter plot of the data. + +<p>A Gaussian mixture model with three components is trained using EM. The +parameter vector is printed before training and after training. The user +should press any key to continue at these points. The parameter vector +consists of priors (the column), and centres (given as (x, y) pairs as +the next two columns). The diagonal entries of the +covariance matrices are printed separately. + +<p>The second figure is a 3 dimensional view of the density function, +while the third shows the axes of the 1-standard deviation circles +for the three components of the mixture model. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE>, <CODE><a href="gmmunpak.htm">gmmunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgmm4.htm b/sourcecodes/bnt-master/nethelp3.3/demgmm4.htm new file mode 100644 index 00000000..95f4bc87 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgmm4.htm @@ -0,0 +1,54 @@ +<html> +<head> +<title> +Netlab Reference Manual demgmm4 +</title> +</head> +<body> +<H1> demgmm4 +</H1> +<h2> +Purpose +</h2> +Demonstrate density modelling with a Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> +demgmm4</PRE> + + +<p><h2> +Description +</h2> + +The problem consists of modelling data generated +by a mixture of three Gaussians in 2 dimensions with a mixture model +using full covariance matrices. The priors are 0.3, 0.5 and 0.2; the +centres are (2, 3.5), (0, 0) and (0,2); the variances are (0.16, 0.64) +axis aligned, (0.25, 1) rotated by 30 degrees and the identity +matrix. The first figure contains a scatter plot of the data. + +<p>A Gaussian mixture model with three components is trained using EM. The +parameter vector is printed before training and after training. The user +should press any key to continue at these points. The parameter vector +consists of priors (the column), and centres (given as (x, y) pairs as +the next two columns). The covariance matrices are printed separately. + +<p>The second figure is a 3 dimensional view of the density function, +while the third shows the axes of the 1-standard deviation ellipses +for the three components of the mixture model. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE>, <CODE><a href="gmmunpak.htm">gmmunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgmm5.htm b/sourcecodes/bnt-master/nethelp3.3/demgmm5.htm new file mode 100644 index 00000000..ed3caf1e --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgmm5.htm @@ -0,0 +1,55 @@ +<html> +<head> +<title> +Netlab Reference Manual demgmm5 +</title> +</head> +<body> +<H1> demgmm5 +</H1> +<h2> +Purpose +</h2> +Demonstrate density modelling with a PPCA mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> +demgmm5</PRE> + + +<p><h2> +Description +</h2> + +The problem consists of modelling data generated +by a mixture of three Gaussians in 2 dimensions with a mixture model +using full covariance matrices. The priors are 0.3, 0.5 and 0.2; the +centres are (2, 3.5), (0, 0) and (0,2); the variances are (0.16, 0.64) +axis aligned, (0.25, 1) rotated by 30 degrees and the identity +matrix. The first figure contains a scatter plot of the data. + +<p>A mixture model with three one-dimensional PPCA components is trained +using EM. The parameter vector is printed before training and after +training. The parameter vector consists of priors (the column), and +centres (given as (x, y) pairs as the next two columns). + +<p>The second figure is a 3 dimensional view of the density function, +while the third shows the axes of the 1-standard deviation ellipses +for the three components of the mixture model together with the one +standard deviation along the principal component of each mixture +model component. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE>, <CODE><a href="ppca.htm">ppca</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgp.htm b/sourcecodes/bnt-master/nethelp3.3/demgp.htm new file mode 100644 index 00000000..9103bfb8 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgp.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demgp +</title> +</head> +<body> +<H1> demgp +</H1> +<h2> +Purpose +</h2> +Demonstrate simple regression using a Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +demgp</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable <CODE>x</CODE> and one target variable +<CODE>t</CODE>. The values in <CODE>x</CODE> are chosen in two separated clusters and the +target data is generated by computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian +noise. Two Gaussian Processes, each with different covariance functions +are trained by optimising the hyperparameters +using the scaled conjugate gradient algorithm. The final predictions are +plotted together with 2 standard deviation error bars. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE>, <CODE><a href="gpinit.htm">gpinit</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgpard.htm b/sourcecodes/bnt-master/nethelp3.3/demgpard.htm new file mode 100644 index 00000000..eb188c19 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgpard.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual demgpard +</title> +</head> +<body> +<H1> demgpard +</H1> +<h2> +Purpose +</h2> +Demonstrate ARD using a Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +demgpare</PRE> + + +<p><h2> +Description +</h2> +The data consists of three input variables <CODE>x1</CODE>, <CODE>x2</CODE> and +<CODE>x3</CODE>, and one target variable +<CODE>t</CODE>. The +target data is generated by computing <CODE>sin(2*pi*x1)</CODE> and adding Gaussian +noise, x2 is a copy of x1 with a higher level of added +noise, and x3 is sampled randomly from a Gaussian distribution. +A Gaussian Process, is +trained by optimising the hyperparameters +using the scaled conjugate gradient algorithm. The final values of the +hyperparameters show that the model successfully identifies the importance +of each input. + +<p><h2> +See Also +</h2> +<CODE><a href="demgp.htm">demgp</a></CODE>, <CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE>, <CODE><a href="gpinit.htm">gpinit</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgpot.htm b/sourcecodes/bnt-master/nethelp3.3/demgpot.htm new file mode 100644 index 00000000..368f222e --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgpot.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demgpot +</title> +</head> +<body> +<H1> demgpot +</H1> +<h2> +Purpose +</h2> +Computes the gradient of the negative log likelihood for a mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> +g = demgpot(x, mix)</PRE> + + +<p><h2> +Description +</h2> +This function computes the gradient of the negative log of the unconditional data +density <CODE>p(x)</CODE> with respect to the coefficients of the +data vector <CODE>x</CODE> for a Gaussian mixture model. The data structure +<CODE>mix</CODE> defines the mixture model, while the matrix <CODE>x</CODE> contains +the data vector as a row vector. Note the unusual order of the arguments: +this is so that the function can be used in <CODE>demhmc1</CODE> directly for +sampling from the distribution <CODE>p(x)</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="demhmc1.htm">demhmc1</a></CODE>, <CODE><a href="demmet1.htm">demmet1</a></CODE>, <CODE><a href="dempot.htm">dempot</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgtm1.htm b/sourcecodes/bnt-master/nethelp3.3/demgtm1.htm new file mode 100644 index 00000000..1422c764 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgtm1.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual demgtm1 +</title> +</head> +<body> +<H1> demgtm1 +</H1> +<h2> +Purpose +</h2> +Demonstrate EM for GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +demgtm1</PRE> + + +<p><h2> +Description +</h2> + +This script demonstrates the use of the EM +algorithm to fit a one-dimensional GTM to a two-dimensional set of data +using maximum likelihood. The location and spread of the Gaussian kernels +in the data space is shown during training. + +<p><h2> +See Also +</h2> +<CODE><a href="demgtm2.htm">demgtm2</a></CODE>, <CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmem.htm">gtmem</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demgtm2.htm b/sourcecodes/bnt-master/nethelp3.3/demgtm2.htm new file mode 100644 index 00000000..4696b152 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demgtm2.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual demgtm2 +</title> +</head> +<body> +<H1> demgtm2 +</H1> +<h2> +Purpose +</h2> +Demonstrate GTM for visualisation. + +<p><h2> +Synopsis +</h2> +<PRE> +demgtm2</PRE> + + +<p><h2> +Description +</h2> + +This script demonstrates the use of a +GTM with a two-dimensional latent space to visualise data in a higher +dimensional space. +This is done through the use of the mean responsibility and magnification +factors. + +<p><h2> +See Also +</h2> +<CODE><a href="demgtm1.htm">demgtm1</a></CODE>, <CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmem.htm">gtmem</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demhint.htm b/sourcecodes/bnt-master/nethelp3.3/demhint.htm new file mode 100644 index 00000000..ac54f77a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demhint.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual demhint +</title> +</head> +<body> +<H1> demhint +</H1> +<h2> +Purpose +</h2> +Demonstration of Hinton diagram for 2-layer feed-forward network. + +<p><h2> +Synopsis +</h2> +<PRE> +demhint +demhint(nin, nhidden, nout)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>demhint</CODE> plots a Hinton diagram for a 2-layer feedforward network +with 5 inputs, 4 hidden units and 3 outputs. The weight vector is +chosen from a Gaussian distribution as described under <CODE>mlp</CODE>. + +<p><CODE>demhint(nin, nhidden, nout)</CODE> allows the user to specify the +number of inputs, hidden units and outputs. + +<p><h2> +See Also +</h2> +<CODE><a href="hinton.htm">hinton</a></CODE>, <CODE><a href="hintmat.htm">hintmat</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demhmc1.htm b/sourcecodes/bnt-master/nethelp3.3/demhmc1.htm new file mode 100644 index 00000000..4ad8b73b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demhmc1.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual demhmc1 +</title> +</head> +<body> +<H1> demhmc1 +</H1> +<h2> +Purpose +</h2> +Demonstrate Hybrid Monte Carlo sampling on mixture of two Gaussians. + +<p><h2> +Synopsis +</h2> +<PRE> +demhmc1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of generating data from a mixture of two Gaussians +in two dimensions using a hybrid Monte Carlo algorithm with persistence. +A mixture model is then fitted to the sample to compare it with the +true underlying generator. + +<p><h2> +See Also +</h2> +<CODE><a href="demhmc3.htm">demhmc3</a></CODE>, <CODE><a href="hmc.htm">hmc</a></CODE>, <CODE><a href="dempot.htm">dempot</a></CODE>, <CODE><a href="demgpot.htm">demgpot</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demhmc2.htm b/sourcecodes/bnt-master/nethelp3.3/demhmc2.htm new file mode 100644 index 00000000..b5657cbe --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demhmc2.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual demhmc2 +</title> +</head> +<body> +<H1> demhmc2 +</H1> +<h2> +Purpose +</h2> +Demonstrate Bayesian regression with Hybrid Monte Carlo sampling. + +<p><h2> +Synopsis +</h2> +<PRE> +demhmc2</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable <CODE>x</CODE> and one target variable +<CODE>t</CODE> with data generated by sampling <CODE>x</CODE> at equal intervals and then +generating target data by computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian +noise. The model is a 2-layer network with linear outputs, and the hybrid Monte +Carlo algorithm (without persistence) is used to sample from the posterior +distribution of the weights. The graph shows the underlying function, +100 samples from the function given by the posterior distribution of the +weights, and the average prediction (weighted by the posterior probabilities). + +<p><h2> +See Also +</h2> +<CODE><a href="demhmc3.htm">demhmc3</a></CODE>, <CODE><a href="hmc.htm">hmc</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demhmc3.htm b/sourcecodes/bnt-master/nethelp3.3/demhmc3.htm new file mode 100644 index 00000000..9ccc16c9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demhmc3.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual demhmc3 +</title> +</head> +<body> +<H1> demhmc3 +</H1> +<h2> +Purpose +</h2> +Demonstrate Bayesian regression with Hybrid Monte Carlo sampling. + +<p><h2> +Synopsis +</h2> +<PRE> +demhmc3</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable <CODE>x</CODE> and one target variable +<CODE>t</CODE> with data generated by sampling <CODE>x</CODE> at equal intervals and then +generating target data by computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian +noise. The model is a 2-layer network with linear outputs, and the hybrid Monte +Carlo algorithm (with persistence) is used to sample from the posterior +distribution of the weights. The graph shows the underlying function, +300 samples from the function given by the posterior distribution of the +weights, and the average prediction (weighted by the posterior probabilities). + +<p><h2> +See Also +</h2> +<CODE><a href="demhmc2.htm">demhmc2</a></CODE>, <CODE><a href="hmc.htm">hmc</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demkmn1.htm b/sourcecodes/bnt-master/nethelp3.3/demkmn1.htm new file mode 100644 index 00000000..f22787df --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demkmn1.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual demkmean +</title> +</head> +<body> +<H1> demkmean +</H1> +<h2> +Purpose +</h2> +Demonstrate simple clustering model trained with K-means. + +<p><h2> +Synopsis +</h2> +<PRE> +demkmean</PRE> + + +<p><h2> +Description +</h2> +The problem consists of data in a two-dimensional space. +The data is +drawn from three spherical Gaussian distributions with priors 0.3, +0.5 and 0.2; centres (2, 3.5), (0, 0) and (0,2); and standard deviations +0.2, 0.5 and 1.0. The first figure contains a +scatter plot of the data. The data is the same as in <CODE>demgmm1</CODE>. + +<p>A cluster model with three components is trained using the batch +K-means algorithm. The matrix of centres is printed after training. +The second +figure shows the data labelled with a colour derived from the corresponding +cluster + +<p><h2> +See Also +</h2> +<CODE><a href="dem2ddat.htm">dem2ddat</a></CODE>, <CODE><a href="demgmm1.htm">demgmm1</a></CODE>, <CODE><a href="knn1.htm">knn1</a></CODE>, <CODE><a href="kmeans.htm">kmeans</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demknn1.htm b/sourcecodes/bnt-master/nethelp3.3/demknn1.htm new file mode 100644 index 00000000..6c0d4031 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demknn1.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual demknn1 +</title> +</head> +<body> +<H1> demknn1 +</H1> +<h2> +Purpose +</h2> +Demonstrate nearest neighbour classifier. + +<p><h2> +Synopsis +</h2> +<PRE> +demknn1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of data in a two-dimensional space. +The data is +drawn from three spherical Gaussian distributions with priors 0.3, +0.5 and 0.2; centres (2, 3.5), (0, 0) and (0,2); and standard deviations +0.2, 0.5 and 1.0. The first figure contains a +scatter plot of the data. The data is the same as in <CODE>demgmm1</CODE>. + +<p>The second +figure shows the data labelled with the corresponding class given +by the classifier. + +<p><h2> +See Also +</h2> +<CODE><a href="dem2ddat.htm">dem2ddat</a></CODE>, <CODE><a href="demgmm1.htm">demgmm1</a></CODE>, <CODE><a href="knn.htm">knn</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demmdn1.htm b/sourcecodes/bnt-master/nethelp3.3/demmdn1.htm new file mode 100644 index 00000000..7401d220 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demmdn1.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual demmdn1 +</title> +</head> +<body> +<H1> demmdn1 +</H1> +<h2> +Purpose +</h2> +Demonstrate fitting a multi-valued function using a Mixture Density Network. + +<p><h2> +Synopsis +</h2> +<PRE> +demmdn1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable +<CODE>x</CODE> and one target variable <CODE>t</CODE> with data generated by +sampling <CODE>t</CODE> at equal intervals and then generating target data by +computing <CODE>t + 0.3*sin(2*pi*t)</CODE> and adding Gaussian noise. A +Mixture Density Network with 3 centres in the mixture model is trained +by minimizing a negative log likelihood error function using the scaled +conjugate gradient optimizer. + +<p>The conditional means, mixing coefficients and variances are plotted +as a function of <CODE>x</CODE>, and a contour plot of the full conditional +density is also generated. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demmet1.htm b/sourcecodes/bnt-master/nethelp3.3/demmet1.htm new file mode 100644 index 00000000..ff5423df --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demmet1.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demmet1 +</title> +</head> +<body> +<H1> demmet1 +</H1> +<h2> +Purpose +</h2> +Demonstrate Markov Chain Monte Carlo sampling on a Gaussian. + +<p><h2> +Synopsis +</h2> +<PRE> +demmet1 +demmet1(plotwait)</PRE> + + +<p><h2> +Description +</h2> +The problem consists of generating data from a Gaussian +in two dimensions using a Markov Chain Monte Carlo algorithm. The points are +plotted one after another to show the path taken by the chain. + +<p><CODE>demmet1(plotwait)</CODE> allows the user to set the time (in a whole number +of seconds) between the plotting of points. This is passed to <CODE>pause</CODE> + +<p><h2> +See Also +</h2> +<CODE><a href="demhmc1.htm">demhmc1</a></CODE>, <CODE><a href="metrop.htm">metrop</a></CODE>, <CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="dempot.htm">dempot</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demmlp1.htm b/sourcecodes/bnt-master/nethelp3.3/demmlp1.htm new file mode 100644 index 00000000..3d9c2079 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demmlp1.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual demmlp1 +</title> +</head> +<body> +<H1> demmlp1 +</H1> +<h2> +Purpose +</h2> +Demonstrate simple regression using a multi-layer perceptron + +<p><h2> +Synopsis +</h2> +<PRE> +demmlp1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable <CODE>x</CODE> and one target variable +<CODE>t</CODE> with data generated by sampling <CODE>x</CODE> at equal intervals and then +generating target data by computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian +noise. A 2-layer network with linear outputs is trained by minimizing a +sum-of-squares error function using the scaled conjugate gradient optimizer. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demmlp2.htm b/sourcecodes/bnt-master/nethelp3.3/demmlp2.htm new file mode 100644 index 00000000..ecb5e002 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demmlp2.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual demmlp2 +</title> +</head> +<body> +<H1> demmlp2 +</H1> +<h2> +Purpose +</h2> +Demonstrate simple classification using a multi-layer perceptron + +<p><h2> +Synopsis +</h2> +<PRE> +demmlp2</PRE> + + +<p><h2> +Description +</h2> +The problem consists of input data in two dimensions drawn from a mixture +of three Gaussians: two of which are assigned to a single class. An MLP +with logistic outputs trained with a quasi-Newton optimisation algorithm is +compared with the optimal Bayesian decision rule. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE>, <CODE><a href="neterr.htm">neterr</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demnlab.htm b/sourcecodes/bnt-master/nethelp3.3/demnlab.htm new file mode 100644 index 00000000..1d46b12c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demnlab.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual demnlab +</title> +</head> +<body> +<H1> demnlab +</H1> +<h2> +Purpose +</h2> +A front-end Graphical User Interface to the demos + +<p><h2> +Synopsis +</h2> +<PRE> +demnlab</PRE> + + +<p><h2> +Description +</h2> +This function will start a user interface allowing the user to select +different demonstration functions to view. The demos are divided into 4 +groups, with the demo being executed by selecting the desired option +from a pop-up menu. + +<p><h2> +See Also +</h2> +<CODE><a href=".htm"></a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demns1.htm b/sourcecodes/bnt-master/nethelp3.3/demns1.htm new file mode 100644 index 00000000..9a6bcae7 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demns1.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual demns1 +</title> +</head> +<body> +<H1> demns1 +</H1> +<h2> +Purpose +</h2> +Demonstrate Neuroscale for visualisation. + +<p><h2> +Synopsis +</h2> +<PRE> +demns1</PRE> + + +<p><h2> +Description +</h2> +This script demonstrates the use of the Neuroscale algorithm for +topographic projection and visualisation. A data sample is generated +from a mixture of two Gaussians in 4d space, and an RBF is trained +with the stress error function to project the data into 2d. The training +data and a test sample are both plotted in this projection. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfprior.htm">rbfprior</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demolgd1.htm b/sourcecodes/bnt-master/nethelp3.3/demolgd1.htm new file mode 100644 index 00000000..76c55303 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demolgd1.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual demolgd1 +</title> +</head> +<body> +<H1> demolgd1 +</H1> +<h2> +Purpose +</h2> +Demonstrate simple MLP optimisation with on-line gradient descent + +<p><h2> +Synopsis +</h2> +<PRE> +demolgd1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable <CODE>x</CODE> and one target variable +<CODE>t</CODE> with data generated by sampling <CODE>x</CODE> at equal intervals and then +generating target data by computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian +noise. A 2-layer network with linear outputs is trained by minimizing a +sum-of-squares error function using on-line gradient descent. + +<p><h2> +See Also +</h2> +<CODE><a href="demmlp1.htm">demmlp1</a></CODE>, <CODE><a href="olgd.htm">olgd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demopt1.htm b/sourcecodes/bnt-master/nethelp3.3/demopt1.htm new file mode 100644 index 00000000..b2511711 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demopt1.htm @@ -0,0 +1,52 @@ +<html> +<head> +<title> +Netlab Reference Manual demopt1 +</title> +</head> +<body> +<H1> demopt1 +</H1> +<h2> +Purpose +</h2> +Demonstrate different optimisers on Rosenbrock's function. + +<p><h2> +Synopsis +</h2> +<PRE> +demopt1 +demopt1(xinit) +</PRE> + + +<p><h2> +Description +</h2> +The four general optimisers (quasi-Newton, conjugate gradients, +scaled conjugate gradients, and gradient descent) are applied to +the minimisation of Rosenbrock's well known `banana' function. +Each optimiser is run for at most 100 cycles, and a stopping +criterion of 1.0e-4 is used for both position and function value. +At the end, the trajectory of each algorithm is shown on a contour +plot of the function. + +<p><CODE>demopt1(xinit)</CODE> allows the user to specify a row vector with +two columns as the starting point. The default is the point [-1 1]. +Note that the contour plot has an x range of [-1.5, 1.5] and a y +range of [-0.5, 2.1], so it is best to choose a starting point in the +same region. + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE>, <CODE><a href="rosen.htm">rosen</a></CODE>, <CODE><a href="rosegrad.htm">rosegrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/dempot.htm b/sourcecodes/bnt-master/nethelp3.3/dempot.htm new file mode 100644 index 00000000..10bc3907 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/dempot.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual dempot +</title> +</head> +<body> +<H1> dempot +</H1> +<h2> +Purpose +</h2> +Computes the negative log likelihood for a mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> +e = dempot(x, mix)</PRE> + + +<p><h2> +Description +</h2> +This function computes the negative log of the unconditional data +density <CODE>p(x)</CODE> for a Gaussian mixture model. The data structure +<CODE>mix</CODE> defines the mixture model, while the matrix <CODE>x</CODE> contains +the data vectors. + +<p><h2> +See Also +</h2> +<CODE><a href="demgpot.htm">demgpot</a></CODE>, <CODE><a href="demhmc1.htm">demhmc1</a></CODE>, <CODE><a href="demmet1.htm">demmet1</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demprgp.htm b/sourcecodes/bnt-master/nethelp3.3/demprgp.htm new file mode 100644 index 00000000..1d7abeca --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demprgp.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demprgp +</title> +</head> +<body> +<H1> demprgp +</H1> +<h2> +Purpose +</h2> +Demonstrate sampling from a Gaussian Process prior. + +<p><h2> +Synopsis +</h2> +<PRE> +demprgp</PRE> + + +<p><h2> +Description +</h2> +This function plots the functions represented by a Gaussian Process +model. The hyperparameter values can be adjusted +on a linear scale using the sliders (though the exponential +of the parameters is used in the covariance function), or +by typing values into the text boxes and pressing the return key. +Both types of covariance function are supported. An extra function +specific parameter is needed for the rational quadratic function. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demprior.htm b/sourcecodes/bnt-master/nethelp3.3/demprior.htm new file mode 100644 index 00000000..02f5a000 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demprior.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual demprior +</title> +</head> +<body> +<H1> demprior +</H1> +<h2> +Purpose +</h2> +Demonstrate sampling from a multi-parameter Gaussian prior. + +<p><h2> +Synopsis +</h2> +<PRE> +demprior</PRE> + + +<p><h2> +Description +</h2> +This function plots the functions represented by a multi-layer perceptron +network when the weights are set to values drawn from a Gaussian prior +distribution. The parameters <CODE>aw1</CODE>, <CODE>ab1</CODE> <CODE>aw2</CODE> and <CODE>ab2</CODE> +control the inverse variances of the first-layer weights, the hidden unit +biases, the second-layer weights and the output unit biases respectively. +Their values can be adjusted on a logarithmic scale using the sliders, or +by typing values into the text boxes and pressing the return key. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demrbf1.htm b/sourcecodes/bnt-master/nethelp3.3/demrbf1.htm new file mode 100644 index 00000000..6c36ed49 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demrbf1.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual demrbf1 +</title> +</head> +<body> +<H1> demrbf1 +</H1> +<h2> +Purpose +</h2> +Demonstrate simple regression using a radial basis function network. + +<p><h2> +Synopsis +</h2> +<PRE> +demrbf1</PRE> + + +<p><h2> +Description +</h2> +The problem consists of one input variable <CODE>x</CODE> and one target variable +<CODE>t</CODE> with data generated by sampling <CODE>x</CODE> at equal intervals and then +generating target data by computing <CODE>sin(2*pi*x)</CODE> and adding Gaussian +noise. This data is the same as that used in demmlp1. + +<p>Three different RBF networks (with different activation functions) +are trained in two stages. First, a Gaussian mixture model is trained using +the EM algorithm, and the centres of this model are used to set the centres +of the RBF. Second, the output weights (and biases) are determined using the +pseudo-inverse of the design matrix. + +<p><h2> +See Also +</h2> +<CODE><a href="demmlp1.htm">demmlp1</a></CODE>, <CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE>, <CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demsom1.htm b/sourcecodes/bnt-master/nethelp3.3/demsom1.htm new file mode 100644 index 00000000..4cc1bbf0 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demsom1.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual demsom1 +</title> +</head> +<body> +<H1> demsom1 +</H1> +<h2> +Purpose +</h2> +Demonstrate SOM for visualisation. + +<p><h2> +Synopsis +</h2> +<PRE> +demsom1</PRE> + + +<p><h2> +Description +</h2> + +This script demonstrates the use of a +SOM with a two-dimensional grid to map onto data in +two-dimensional space. Both on-line and batch training algorithms +are shown. + +<p><h2> +See Also +</h2> +<CODE><a href="som.htm">som</a></CODE>, <CODE><a href="sompak.htm">sompak</a></CODE>, <CODE><a href="somtrain.htm">somtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/demtrain.htm b/sourcecodes/bnt-master/nethelp3.3/demtrain.htm new file mode 100644 index 00000000..f3c8d8d5 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/demtrain.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual demtrain +</title> +</head> +<body> +<H1> demtrain +</H1> +<h2> +Purpose +</h2> +Demonstrate training of MLP network. + +<p><h2> +Synopsis +</h2> +<PRE> +demtrain</PRE> + + +<p><h2> +Description +</h2> +<CODE>demtrain</CODE> brings up a simple GUI to show the training of +an MLP network on classification and regression problems. The user +should load in a dataset (which should be in Netlab format: see +<CODE>datread</CODE>), select the output activation function, the + number of cycles and hidden units and then +train the network. The scaled conjugate gradient algorithm is used. +A graph shows the evolution of the error: the value is shown +<CODE>max(ceil(iterations / 50), 5)</CODE> cycles. + +<p>Once the network is trained, it is saved to the file <CODE>mlptrain.net</CODE>. +The results can then be viewed as a confusion matrix (for classification +problems) or a plot of output versus target (for regression problems). + +<p><h2> +See Also +</h2> +<CODE><a href="confmat.htm">confmat</a></CODE>, <CODE><a href="datread.htm">datread</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="netopt.htm">netopt</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/dist2.htm b/sourcecodes/bnt-master/nethelp3.3/dist2.htm new file mode 100644 index 00000000..80dd82b9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/dist2.htm @@ -0,0 +1,57 @@ +<html> +<head> +<title> +Netlab Reference Manual dist2 +</title> +</head> +<body> +<H1> dist2 +</H1> +<h2> +Purpose +</h2> +Calculates squared distance between two sets of points. + +<p><h2> +Synopsis +</h2> +<PRE> +d = dist2(x, c) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>d = dist2(x, c)</CODE> takes two matrices of vectors and calculates the +squared Euclidean distance between them. Both matrices must be of the +same column dimension. If <CODE>x</CODE> has <CODE>m</CODE> rows and <CODE>n</CODE> columns, and +<CODE>c</CODE> has <CODE>l</CODE> rows and <CODE>n</CODE> columns, then the result has +<CODE>m</CODE> rows and <CODE>l</CODE> columns. The <CODE>i, j</CODE>th entry is the +squared distance from the <CODE>i</CODE>th row of <CODE>x</CODE> to the <CODE>j</CODE>th +row of <CODE>c</CODE>. + +<p><h2> +Example +</h2> +The following code is used in <CODE>rbffwd</CODE> to calculate the activation of +a thin plate spline function. +<PRE> + +n2 = dist2(x, c); +z = log(n2.^(n2.^2)); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gmmactiv.htm">gmmactiv</a></CODE>, <CODE><a href="kmeans.htm">kmeans</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/eigdec.htm b/sourcecodes/bnt-master/nethelp3.3/eigdec.htm new file mode 100644 index 00000000..b981a96c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/eigdec.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual eigdec +</title> +</head> +<body> +<H1> eigdec +</H1> +<h2> +Purpose +</h2> +Sorted eigendecomposition + +<p><h2> +Synopsis +</h2> +<PRE> +evals = eigdec(x, N) +[evals, evec] = eigdec(x, N) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>evals = eigdec(x, N</CODE> computes the largest <CODE>N</CODE> eigenvalues of the +matrix <CODE>x</CODE> in descending order. <CODE>[evals, evec] = eigdec(x, N)</CODE> +also computes the corresponding eigenvectors. + +<p><h2> +See Also +</h2> +<CODE><a href="pca.htm">pca</a></CODE>, <CODE><a href="ppca.htm">ppca</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/errbayes.htm b/sourcecodes/bnt-master/nethelp3.3/errbayes.htm new file mode 100644 index 00000000..d3aaa1da --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/errbayes.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual errbayes +</title> +</head> +<body> +<H1> errbayes +</H1> +<h2> +Purpose +</h2> +Evaluate Bayesian error function for network. + +<p><h2> +Synopsis +</h2> +<PRE> +e = errbayes(net, edata) +[e, edata, eprior] = errbayes(net, edata) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>e = errbayes(net, edata)</CODE> takes a network data structure +<CODE>net</CODE> together +the data contribution to the error for a set of inputs and targets. +It returns the regularised error using any zero mean Gaussian priors +on the weights defined in +<CODE>net</CODE>. + +<p><CODE>[e, edata, eprior] = errbayes(net, x, t)</CODE> additionally returns the +data and prior components of the error. + +<p><h2> +See Also +</h2> +<CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="rbferr.htm">rbferr</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/evidence.htm b/sourcecodes/bnt-master/nethelp3.3/evidence.htm new file mode 100644 index 00000000..7e319484 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/evidence.htm @@ -0,0 +1,57 @@ +<html> +<head> +<title> +Netlab Reference Manual evidence +</title> +</head> +<body> +<H1> evidence +</H1> +<h2> +Purpose +</h2> +Re-estimate hyperparameters using evidence approximation. + +<p><h2> +Synopsis +</h2> +<PRE> +[net] = evidence(net, x, t) +[net, gamma, logev] = evidence(net, x, t, num) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>[net] = evidence(net, x, t)</CODE> re-estimates the +hyperparameters <CODE>alpha</CODE> and <CODE>beta</CODE> by applying Bayesian +re-estimation formulae for <CODE>num</CODE> iterations. The hyperparameter +<CODE>alpha</CODE> can be a simple scalar associated with an isotropic prior +on the weights, or can be a vector in which each component is +associated with a group of weights as defined by the <CODE>index</CODE> +matrix in the <CODE>net</CODE> data structure. These more complex priors can +be set up for an MLP using <CODE>mlpprior</CODE>. Initial values for the iterative +re-estimation are taken from the network data structure <CODE>net</CODE> +passed as an input argument, while the return argument <CODE>net</CODE> +contains the re-estimated values. + +<p><CODE>[net, gamma, logev] = evidence(net, x, t, num)</CODE> allows the re-estimation +formula to be applied for <CODE>num</CODE> cycles in which the re-estimated +values for the hyperparameters from each cycle are used to re-evaluate +the Hessian matrix for the next cycle. The return value <CODE>gamma</CODE> is +the number of well-determined parameters and <CODE>logev</CODE> is the log +of the evidence. + +<p><h2> +See Also +</h2> +<CODE><a href="mlpprior.htm">mlpprior</a></CODE>, <CODE><a href="netgrad.htm">netgrad</a></CODE>, <CODE><a href="nethess.htm">nethess</a></CODE>, <CODE><a href="demev1.htm">demev1</a></CODE>, <CODE><a href="demard.htm">demard</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/fevbayes.htm b/sourcecodes/bnt-master/nethelp3.3/fevbayes.htm new file mode 100644 index 00000000..42289df9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/fevbayes.htm @@ -0,0 +1,53 @@ +<html> +<head> +<title> +Netlab Reference Manual fevbayes +</title> +</head> +<body> +<H1> fevbayes +</H1> +<h2> +Purpose +</h2> +Evaluate Bayesian regularisation for network forward propagation. + +<p><h2> +Synopsis +</h2> +<PRE> +extra = fevbayes(net, y, a, x, t, x_test) +[extra, invhess] = fevbayes(net, y, a, x, t, x_test, invhess) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>extra = fevbayes(net, y, a, x, t, x_test)</CODE> takes a network data structure +<CODE>net</CODE> together with a set of hidden unit activations <CODE>a</CODE> from +test inputs <CODE>x_test</CODE>, training data inputs <CODE>x</CODE> and <CODE>t</CODE> and +outputs a matrix of extra information <CODE>extra</CODE> that consists of +error bars (variance) +for a regression problem or moderated outputs for a classification problem. +The optional argument (and return value) +<CODE>invhess</CODE> is the inverse of the network Hessian +computed on the training data inputs and targets. Passing it in avoids +recomputing it, which can be a significant saving for large training sets. + +<p>This is called by network-specific functions such as <CODE>mlpevfwd</CODE> which +are needed since the return values (predictions and hidden unit activations) +for different network types are in different orders (for good reasons). + +<p><h2> +See Also +</h2> +<CODE><a href="mlpevfwd.htm">mlpevfwd</a></CODE>, <CODE><a href="rbfevfwd.htm">rbfevfwd</a></CODE>, <CODE><a href="glmevfwd.htm">glmevfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gauss.htm b/sourcecodes/bnt-master/nethelp3.3/gauss.htm new file mode 100644 index 00000000..4f0f0d88 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gauss.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual gauss +</title> +</head> +<body> +<H1> gauss +</H1> +<h2> +Purpose +</h2> +Evaluate a Gaussian distribution. + +<p><h2> +Synopsis +</h2> +<PRE> +y = gauss(mu, covar, x) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>y = gauss(mu, covar, x)</CODE> evaluates a multi-variate Gaussian +density in <CODE>d</CODE>-dimensions at a set of points given by the rows +of the matrix <CODE>x</CODE>. The Gaussian density has mean vector <CODE>mu</CODE> +and covariance matrix <CODE>covar</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gsamp.htm">gsamp</a></CODE>, <CODE><a href="demgauss.htm">demgauss</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gbayes.htm b/sourcecodes/bnt-master/nethelp3.3/gbayes.htm new file mode 100644 index 00000000..3e123fdf --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gbayes.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual gbayes +</title> +</head> +<body> +<H1> gbayes +</H1> +<h2> +Purpose +</h2> +Evaluate gradient of Bayesian error function for network. + +<p><h2> +Synopsis +</h2> +<PRE> +g = gbayes(net, gdata) +[g, gdata, gprior] = gbayes(net, gdata) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = gbayes(net, gdata)</CODE> takes a network data structure <CODE>net</CODE> together +the data contribution to the error gradient +for a set of inputs and targets. +It returns the regularised error gradient using any zero mean Gaussian priors +on the weights defined in +<CODE>net</CODE>. In addition, if a <CODE>mask</CODE> is defined in <CODE>net</CODE>, then +the entries in <CODE>g</CODE> that correspond to weights with a 0 in the +mask are removed. + +<p><CODE>[g, gdata, gprior] = gbayes(net, gdata)</CODE> additionally returns the +data and prior components of the error. + +<p><h2> +See Also +</h2> +<CODE><a href="errbayes.htm">errbayes</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glm.htm b/sourcecodes/bnt-master/nethelp3.3/glm.htm new file mode 100644 index 00000000..a860372f --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glm.htm @@ -0,0 +1,85 @@ +<html> +<head> +<title> +Netlab Reference Manual glm +</title> +</head> +<body> +<H1> glm +</H1> +<h2> +Purpose +</h2> +Create a generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +net = glm(nin, nout, func) +net = glm(nin, nout, func, prior) +net = glm(nin, nout, func, prior, beta) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = glm(nin, nout, func)</CODE> takes the number of inputs +and outputs for a generalized linear model, together +with a string <CODE>func</CODE> which specifies the output unit activation function, +and returns a data structure <CODE>net</CODE>. The weights are drawn from a zero mean, +isotropic Gaussian, with variance scaled by the fan-in of the +output units. This makes use of the Matlab function +<CODE>randn</CODE> and so the seed for the random weight initialization can be +set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the seed value. The optional +argument <CODE>alpha</CODE> sets the inverse variance for the weight +initialization. + +<p>The fields in <CODE>net</CODE> are +<PRE> + type = 'glm' + nin = number of inputs + nout = number of outputs + nwts = total number of weights and biases + actfn = string describing the output unit activation function: + 'linear' + 'logistic' + 'softmax' + w1 = first-layer weight matrix + b1 = first-layer bias vector +</PRE> + + +<p><CODE>net = glm(nin, nout, func, prior)</CODE>, in which <CODE>prior</CODE> is +a scalar, allows the field +<CODE>net.alpha</CODE> in the data structure <CODE>net</CODE> to be set, corresponding +to a zero-mean isotropic Gaussian prior with inverse variance with +value <CODE>prior</CODE>. Alternatively, <CODE>prior</CODE> can consist of a data +structure with fields <CODE>alpha</CODE> and <CODE>index</CODE>, allowing individual +Gaussian priors to be set over groups of weights in the network. Here +<CODE>alpha</CODE> is a column vector in which each element corresponds to a +separate group of weights, which need not be mutually exclusive. The +membership of the groups is defined by the matrix <CODE>index</CODE> in which +the columns correspond to the elements of <CODE>alpha</CODE>. Each column has +one element for each weight in the matrix, in the order defined by the +function <CODE>glmpak</CODE>, and each element is 1 or 0 according to whether +the weight is a member of the corresponding group or not. + +<p><CODE>net = glm(nin, nout, func, prior, beta)</CODE> also sets the +additional field <CODE>net.beta</CODE> in the data structure <CODE>net</CODE>, where +beta corresponds to the inverse noise variance. + +<p><h2> +See Also +</h2> +<CODE><a href="glmpak.htm">glmpak</a></CODE>, <CODE><a href="glmunpak.htm">glmunpak</a></CODE>, <CODE><a href="glmfwd.htm">glmfwd</a></CODE>, <CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmderiv.htm b/sourcecodes/bnt-master/nethelp3.3/glmderiv.htm new file mode 100644 index 00000000..56887889 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmderiv.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual glmderiv +</title> +</head> +<body> +<H1> glmderiv +</H1> +<h2> +Purpose +</h2> +Evaluate derivatives of GLM outputs with respect to weights. + +<p><h2> +Synopsis +</h2> +<PRE> + +g = glmderiv(net, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = glmderiv(net, x)</CODE> takes a network data structure <CODE>net</CODE> and a matrix +of input vectors <CODE>x</CODE> and returns a three-index matrix mat{g} whose +<CODE>i</CODE>, <CODE>j</CODE>, <CODE>k</CODE> +element contains the derivative of network output <CODE>k</CODE> with respect to +weight or bias parameter <CODE>j</CODE> for input pattern <CODE>i</CODE>. The ordering of the +weight and bias parameters is defined by <CODE>glmunpak</CODE>. + +<p><h2> +See also +</h2> +<PRE> +glm, glmunpak, glmgrad</PRE> + + +<p><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmerr.htm b/sourcecodes/bnt-master/nethelp3.3/glmerr.htm new file mode 100644 index 00000000..fde8a08b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmerr.htm @@ -0,0 +1,56 @@ +<html> +<head> +<title> +Netlab Reference Manual glmerr +</title> +</head> +<body> +<H1> glmerr +</H1> +<h2> +Purpose +</h2> +Evaluate error function for generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +e = glmerr(net, x, t) +[e, edata, eprior] = glmerr(net, x, t) +[e, edata, eprior, y, a] = glmerr(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>e = glmerr(net, x, t)</CODE> takes a generalized +linear model data structure <CODE>net</CODE> together with a matrix <CODE>x</CODE> +of input vectors and a matrix <CODE>t</CODE> of target vectors, and evaluates +the error function <CODE>e</CODE>. The choice of error function corresponds +to the output unit activation function. Each row of <CODE>x</CODE> +corresponds to one input vector and each row of <CODE>t</CODE> corresponds to +one target vector. + +<p><CODE>[e, edata, eprior, y, a] = glmerr(net, x, t)</CODE> also returns +the data and prior components of the total error. + +<p><CODE>[e, edata, eprior, y, a] = glmerr(net, x)</CODE> also returns a matrix <CODE>y</CODE> +giving the outputs of the models and a matrix <CODE>a</CODE> +giving the summed inputs to each output unit, where each row +corresponds to one pattern. + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmpak.htm">glmpak</a></CODE>, <CODE><a href="glmunpak.htm">glmunpak</a></CODE>, <CODE><a href="glmfwd.htm">glmfwd</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmevfwd.htm b/sourcecodes/bnt-master/nethelp3.3/glmevfwd.htm new file mode 100644 index 00000000..fc2f4749 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmevfwd.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual glmevfwd +</title> +</head> +<body> +<H1> glmevfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation with evidence for GLM + +<p><h2> +Synopsis +</h2> +<PRE> + +[y, extra] = glmevfwd(net, x, t, x_test) +[y, extra, invhess] = glmevfwd(net, x, t, x_test, invhess) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = glmevfwd(net, x, t, x_test)</CODE> takes a network data structure +<CODE>net</CODE> together with the input <CODE>x</CODE> and target <CODE>t</CODE> training data +and input test data <CODE>x_test</CODE>. +It returns the normal forward propagation through the network <CODE>y</CODE> +together with a matrix <CODE>extra</CODE> which consists of error bars (variance) +for a regression problem or moderated outputs for a classification problem. + +<p>The optional argument (and return value) +<CODE>invhess</CODE> is the inverse of the network Hessian +computed on the training data inputs and targets. Passing it in avoids +recomputing it, which can be a significant saving for large training sets. + +<p><h2> +See Also +</h2> +<CODE><a href="fevbayes.htm">fevbayes</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmfwd.htm b/sourcecodes/bnt-master/nethelp3.3/glmfwd.htm new file mode 100644 index 00000000..9e8f1061 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmfwd.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual glmfwd +</title> +</head> +<body> +<H1> glmfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +y = glmfwd(net, x) +[y, a] = glmfwd(net, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = glmfwd(net, x)</CODE> takes a generalized linear model +data structure <CODE>net</CODE> together with +a matrix <CODE>x</CODE> of input vectors, and forward propagates the inputs +through the network to generate a matrix <CODE>y</CODE> of output +vectors. Each row of <CODE>x</CODE> corresponds to one input vector and each +row of <CODE>y</CODE> corresponds to one output vector. + +<p><CODE>[y, a] = glmfwd(net, x)</CODE> also returns a matrix <CODE>a</CODE> +giving the summed inputs to each output unit, where each row +corresponds to one pattern. + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmpak.htm">glmpak</a></CODE>, <CODE><a href="glmunpak.htm">glmunpak</a></CODE>, <CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmgrad.htm b/sourcecodes/bnt-master/nethelp3.3/glmgrad.htm new file mode 100644 index 00000000..024a5d19 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmgrad.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual glmgrad +</title> +</head> +<body> +<H1> glmgrad +</H1> +<h2> +Purpose +</h2> +Evaluate gradient of error function for generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> + +g = glmgrad(net, x, t) +[g, gdata, gprior] = glmgrad(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = glmgrad(net, x, t)</CODE> takes a generalized linear model +data structure <CODE>net</CODE> +together with a matrix <CODE>x</CODE> of input vectors and a matrix <CODE>t</CODE> +of target vectors, and evaluates the gradient <CODE>g</CODE> of the error +function with respect to the network weights. The error function +corresponds to the choice of output unit activation function. Each row +of <CODE>x</CODE> corresponds to one input vector and each row of <CODE>t</CODE> +corresponds to one target vector. + +<p><CODE>[g, gdata, gprior] = glmgrad(net, x, t)</CODE> also returns separately +the data and prior contributions to the gradient. + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmpak.htm">glmpak</a></CODE>, <CODE><a href="glmunpak.htm">glmunpak</a></CODE>, <CODE><a href="glmfwd.htm">glmfwd</a></CODE>, <CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmhess.htm b/sourcecodes/bnt-master/nethelp3.3/glmhess.htm new file mode 100644 index 00000000..481e3220 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmhess.htm @@ -0,0 +1,74 @@ +<html> +<head> +<title> +Netlab Reference Manual glmhess +</title> +</head> +<body> +<H1> glmhess +</H1> +<h2> +Purpose +</h2> +Evaluate the Hessian matrix for a generalised linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +h = glmhess(net, x, t) +[h, hdata] = glmhess(net, x, t) +h = glmhess(net, x, t, hdata) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>h = glmhess(net, x, t)</CODE> takes a GLM network data structure <CODE>net</CODE>, +a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of target +values and returns the full Hessian matrix <CODE>h</CODE> corresponding to +the second derivatives of the negative log posterior distribution, +evaluated for the current weight and bias values as defined by +<CODE>net</CODE>. Note that the target data is not required in the calculation, +but is included to make the interface uniform with <CODE>nethess</CODE>. For +linear and logistic outputs, the computation is very simple and is +done (in effect) in one line in <CODE>glmtrain</CODE>. + +<p><CODE>[h, hdata] = glmhess(net, x, t)</CODE> returns both the Hessian matrix +<CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependent +term in the Hessian. + +<p><CODE>h = glmhess(net, x, t, hdata)</CODE> takes a network data structure +<CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of +target values, together with the contribution <CODE>hdata</CODE> arising from +the data dependent term in the Hessian, and returns the full Hessian +matrix <CODE>h</CODE> corresponding to the second derivatives of the negative +log posterior distribution. This version saves computation time if +<CODE>hdata</CODE> has already been evaluated for the current weight and bias +values. + +<p><h2> +Example +</h2> +The Hessian matrix is used by <CODE>glmtrain</CODE> to take a Newton step for +softmax outputs. +<PRE> + +Hessian = glmhess(net, x, t); +deltaw = -gradient*pinv(Hessian); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE>, <CODE><a href="nethess.htm">nethess</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glminit.htm b/sourcecodes/bnt-master/nethelp3.3/glminit.htm new file mode 100644 index 00000000..e19369d3 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glminit.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual glminit +</title> +</head> +<body> +<H1> glminit +</H1> +<h2> +Purpose +</h2> +Initialise the weights in a generalized linear model. + +<p><h2> +Synopsis +</h2> +<PRE> +net = glminit(net, prior) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = glminit(net, prior)</CODE> takes a generalized linear model +<CODE>net</CODE> and sets the weights and biases by sampling from a Gaussian +distribution. If <CODE>prior</CODE> is a scalar, then all of the parameters +(weights and biases) are sampled from a single isotropic Gaussian with +inverse variance equal to <CODE>prior</CODE>. If <CODE>prior</CODE> is a data +structure similar to that in <CODE>mlpprior</CODE> but for a single layer of +weights, then the parameters +are sampled from multiple Gaussians according to their groupings +(defined by the <CODE>index</CODE> field) with corresponding variances +(defined by the <CODE>alpha</CODE> field). + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmpak.htm">glmpak</a></CODE>, <CODE><a href="glmunpak.htm">glmunpak</a></CODE>, <CODE><a href="mlpinit.htm">mlpinit</a></CODE>, <CODE><a href="mlpprior.htm">mlpprior</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmpak.htm b/sourcecodes/bnt-master/nethelp3.3/glmpak.htm new file mode 100644 index 00000000..8e1af1ad --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmpak.htm @@ -0,0 +1,40 @@ +<html> +<head> +<title> +Netlab Reference Manual glmpak +</title> +</head> +<body> +<H1> glmpak +</H1> +<h2> +Purpose +</h2> +Combines weights and biases into one weights vector. + +<p><h2> +Synopsis +</h2> +<PRE> +w = glmpak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>w = glmpak(net)</CODE> takes a network data structure <CODE>net</CODE> and +combines them into a single row vector <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmunpak.htm">glmunpak</a></CODE>, <CODE><a href="glmfwd.htm">glmfwd</a></CODE>, <CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmtrain.htm b/sourcecodes/bnt-master/nethelp3.3/glmtrain.htm new file mode 100644 index 00000000..a52ada6d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmtrain.htm @@ -0,0 +1,71 @@ +<html> +<head> +<title> +Netlab Reference Manual glmtrain +</title> +</head> +<body> +<H1> glmtrain +</H1> +<h2> +Purpose +</h2> +Specialised training of generalized linear model + +<p><h2> +Description +</h2> +<CODE>net = glmtrain(net, options, x, t)</CODE> uses +the iterative reweighted least squares (IRLS) +algorithm to set the weights in the generalized linear model structure +<CODE>net</CODE>. This is a more efficient alternative to using <CODE>glmerr</CODE> +and <CODE>glmgrad</CODE> and a non-linear optimisation routine through +<CODE>netopt</CODE>. +Note that for linear outputs, a single pass through the +algorithm is all that is required, since the error function is quadratic in +the weights. The algorithm also handles scalar <CODE>alpha</CODE> and <CODE>beta</CODE> +terms. If you want to use more complicated priors, you should use +general-purpose non-linear optimisation algorithms. + +<p>For logistic and softmax outputs, general priors can be handled, although +this requires the pseudo-inverse of the Hessian, giving up the better +conditioning and some of the speed advantage of the normal form equations. + +<p>The error function value at the final set of weights is returned +in <CODE>options(8)</CODE>. +Each row of <CODE>x</CODE> corresponds to one +input vector and each row of <CODE>t</CODE> corresponds to one target vector. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values during training. +If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is a measure of the precision required for the value +of the weights <CODE>w</CODE> at the solution. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(5)</CODE> is set to 1 if an approximation to the Hessian (which assumes +that all outputs are independent) is used for softmax outputs. With the default +value of 0 the exact Hessian (which is more expensive to compute) is used. + +<p><CODE>options(14)</CODE> is the maximum number of iterations for the IRLS algorithm; +default 100. + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/glmunpak.htm b/sourcecodes/bnt-master/nethelp3.3/glmunpak.htm new file mode 100644 index 00000000..73fd5054 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/glmunpak.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual glmunpak +</title> +</head> +<body> +<H1> glmunpak +</H1> +<h2> +Purpose +</h2> +Separates weights vector into weight and bias matrices. + +<p><h2> +Synopsis +</h2> +<PRE> +net = glmunpak(net, w) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = glmunpak(net, w)</CODE> takes a glm network data structure <CODE>net</CODE> and +a weight vector <CODE>w</CODE>, and returns a network data structure identical to +the input network, except that the first-layer weight matrix +<CODE>w1</CODE> and the first-layer bias vector <CODE>b1</CODE> have +been set to the corresponding elements of <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="glm.htm">glm</a></CODE>, <CODE><a href="glmpak.htm">glmpak</a></CODE>, <CODE><a href="glmfwd.htm">glmfwd</a></CODE>, <CODE><a href="glmerr.htm">glmerr</a></CODE>, <CODE><a href="glmgrad.htm">glmgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmm.htm b/sourcecodes/bnt-master/nethelp3.3/gmm.htm new file mode 100644 index 00000000..c815b3cb --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmm.htm @@ -0,0 +1,96 @@ +<html> +<head> +<title> +Netlab Reference Manual gmm +</title> +</head> +<body> +<H1> gmm +</H1> +<h2> +Purpose +</h2> +Creates a Gaussian mixture model with specified architecture. + +<p><h2> +Synopsis +</h2> +<PRE> +mix = gmm(dim, ncentres, covartype) +mix = gmm(dim, ncentres, covartype, ppca_dim) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>mix = gmm(dim, ncentres, covartype)</CODE> takes +the dimension of the space <CODE>dim</CODE>, the number of centres in the +mixture model and the type of the mixture model, and returns a data +structure <CODE>mix</CODE>. +The mixture model type defines the covariance structure of each component +Gaussian: +<PRE> + + 'spherical' = single variance parameter for each component: stored as a vector + 'diag' = diagonal matrix for each component: stored as rows of a matrix + 'full' = full matrix for each component: stored as 3d array + 'ppca' = probabilistic PCA: stored as principal components (in a 3d array + and associated variances and off-subspace noise +</PRE> + +<CODE>mix = gmm(dim, ncentres, covartype, ppca_dim)</CODE> also sets the dimension of +the PPCA sub-spaces: the default value is one. + +<p>The priors are initialised to equal values summing to one, and the covariances +are all the identity matrix (or equivalent). The centres are +initialised randomly from a zero mean unit variance Gaussian. This makes use +of the MATLAB function <CODE>randn</CODE> and so the seed for the random weight +initialisation can be set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the +state value. + +<p>The fields in <CODE>mix</CODE> are +<PRE> + + type = 'gmm' + nin = the dimension of the space + ncentres = number of mixture components + covartype = string for type of variance model + priors = mixing coefficients + centres = means of Gaussians: stored as rows of a matrix + covars = covariances of Gaussians +</PRE> + +The additional fields for mixtures of PPCA are +<PRE> + + U = principal component subspaces + lambda = in-space covariances: stored as rows of a matrix +</PRE> + +The off-subspace noise is stored in <CODE>covars</CODE>. + +<p><h2> +Example +</h2> +<PRE> + +mix = gmm(2, 4, 'spherical'); +</PRE> + +This creates a Gaussian mixture model with 4 components in 2 dimensions. +The covariance structure is a spherical model. + +<p><h2> +See Also +</h2> +<CODE><a href="gmmpak.htm">gmmpak</a></CODE>, <CODE><a href="gmmunpak.htm">gmmunpak</a></CODE>, <CODE><a href="gmmsamp.htm">gmmsamp</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="gmmactiv.htm">gmmactiv</a></CODE>, <CODE><a href="gmmpost.htm">gmmpost</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmactiv.htm b/sourcecodes/bnt-master/nethelp3.3/gmmactiv.htm new file mode 100644 index 00000000..0c3c5c8f --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmactiv.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmactiv +</title> +</head> +<body> +<H1> gmmactiv +</H1> +<h2> +Purpose +</h2> +Computes the activations of a Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> + +a = gmmactiv(mix, x) +</PRE> + + +<p><h2> +Description +</h2> +This function computes the activations <CODE>a</CODE> (i.e. the +probability <CODE>p(x|j)</CODE> of the data conditioned on each component density) +for a Gaussian mixture model. For the PPCA model, each activation +is the conditional probability of <CODE>x</CODE> given that it is generated +by the component subspace. +The data structure <CODE>mix</CODE> defines the mixture model, while the matrix +<CODE>x</CODE> contains the data vectors. Each row of <CODE>x</CODE> represents a single +vector. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmpost.htm">gmmpost</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmem.htm b/sourcecodes/bnt-master/nethelp3.3/gmmem.htm new file mode 100644 index 00000000..6c0f46dd --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmem.htm @@ -0,0 +1,87 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmem +</title> +</head> +<body> +<H1> gmmem +</H1> +<h2> +Purpose +</h2> +EM algorithm for Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> + +[mix, options, errlog] = gmmem(mix, x, options) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>[mix, options, errlog] = gmmem(mix, x, options)</CODE> uses the Expectation +Maximization algorithm of Dempster et al. to estimate the parameters of +a Gaussian mixture model defined by a data structure <CODE>mix</CODE>. +The matrix <CODE>x</CODE> represents the data whose expectation +is maximized, with each row corresponding to a vector. + +The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>. +If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(3)</CODE> is a measure of the absolute precision required of the error +function at the solution. If the change in log likelihood between two steps of +the EM algorithm is less than this value, then the function terminates. + +<p><CODE>options(5)</CODE> is set to 1 if a covariance matrix is reset to its +original value when any of its singular values are too small (less +than MIN_COVAR which has the value eps). +With the default value of 0 no action is taken. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p>The optional return value <CODE>options</CODE> contains the final error value +(i.e. data log likelihood) in +<CODE>options(8)</CODE>. + +<p><h2> +Examples +</h2> +The following code fragment sets up a Gaussian mixture model, initialises +the parameters from the data, sets the options and trains the model. +<PRE> + +mix = gmm(inputdim, ncentres, 'full'); + +<p>options = foptions; +options(14) = 5; +mix = gmminit(mix, data, options); + +<p>options(1) = 1; % Prints out error values. +options(14) = 30; % Max. number of iterations. + +<p>mix = gmmem(mix, data, options); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmminit.htm b/sourcecodes/bnt-master/nethelp3.3/gmminit.htm new file mode 100644 index 00000000..3108da74 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmminit.htm @@ -0,0 +1,65 @@ +<html> +<head> +<title> +Netlab Reference Manual gmminit +</title> +</head> +<body> +<H1> gmminit +</H1> +<h2> +Purpose +</h2> +Initialises Gaussian mixture model from data + +<p><h2> +Synopsis +</h2> +<PRE> + +mix = gmminit(mix, x, options) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>mix = gmminit(mix, x, options)</CODE> uses a dataset <CODE>x</CODE> +to initialise the parameters of a Gaussian mixture +model defined by the data structure <CODE>mix</CODE>. The k-means algorithm +is used to determine the centres. The priors are computed from the +proportion of examples belonging to each cluster. +The covariance matrices are calculated as the sample covariance of the +points associated with (i.e. closest to) the corresponding centres. +For a mixture of PPCA model, the PPCA decomposition is calculated +for the points closest to a given centre. +This initialisation can be used as the starting point for training the +model using the EM algorithm. + +<p><h2> +Example +</h2> +<PRE> + +mix = gmm(3, 2); +options = foptions; +options(14) = 5; +mix = gmminit(mix, data, options); +</PRE> + +This code sets up a Gaussian mixture model with 3 centres in 2 dimensions, and +then initialises the parameters from the data set <CODE>data</CODE> with 5 iterations +of the k means algorithm. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmpak.htm b/sourcecodes/bnt-master/nethelp3.3/gmmpak.htm new file mode 100644 index 00000000..0ef370a9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmpak.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmpak +</title> +</head> +<body> +<H1> gmmpak +</H1> +<h2> +Purpose +</h2> +Combines all the parameters in a Gaussian mixture model into one vector. + +<p><h2> +Synopsis +</h2> +<PRE> +p = gmmpak(mix) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>p = gmmpak(net)</CODE> takes a mixture data structure <CODE>mix</CODE> +and combines the component parameter matrices into a single row +vector <CODE>p</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmunpak.htm">gmmunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmpost.htm b/sourcecodes/bnt-master/nethelp3.3/gmmpost.htm new file mode 100644 index 00000000..d323115f --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmpost.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmpost +</title> +</head> +<body> +<H1> gmmpost +</H1> +<h2> +Purpose +</h2> +Computes the class posterior probabilities of a Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> + +function post = gmmpost(mix, x) +</PRE> + + +<p><h2> +Description +</h2> +This function computes the posteriors <CODE>post</CODE> (i.e. the probability of each +component conditioned on the data <CODE>p(j|x)</CODE>) for a Gaussian mixture model. +The data structure <CODE>mix</CODE> defines the mixture model, while the matrix +<CODE>x</CODE> contains the data vectors. Each row of <CODE>x</CODE> represents a single +vector. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmactiv.htm">gmmactiv</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmprob.htm b/sourcecodes/bnt-master/nethelp3.3/gmmprob.htm new file mode 100644 index 00000000..acc3fb65 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmprob.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmprob +</title> +</head> +<body> +<H1> gmmprob +</H1> +<h2> +Purpose +</h2> +Computes the data probability for a Gaussian mixture model. + +<p><h2> +Synopsis +</h2> +<PRE> + +function prob = gmmprob(mix, x) +</PRE> + + +<p><h2> +Description +</h2> + +This function computes the unconditional data +density <CODE>p(x)</CODE> for a Gaussian mixture model. The data structure +<CODE>mix</CODE> defines the mixture model, while the matrix <CODE>x</CODE> contains +the data vectors. Each row of <CODE>x</CODE> represents a single vector. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmpost.htm">gmmpost</a></CODE>, <CODE><a href="gmmactiv.htm">gmmactiv</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmsamp.htm b/sourcecodes/bnt-master/nethelp3.3/gmmsamp.htm new file mode 100644 index 00000000..30f6821c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmsamp.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmsamp +</title> +</head> +<body> +<H1> gmmsamp +</H1> +<h2> +Purpose +</h2> +Sample from a Gaussian mixture distribution. + +<p><h2> +Synopsis +</h2> +<PRE> +data = gmmsamp(mix, n) +[data, label] = gmmsamp(mix, n) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>data = gsamp(mix, n)</CODE> generates a sample of size <CODE>n</CODE> from a +Gaussian mixture distribution defined by the <CODE>mix</CODE> data +structure. The matrix <CODE>x</CODE> has <CODE>n</CODE> +rows in which each row represents a <CODE>mix.nin</CODE>-dimensional sample vector. + +<p><CODE>[data, label] = gmmsamp(mix, n)</CODE> also returns a column vector of +classes (as an index 1..N) <CODE>label</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gsamp.htm">gsamp</a></CODE>, <CODE><a href="gmm.htm">gmm</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gmmunpak.htm b/sourcecodes/bnt-master/nethelp3.3/gmmunpak.htm new file mode 100644 index 00000000..2287fb3b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gmmunpak.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual gmmunpak +</title> +</head> +<body> +<H1> gmmunpak +</H1> +<h2> +Purpose +</h2> +Separates a vector of Gaussian mixture model parameters into its components. + +<p><h2> +Synopsis +</h2> +<PRE> +mix = gmmunpak(mix, p) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>mix = gmmunpak(mix, p)</CODE> +takes a GMM data structure <CODE>mix</CODE> and +a single row vector of parameters <CODE>p</CODE> and returns a mixture data structure +identical to the input <CODE>mix</CODE>, except that the mixing coefficients +<CODE>priors</CODE>, centres <CODE>centres</CODE> and covariances <CODE>covars</CODE> +(and, for PPCA, the lambdas and U (PCA sub-spaces)) are all set +to the corresponding elements of <CODE>p</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="gmmpak.htm">gmmpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gp.htm b/sourcecodes/bnt-master/nethelp3.3/gp.htm new file mode 100644 index 00000000..77d6ab1a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gp.htm @@ -0,0 +1,80 @@ +<html> +<head> +<title> +Netlab Reference Manual gp +</title> +</head> +<body> +<H1> gp +</H1> +<h2> +Purpose +</h2> +Create a Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +net = gp(nin, covarfn) +net = gp(nin, covarfn, prior) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = gp(nin, covarfn)</CODE> takes the number of inputs <CODE>nin</CODE> +for a Gaussian Process model with a single output, together +with a string <CODE>covarfn</CODE> which specifies the type of the covariance function, +and returns a data structure <CODE>net</CODE>. The parameters are set to zero. + +<p>The fields in <CODE>net</CODE> are +<PRE> + type = 'gp' + nin = number of inputs + nout = number of outputs: always 1 + nwts = total number of weights and covariance function parameters + bias = logarithm of constant offset in covariance function + noise = logarithm of output noise variance + inweights = logarithm of inverse length scale for each input + covarfn = string describing the covariance function: + 'sqexp' + 'ratquad' + fpar = covariance function specific parameters (1 for squared exponential, + 2 for rational quadratic) + trin = training input data (initially empty) + trtargets = training target data (initially empty) +</PRE> + + +<p><CODE>net = gp(nin, covarfn, prior)</CODE> sets a Gaussian prior on the +parameters of the model. <CODE>prior</CODE> must contain the fields +<CODE>pr_mean</CODE> and <CODE>pr_variance</CODE>. If <CODE>pr_mean</CODE> is a scalar, +then the Gaussian is assumed to be isotropic and the additional fields +<CODE>net.pr_mean</CODE> and <CODE>pr_variance</CODE> are set. Otherwise, +the Gaussian prior has a mean +defined by a column vector of parameters <CODE>prior.pr_mean</CODE> and +covariance defined by a column vector of parameters <CODE>prior.pr_variance</CODE>. +Each element of <CODE>prmean</CODE> corresponds to a separate group of parameters, which +need not be mutually exclusive. The membership of the groups is defined +by the matrix <CODE>prior.index</CODE> in which the columns correspond to the elements of +<CODE>prmean</CODE>. Each column has one element for each weight in the matrix, +in the order defined by the function <CODE>gppak</CODE>, and each element +is 1 or 0 according to whether the parameter is a member of the +corresponding group or not. The additional field <CODE>net.index</CODE> is set +in this case. + +<p><h2> +See Also +</h2> +<CODE><a href="gppak.htm">gppak</a></CODE>, <CODE><a href="gpunpak.htm">gpunpak</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpcovar.htm">gpcovar</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpcovar.htm b/sourcecodes/bnt-master/nethelp3.3/gpcovar.htm new file mode 100644 index 00000000..f626f8fd --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpcovar.htm @@ -0,0 +1,64 @@ +<html> +<head> +<title> +Netlab Reference Manual gpcovar +</title> +</head> +<body> +<H1> gpcovar +</H1> +<h2> +Purpose +</h2> +Calculate the covariance for a Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +cov = gpcovar(net, x) +[cov, covf] = gpcovar(net, x) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>cov = gpcovar(net, x)</CODE> takes +a Gaussian Process data structure <CODE>net</CODE> together with +a matrix <CODE>x</CODE> of input vectors, and computes the covariance +matrix <CODE>cov</CODE>. The inverse of this matrix is used when calculating +the mean and variance of the predictions made by <CODE>net</CODE>. + +<p><CODE>[cov, covf] = gpcovar(net, x)</CODE> also generates the covariance +matrix due to the covariance function specified by <CODE>net.covarfn</CODE> +as calculated by <CODE>gpcovarf</CODE>. + +<p><h2> +Example +</h2> +In the following example, the inverse covariance matrix is calculated +for a set of training inputs <CODE>x</CODE> and is then +passed to <CODE>gpfwd</CODE> so that predictions (with mean <CODE>ytest</CODE> and +variance <CODE>sigsq</CODE>) can be made for the test inputs +<CODE>xtest</CODE>. +<PRE> + +cninv = inv(gpcovar(net, x)); +[ytest, sigsq] = gpfwd(net, xtest, cninv); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gppak.htm">gppak</a></CODE>, <CODE><a href="gpunpak.htm">gpunpak</a></CODE>, <CODE><a href="gpcovarp.htm">gpcovarp</a></CODE>, <CODE><a href="gpcovarf.htm">gpcovarf</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpcovarf.htm b/sourcecodes/bnt-master/nethelp3.3/gpcovarf.htm new file mode 100644 index 00000000..5bce6b98 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpcovarf.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual gpcovarf +</title> +</head> +<body> +<H1> gpcovarf +</H1> +<h2> +Purpose +</h2> +Calculate the covariance function for a Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +covf = gpcovarf(net, x1, x2) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>covf = gpcovarf(net, x1, x2)</CODE> takes +a Gaussian Process data structure <CODE>net</CODE> together with +two matrices <CODE>x1</CODE> and <CODE>x2</CODE> of input vectors, +and computes the matrix of the covariance function values +<CODE>covf</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gpcovar.htm">gpcovar</a></CODE>, <CODE><a href="gpcovarp.htm">gpcovarp</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpcovarp.htm b/sourcecodes/bnt-master/nethelp3.3/gpcovarp.htm new file mode 100644 index 00000000..616664ce --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpcovarp.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual gpcovarp +</title> +</head> +<body> +<H1> gpcovarp +</H1> +<h2> +Purpose +</h2> +Calculate the prior covariance for a Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +covp = gpcovarp(net, x1, x2) +[covp, covf] = gpcovarp(net, x1, x2) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>covp = gpcovarp(net, x1, x2)</CODE> takes +a Gaussian Process data structure <CODE>net</CODE> together with +two matrices <CODE>x1</CODE> and <CODE>x2</CODE> of input vectors, +and computes the matrix of the prior covariance. This is +the function component of the covariance plus the exponential of the bias +term. + +<p><CODE>[covp, covf] = gpcovarp(net, x1, x2)</CODE> also returns the function +component of the covariance. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gpcovar.htm">gpcovar</a></CODE>, <CODE><a href="gpcovarf.htm">gpcovarf</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gperr.htm b/sourcecodes/bnt-master/nethelp3.3/gperr.htm new file mode 100644 index 00000000..de8d9831 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gperr.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual gperr +</title> +</head> +<body> +<H1> gperr +</H1> +<h2> +Purpose +</h2> +Evaluate error function for Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +edata = gperr(net, x, t) +[e, edata, eprior] = gperr(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>e = gperr(net, x, t)</CODE> takes a Gaussian Process data structure <CODE>net</CODE> together +with a matrix <CODE>x</CODE> of input vectors and a matrix <CODE>t</CODE> of target +vectors, and evaluates the error function <CODE>e</CODE>. Each row +of <CODE>x</CODE> corresponds to one input vector and each row of <CODE>t</CODE> +corresponds to one target vector. + +<p><CODE>[e, edata, eprior] = gperr(net, x, t)</CODE> additionally returns the +data and hyperprior components of the error, assuming a Gaussian +prior on the weights with mean and variance parameters <CODE>prmean</CODE> and +<CODE>prvariance</CODE> taken from the network data structure <CODE>net</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gpcovar.htm">gpcovar</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpfwd.htm b/sourcecodes/bnt-master/nethelp3.3/gpfwd.htm new file mode 100644 index 00000000..51fc239c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpfwd.htm @@ -0,0 +1,73 @@ +<html> +<head> +<title> +Netlab Reference Manual gpfwd +</title> +</head> +<body> +<H1> gpfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +y = gpfwd(net, x) +[y, sigsq] = gpfwd(net, x) +[y, sigsq] = gpfwd(net, x, cninv) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = gpfwd(net, x)</CODE> takes a Gaussian Process data structure <CODE>net</CODE> +together +with a matrix <CODE>x</CODE> of input vectors, and forward propagates the inputs +through the model to generate a matrix <CODE>y</CODE> of output +vectors. Each row of <CODE>x</CODE> corresponds to one input vector and each +row of <CODE>y</CODE> corresponds to one output vector. This assumes that the +training data (both inputs and targets) has been stored in <CODE>net</CODE> by +a call to <CODE>gpinit</CODE>; these are needed to compute the training +data covariance matrix. + +<p><CODE>[y, sigsq] = gpfwd(net, x)</CODE> also generates a column vector <CODE>sigsq</CODE> of +conditional variances (or squared error bars) where each value corresponds to a pattern. + +<p><CODE>[y, sigsq] = gpfwd(net, x, cninv)</CODE> uses the pre-computed inverse covariance +matrix <CODE>cninv</CODE> in the forward propagation. This increases efficiency if +several calls to <CODE>gpfwd</CODE> are made. + +<p><h2> +Example +</h2> +The following code creates a Gaussian Process, trains it, and then plots the +predictions on a test set with one standard deviation error bars: +<PRE> + +net = gp(1, 'sqexp'); +net = gpinit(net, x, t); +net = netopt(net, options, x, t, 'scg'); +[pred, sigsq] = gpfwd(net, xtest); +plot(xtest, pred, '-k'); +hold on +plot(xtest, pred+sqrt(sigsq), '-b', xtest, pred-sqrt(sigsq), '-b'); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="demgp.htm">demgp</a></CODE>, <CODE><a href="gpinit.htm">gpinit</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpgrad.htm b/sourcecodes/bnt-master/nethelp3.3/gpgrad.htm new file mode 100644 index 00000000..887cdf1b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpgrad.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual gpgrad +</title> +</head> +<body> +<H1> gpgrad +</H1> +<h2> +Purpose +</h2> +Evaluate error gradient for Gaussian Process. + +<p><h2> +Synopsis +</h2> +<PRE> +g = gpgrad(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = gpgrad(net, x, t)</CODE> takes a Gaussian Process data structure <CODE>net</CODE> together +with a matrix <CODE>x</CODE> of input vectors and a matrix <CODE>t</CODE> of target +vectors, and evaluates the error gradient <CODE>g</CODE>. Each row +of <CODE>x</CODE> corresponds to one input vector and each row of <CODE>t</CODE> +corresponds to one target vector. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gpcovar.htm">gpcovar</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpinit.htm b/sourcecodes/bnt-master/nethelp3.3/gpinit.htm new file mode 100644 index 00000000..1874dde7 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpinit.htm @@ -0,0 +1,76 @@ +<html> +<head> +<title> +Netlab Reference Manual gpinit +</title> +</head> +<body> +<H1> gpinit +</H1> +<h2> +Purpose +</h2> +Initialise Gaussian Process model. + +<p><h2> +Synopsis +</h2> +<PRE> +net = gpinit(net, trin, trtargets, prior) +net = gpinit(net, trin, trtargets, prior) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = gpinit(net, trin, trtargets)</CODE> takes a Gaussian Process data structure <CODE>net</CODE> +together +with a matrix <CODE>trin</CODE> of training input vectors and a matrix <CODE>trtargets</CODE> of +training target +vectors, and stores them in <CODE>net</CODE>. These datasets are required if +the corresponding inverse covariance matrix is not supplied to <CODE>gpfwd</CODE>. +This is important if the data structure is saved and then reloaded before +calling <CODE>gpfwd</CODE>. +Each row +of <CODE>trin</CODE> corresponds to one input vector and each row of <CODE>trtargets</CODE> +corresponds to one target vector. + +<p><CODE>net = gpinit(net, trin, trtargets, prior)</CODE> additionally initialises the +parameters in <CODE>net</CODE> from the <CODE>prior</CODE> data structure which contains the +mean and variance of the Gaussian distribution which is sampled from. + +<p><h2> +Example +</h2> +Suppose that a Gaussian Process model is created and trained with input data <CODE>x</CODE> +and targets <CODE>t</CODE>: +<PRE> + +net = gp(2, 'sqexp'); +net = gpinit(net, x, t); +% Train the network +save 'gp.net' net; +</PRE> + +Another Matlab program can now read in the network and make predictions on a data set +<CODE>testin</CODE>: +<PRE> + +load 'gp.net'; +pred = gpfwd(net, testin); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gppak.htm b/sourcecodes/bnt-master/nethelp3.3/gppak.htm new file mode 100644 index 00000000..e913dd2c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gppak.htm @@ -0,0 +1,40 @@ +<html> +<head> +<title> +Netlab Reference Manual gppak +</title> +</head> +<body> +<H1> gppak +</H1> +<h2> +Purpose +</h2> +Combines GP hyperparameters into one vector. + +<p><h2> +Synopsis +</h2> +<PRE> +hp = gppak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>hp = gppak(net)</CODE> takes a Gaussian Process data structure <CODE>net</CODE> and +combines the hyperparameters into a single row vector <CODE>hp</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gpunpak.htm">gpunpak</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gpunpak.htm b/sourcecodes/bnt-master/nethelp3.3/gpunpak.htm new file mode 100644 index 00000000..593dbb04 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gpunpak.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual gpunpak +</title> +</head> +<body> +<H1> gpunpak +</H1> +<h2> +Purpose +</h2> +Separates hyperparameter vector into components. + +<p><h2> +Synopsis +</h2> +<PRE> +net = gpunpak(net, hp) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = gpunpak(net, hp)</CODE> takes an Gaussian Process data structure <CODE>net</CODE> and +a hyperparameter vector <CODE>hp</CODE>, and returns a Gaussian Process data structure +identical to +the input model, except that the covariance bias +<CODE>bias</CODE>, output noise <CODE>noise</CODE>, the input weight vector +<CODE>inweights</CODE> and the vector of covariance function specific parameters + <CODE>fpar</CODE> have all +been set to the corresponding elements of <CODE>hp</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gp.htm">gp</a></CODE>, <CODE><a href="gppak.htm">gppak</a></CODE>, <CODE><a href="gpfwd.htm">gpfwd</a></CODE>, <CODE><a href="gperr.htm">gperr</a></CODE>, <CODE><a href="gpgrad.htm">gpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gradchek.htm b/sourcecodes/bnt-master/nethelp3.3/gradchek.htm new file mode 100644 index 00000000..0a7df6ea --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gradchek.htm @@ -0,0 +1,58 @@ +<html> +<head> +<title> +Netlab Reference Manual gradchek +</title> +</head> +<body> +<H1> gradchek +</H1> +<h2> +Purpose +</h2> +Checks a user-defined gradient function using finite differences. + +<p><h2> +Synopsis +</h2> +<PRE> + +gradchek(w, func, grad) +[gradient, delta] = gradchek(w, func, grad) +gradchek(w, func, grad, p1, p2, ...) +</PRE> + + +<p><h2> +Description +</h2> +This function is intended as a utility for other netlab functions +(particularly optimisation functions) to use. It enables the user +to check whether a gradient calculation has been correctly implmented +for a given function. +<CODE>gradchek(w, func, grad)</CODE> checks how accurate the gradient +<CODE>grad</CODE> of a function <CODE>func</CODE> is at a parameter vector <CODE>x</CODE>. +A central +difference formula with step size 1.0e-6 is used, and the results +for both gradient function and finite difference approximation are +printed. +The optional return value <CODE>gradient</CODE> is the gradient calculated +using the function <CODE>grad</CODE> and the return value <CODE>delta</CODE> is the +difference between the functional and finite difference methods of +calculating the graident. + +<p><CODE>gradchek(x, func, grad, p1, p2, ...)</CODE> allows additional arguments +to be passed to <CODE>func</CODE> and <CODE>grad</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="hmc.htm">hmc</a></CODE>, <CODE><a href="olgd.htm">olgd</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/graddesc.htm b/sourcecodes/bnt-master/nethelp3.3/graddesc.htm new file mode 100644 index 00000000..fe8a3df1 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/graddesc.htm @@ -0,0 +1,104 @@ +<html> +<head> +<title> +Netlab Reference Manual graddesc +</title> +</head> +<body> +<H1> graddesc +</H1> +<h2> +Purpose +</h2> +Gradient descent optimization. + +<p><h2> +Description +</h2> +<CODE>[x, options, flog, pointlog] = graddesc(f, x, options, gradf)</CODE> uses +batch gradient descent to find a local minimum of the function +<CODE>f(x)</CODE> whose gradient is given by <CODE>gradf(x)</CODE>. A log of the function values +after each cycle is (optionally) returned in <CODE>errlog</CODE>, and a log +of the points visited is (optionally) returned in <CODE>pointlog</CODE>. + +<p>Note that <CODE>x</CODE> is a row vector +and <CODE>f</CODE> returns a scalar value. +The point at which <CODE>f</CODE> has a local minimum +is returned as <CODE>x</CODE>. The function value at that point is returned +in <CODE>options(8)</CODE>. + +<p><CODE>graddesc(f, x, options, gradf, p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>, and the points visited +in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is the absolute precision required for the value +of <CODE>x</CODE> at the solution. If the absolute difference between +the values of <CODE>x</CODE> between two successive steps is less than +<CODE>options(2)</CODE>, then this condition is satisfied. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. If the absolute difference between the +objective function values between two successive steps is less than +<CODE>options(3)</CODE>, then this condition is satisfied. +Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(7)</CODE> determines the line minimisation method used. If it +is set to 1 then a line minimiser is used (in the direction of the negative +gradient). If it is 0 (the default), then each parameter update +is a fixed multiple (the learning rate) +of the negative gradient added to a fixed multiple (the momentum) of +the previous parameter update. + +<p><CODE>options(9)</CODE> should be set to 1 to check the user defined gradient +function <CODE>gradf</CODE> with <CODE>gradchek</CODE>. This is carried out at +the initial parameter vector <CODE>x</CODE>. + +<p><CODE>options(10)</CODE> returns the total number of function evaluations (including +those in any line searches). + +<p><CODE>options(11)</CODE> returns the total number of gradient evaluations. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p><CODE>options(15)</CODE> is the precision in parameter space of the line search; +default <CODE>foptions(2)</CODE>. + +<p><CODE>options(17)</CODE> is the momentum; default 0.5. It should be scaled by the +inverse of the number of data points. + +<p><CODE>options(18)</CODE> is the learning rate; default 0.01. It should be +scaled by the inverse of the number of data points. + +<p><h2> +Examples +</h2> +An example of how this function can be used to train a neural network is: +<PRE> + +options = zeros(1, 18); +options(17) = 0.1/size(x, 1); +net = netopt(net, options, x, t, 'graddesc'); +</PRE> + +Note how the learning rate is scaled by the number of data points. + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="olgd.htm">olgd</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gsamp.htm b/sourcecodes/bnt-master/nethelp3.3/gsamp.htm new file mode 100644 index 00000000..0f5e5ead --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gsamp.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual gsamp +</title> +</head> +<body> +<H1> gsamp +</H1> +<h2> +Purpose +</h2> +Sample from a Gaussian distribution. + +<p><h2> +Synopsis +</h2> +<PRE> +x = gsamp(mu, covar, nsamp) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>x = gsamp(mu, covar, nsamp)</CODE> generates a sample of size <CODE>nsamp</CODE> +from a <CODE>d</CODE>-dimensional Gaussian distribution. The Gaussian density +has mean vector <CODE>mu</CODE> and covariance matrix <CODE>covar</CODE>, and the +matrix <CODE>x</CODE> has <CODE>nsamp</CODE> rows in which each row represents a +<CODE>d</CODE>-dimensional sample vector. + +<p><h2> +See Also +</h2> +<CODE><a href="gauss.htm">gauss</a></CODE>, <CODE><a href="demgauss.htm">demgauss</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtm.htm b/sourcecodes/bnt-master/nethelp3.3/gtm.htm new file mode 100644 index 00000000..e02ef536 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtm.htm @@ -0,0 +1,66 @@ +<html> +<head> +<title> +Netlab Reference Manual gtm +</title> +</head> +<body> +<H1> gtm +</H1> +<h2> +Purpose +</h2> +Create a Generative Topographic Map. + +<p><h2> +Synopsis +</h2> +<PRE> +net = gtm(dimlatent, nlatent, dimdata, ncentres, rbfunc) +net = gtm(dimlatent, nlatent, dimdata, ncentres, rbfunc, prior) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = gtm(dimlatent, nlatent, dimdata, ncentres, rbfunc)</CODE>, +takes the dimension of the latent space <CODE>dimlatent</CODE>, the +number of data points sampled in the latent space <CODE>nlatent</CODE>, the +dimension of the data space <CODE>dimdata</CODE>, the number of centres in the +RBF model <CODE>ncentres</CODE>, the activation function for the RBF +<CODE>rbfunc</CODE> +and returns a data structure <CODE>net</CODE>. The parameters in the +RBF and GMM sub-models are set by calls to the corresponding creation routines +<CODE>rbf</CODE> and <CODE>gmm</CODE>. + +<p>The fields in <CODE>net</CODE> are +<PRE> + type = 'gtm' + nin = dimension of data space + dimlatent = dimension of latent space + rbfnet = RBF network data structure + gmmnet = GMM data structure + X = sample of latent points +</PRE> + + +<p><CODE>net = gtm(dimlatent, nlatent, dimdata, ncentres, rbfunc, prior)</CODE>, + sets a Gaussian zero mean prior on the +parameters of the RBF model. <CODE>prior</CODE> must be a scalar and represents +the inverse variance of the prior distribution. This gives rise to +a weight decay term in the error function. + +<p><h2> +See Also +</h2> +<CODE><a href="gtmfwd.htm">gtmfwd</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE>, <CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="gmm.htm">gmm</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmem.htm b/sourcecodes/bnt-master/nethelp3.3/gtmem.htm new file mode 100644 index 00000000..95c385b1 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmem.htm @@ -0,0 +1,88 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmem +</title> +</head> +<body> +<H1> gtmem +</H1> +<h2> +Purpose +</h2> +EM algorithm for Generative Topographic Mapping. + +<p><h2> +Synopsis +</h2> +<PRE> + +[net, options, errlog] = gtmem(net, t, options) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>[net, options, errlog] = gtmem(net, t, options)</CODE> uses the Expectation +Maximization algorithm to estimate the parameters of +a GTM defined by a data structure <CODE>net</CODE>. +The matrix <CODE>t</CODE> represents the data whose expectation +is maximized, with each row corresponding to a vector. It is assumed +that the latent data <CODE>net.X</CODE> has been set following a call to +<CODE>gtminit</CODE>, for example. + +The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>. +If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(3)</CODE> is a measure of the absolute precision required of the error +function at the solution. If the change in log likelihood between two steps of +the EM algorithm is less than this value, then the function terminates. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p>The optional return value <CODE>options</CODE> contains the final error value +(i.e. data log likelihood) in +<CODE>options(8)</CODE>. + +<p><h2> +Examples +</h2> +The following code fragment sets up a GTM, initialises +the latent data sample and RBF +parameters from the data, sets the options and trains the model. +<PRE> + +% Create and initialise GTM model +net = gtm(latentdim, nlatent, datadim, numrbfcentres, ... + 'gaussian', 0.1); + +<p>options = foptions; +options(1) = -1; +options(7) = 1; % Set width factor of RBF +net = gtminit(net, options, data, 'regular', latentshape, [4 4]); + +<p>options = foptions; +options(14) = 30; +options(1) = 1; +[net, options] = gtmem(net, data, options); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtminit.htm">gtminit</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmfwd.htm b/sourcecodes/bnt-master/nethelp3.3/gtmfwd.htm new file mode 100644 index 00000000..2ba02a35 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmfwd.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmfwd +</title> +</head> +<body> +<H1> gtmfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +mix = gtmfwd(net) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>mix = gtmfwd(net)</CODE> takes a GTM +structure <CODE>net</CODE>, and forward +propagates the latent data sample <CODE>net.X</CODE> through the GTM to generate +the structure +<CODE>mix</CODE> which represents the Gaussian mixture model in data space. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtminit.htm b/sourcecodes/bnt-master/nethelp3.3/gtminit.htm new file mode 100644 index 00000000..8ac58331 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtminit.htm @@ -0,0 +1,66 @@ +<html> +<head> +<title> +Netlab Reference Manual gtminit +</title> +</head> +<body> +<H1> gtminit +</H1> +<h2> +Purpose +</h2> +Initialise the weights and latent sample in a GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +net = gtminit(net, options, data, samptype) +net = gtminit(net, options, data, samptype, lsampsize, rbfsampsize) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = gtminit(net, options, data, samptype)</CODE> takes a GTM <CODE>net</CODE> +and generates a sample of latent data points and sets the centres (and +widths if appropriate) of +<CODE>net.rbfnet</CODE>. + +<p>If the <CODE>samptype</CODE> is <CODE>'regular'</CODE>, then regular grids of latent +data points and RBF centres are created. The dimension of the latent data +space must be +1 or 2. For one-dimensional latent space, the <CODE>lsampsize</CODE> parameter +gives the number of latent points and the <CODE>rbfsampsize</CODE> parameter +gives the number of RBF centres. For a two-dimensional latent space, +these parameters must be vectors of length 2 with the number of points +in each of the x and y directions to create a rectangular grid. The +widths of the RBF basis functions are set by a call to <CODE>rbfsetfw</CODE> +passing <CODE>options(7)</CODE> as the scaling parameter. + +<p>If the <CODE>samptype</CODE> is <CODE>'uniform'</CODE> or <CODE>'gaussian'</CODE> then the +latent data is found by sampling from a uniform or +Gaussian distribution correspondingly. The RBF basis function parameters +are set +by a call to <CODE>rbfsetbf</CODE> with the <CODE>data</CODE> parameter +as dataset and the <CODE>options</CODE> vector. + +<p>Finally, the output layer weights of the RBF are initialised by +mapping the mean of the latent variable to the mean of the target variable, +and the L-dimensional latent variale variance to the variance of the +targets along the first L principal components. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmem.htm">gtmem</a></CODE>, <CODE><a href="pca.htm">pca</a></CODE>, <CODE><a href="rbfsetbf.htm">rbfsetbf</a></CODE>, <CODE><a href="rbfsetfw.htm">rbfsetfw</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmlmean.htm b/sourcecodes/bnt-master/nethelp3.3/gtmlmean.htm new file mode 100644 index 00000000..1736c0ed --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmlmean.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmlmean +</title> +</head> +<body> +<H1> gtmlmean +</H1> +<h2> +Purpose +</h2> +Mean responsibility for data in a GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +means = gtmlmean(net, data) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>means = gtmlmean(net, data)</CODE> takes a GTM +structure <CODE>net</CODE>, and computes the means of the responsibility +distributions for each data point in <CODE>data</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE>, <CODE><a href="gtmlmode.htm">gtmlmode</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmlmode.htm b/sourcecodes/bnt-master/nethelp3.3/gtmlmode.htm new file mode 100644 index 00000000..ab37c6ff --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmlmode.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmlmode +</title> +</head> +<body> +<H1> gtmlmode +</H1> +<h2> +Purpose +</h2> +Mode responsibility for data in a GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +modes = gtmlmode(net, data) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>modes = gtmlmode(net, data)</CODE> takes a GTM +structure <CODE>net</CODE>, and computes the modes of the responsibility +distributions for each data point in <CODE>data</CODE>. These will always lie +at one of the latent space sample points <CODE>net.X</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE>, <CODE><a href="gtmlmean.htm">gtmlmean</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmmag.htm b/sourcecodes/bnt-master/nethelp3.3/gtmmag.htm new file mode 100644 index 00000000..f8590da7 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmmag.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmmag +</title> +</head> +<body> +<H1> gtmmag +</H1> +<h2> +Purpose +</h2> +Magnification factors for a GTM + +<p><h2> +Synopsis +</h2> +<PRE> +mags = gtmmag(net, latentdata) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>mags = gtmmag(net, latentdata)</CODE> takes a GTM +structure <CODE>net</CODE>, and computes the magnification factors +for each point the latent space contained in <CODE>latentdata</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE>, <CODE><a href="gtmlmean.htm">gtmlmean</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmpost.htm b/sourcecodes/bnt-master/nethelp3.3/gtmpost.htm new file mode 100644 index 00000000..a64ce88a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmpost.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmpost +</title> +</head> +<body> +<H1> gtmpost +</H1> +<h2> +Purpose +</h2> +Latent space responsibility for data in a GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +post = gtmpost(net, data) +[post, a] = gtmpost(net, data) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>post = gtmpost(net, data)</CODE> takes a GTM +structure <CODE>net</CODE>, and computes the responsibility at each latent space +sample point <CODE>net.X</CODE> +for each data point in <CODE>data</CODE>. + +<p><CODE>[post, a] = gtmpost(net, data)</CODE> also returns the activations +<CODE>a</CODE> of the GMM <CODE>net.gmmnet</CODE> as computed by <CODE>gmmpost</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmem.htm">gtmem</a></CODE>, <CODE><a href="gtmlmean.htm">gtmlmean</a></CODE>, <CODE><a href="gmlmode.htm">gmlmode</a></CODE>, <CODE><a href="gmmprob.htm">gmmprob</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/gtmprob.htm b/sourcecodes/bnt-master/nethelp3.3/gtmprob.htm new file mode 100644 index 00000000..d3a44e30 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/gtmprob.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual gtmprob +</title> +</head> +<body> +<H1> gtmprob +</H1> +<h2> +Purpose +</h2> +Probability for data under a GTM. + +<p><h2> +Synopsis +</h2> +<PRE> +prob = gtmprob(net, data) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>prob = gtmprob(net, data)</CODE> takes a GTM +structure <CODE>net</CODE>, and computes the probability of each point in the +dataset <CODE>data</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gtm.htm">gtm</a></CODE>, <CODE><a href="gtmem.htm">gtmem</a></CODE>, <CODE><a href="gtmlmean.htm">gtmlmean</a></CODE>, <CODE><a href="gtmlmode.htm">gtmlmode</a></CODE>, <CODE><a href="gtmpost.htm">gtmpost</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/hbayes.htm b/sourcecodes/bnt-master/nethelp3.3/hbayes.htm new file mode 100644 index 00000000..5fa0783d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/hbayes.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual hbayes +</title> +</head> +<body> +<H1> hbayes +</H1> +<h2> +Purpose +</h2> +Evaluate Hessian of Bayesian error function for network. + +<p><h2> +Synopsis +</h2> +<PRE> +h = hbayes(net, hdata) +[h, hdata] = hbayes(net, hdata) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>h = hbayes(net, hdata)</CODE> takes a network data structure <CODE>net</CODE> together +the data contribution to the Hessian +for a set of inputs and targets. +It returns the regularised Hessian using any zero mean Gaussian priors +on the weights defined in +<CODE>net</CODE>. In addition, if a <CODE>mask</CODE> is defined in <CODE>net</CODE>, then +the entries in <CODE>h</CODE> that correspond to weights with a 0 in the +mask are removed. + +<p><CODE>[h, hdata] = hbayes(net, hdata)</CODE> additionally returns the +data component of the Hessian. + +<p><h2> +See Also +</h2> +<CODE><a href="gbayes.htm">gbayes</a></CODE>, <CODE><a href="glmhess.htm">glmhess</a></CODE>, <CODE><a href="mlphess.htm">mlphess</a></CODE>, <CODE><a href="rbfhess.htm">rbfhess</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/hesschek.htm b/sourcecodes/bnt-master/nethelp3.3/hesschek.htm new file mode 100644 index 00000000..34a4f591 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/hesschek.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual hesschek +</title> +</head> +<body> +<H1> hesschek +</H1> +<h2> +Purpose +</h2> +Use central differences to confirm correct evaluation of Hessian matrix. + +<p><h2> +Synopsis +</h2> +<PRE> +hesschek(net, x, t) +h = hesschek(net, x, t)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>hesschek(net, x, t)</CODE> takes a network data structure <CODE>net</CODE>, together +with input and target data matrices <CODE>x</CODE> and <CODE>t</CODE>, and compares +the evaluation of the Hessian matrix using the function <CODE>nethess</CODE> +and using central differences with the function <CODE>neterr</CODE>. + +<p>The optional return value <CODE>h</CODE> is the Hessian computed using +<CODE>nethess</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="nethess.htm">nethess</a></CODE>, <CODE><a href="neterr.htm">neterr</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/hintmat.htm b/sourcecodes/bnt-master/nethelp3.3/hintmat.htm new file mode 100644 index 00000000..5363385d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/hintmat.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual hintmat +</title> +</head> +<body> +<H1> hintmat +</H1> +<h2> +Purpose +</h2> +Evaluates the coordinates of the patches for a Hinton diagram. + +<p><h2> +Synopsis +</h2> +<PRE> +[xvals, yvals, color] = hintmat(w)</PRE> + + +<p><h2> +Description +</h2> +<PRE> +[xvals, yvals, color] = hintmat(w)</PRE> + +takes a matrix <CODE>w</CODE> and +returns coordinates <CODE>xvals, yvals</CODE> for the patches comrising the +Hinton diagram, together with a vector <CODE>color</CODE> labelling the color +(black or white) of the corresponding elements according to their +sign. + +<p><h2> +See Also +</h2> +<CODE><a href="hinton.htm">hinton</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/hinton.htm b/sourcecodes/bnt-master/nethelp3.3/hinton.htm new file mode 100644 index 00000000..570f3fb0 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/hinton.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual hinton +</title> +</head> +<body> +<H1> hinton +</H1> +<h2> +Purpose +</h2> +Plot Hinton diagram for a weight matrix. + +<p><h2> +Synopsis +</h2> +<PRE> +hinton(w) +h = hinton(w)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>hinton(w)</CODE> takes a matrix <CODE>w</CODE> +and plots the Hinton diagram. + +<p><CODE>h = hinton(net)</CODE> also returns the figure handle <CODE>h</CODE> +which can be used, for instance, to delete the +figure when it is no longer needed. + +<p>To print the figure correctly in black and white, you should call +<CODE>set(h, 'InvertHardCopy', 'off')</CODE> before printing. + +<p><h2> +See Also +</h2> +<CODE><a href="demhint.htm">demhint</a></CODE>, <CODE><a href="hintmat.htm">hintmat</a></CODE>, <CODE><a href="mlphint.htm">mlphint</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/histp.htm b/sourcecodes/bnt-master/nethelp3.3/histp.htm new file mode 100644 index 00000000..fd1fa111 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/histp.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual histp +</title> +</head> +<body> +<H1> histp +</H1> +<h2> +Purpose +</h2> +Histogram estimate of 1-dimensional probability distribution. + +<p><h2> +Synopsis +</h2> +<PRE> +h = histp(x, xmin, xmax, nbins) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>histp(x, xmin, xmax, nbins)</CODE> takes a column vector <CODE>x</CODE> +of data values and generates a normalized histogram plot of the +distribution. The histogram has <CODE>nbins</CODE> bins lying in the +range <CODE>xmin</CODE> to <CODE>xmax</CODE>. + +<p><CODE>h = histp(...)</CODE> returns a vector of patch handles. + +<p><h2> +See Also +</h2> +<CODE><a href="demgauss.htm">demgauss</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/hmc.htm b/sourcecodes/bnt-master/nethelp3.3/hmc.htm new file mode 100644 index 00000000..53afeb31 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/hmc.htm @@ -0,0 +1,129 @@ +<html> +<head> +<title> +Netlab Reference Manual hmc +</title> +</head> +<body> +<H1> hmc +</H1> +<h2> +Purpose +</h2> +Hybrid Monte Carlo sampling. + +<p><h2> +Synopsis +</h2> +<PRE> + +samples = hmc(f, x, options, gradf) +samples = hmc(f, x, options, gradf, P1, P2, ...) +[samples, energies, diagn] = hmc(f, x, options, gradf) +s = hmc('state') +hmc('state', s) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>samples = hmc(f, x, options, gradf)</CODE> uses a +hybrid Monte Carlo algorithm to sample from the distribution <CODE>p ~ exp(-f)</CODE>, +where <CODE>f</CODE> is the first argument to <CODE>hmc</CODE>. +The Markov chain starts at the point <CODE>x</CODE>, and the function <CODE>gradf</CODE> +is the gradient of the `energy' function <CODE>f</CODE>. + +<p><CODE>hmc(f, x, options, gradf, p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. + +<p><CODE>[samples, energies, diagn] = hmc(f, x, options, gradf)</CODE> also returns +a log of the energy values (i.e. negative log probabilities) for the +samples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containing +diagnostic information (position, momentum and +acceptance threshold) for each step of the chain in <CODE>diagn.pos</CODE>, +<CODE>diagn.mom</CODE> and +<CODE>diagn.acc</CODE> respectively. All candidate states (including rejected ones) +are stored in <CODE>diagn.pos</CODE>. + +<p><CODE>[samples, energies, diagn] = hmc(f, x, options, gradf)</CODE> also returns the +<CODE>energies</CODE> (i.e. negative log probabilities) corresponding to the samples. +The <CODE>diagn</CODE> structure contains three fields: + +<p><CODE>pos</CODE> the position vectors of the dynamic process. + +<p><CODE>mom</CODE> the momentum vectors of the dynamic process. + +<p><CODE>acc</CODE> the acceptance thresholds. + +<p><CODE>s = hmc('state')</CODE> returns a state structure that contains the state of the +two random number generators <CODE>rand</CODE> and <CODE>randn</CODE> and the momentum of +the dynamic process. These are contained in fields +<CODE>randstate</CODE>, <CODE>randnstate</CODE> +and <CODE>mom</CODE> respectively. The momentum state is +only used for a persistent momentum update. + +<p><CODE>hmc('state', s)</CODE> resets the state to <CODE>s</CODE>. If <CODE>s</CODE> is an integer, +then it is passed to <CODE>rand</CODE> and <CODE>randn</CODE> and the momentum variable +is randomised. If <CODE>s</CODE> is a structure returned by <CODE>hmc('state')</CODE> then +it resets the generator to exactly the same state. + +<p>The optional parameters in the <CODE>options</CODE> vector have the following +interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejection +threshold at each step of the Markov chain. If the value is 2, then the +position vectors at each step are also displayed. + +<p><CODE>options(5)</CODE> is set to 1 if momentum persistence is used; default 0, for +complete replacement of momentum variables. + +<p><CODE>options(7)</CODE> defines the trajectory length (i.e. the number of leap-frog +steps at each iteration). Minimum value 1. + +<p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function. + +<p><CODE>options(14)</CODE> is the number of samples retained from the Markov chain; +default 100. + +<p><CODE>options(15)</CODE> is the number of samples omitted from the start of the +chain; default 0. + +<p><CODE>options(17)</CODE> defines the momentum used when a persistent update of +(leap-frog) momentum is used. This is bounded to the interval [0, 1). + +<p><CODE>options(18)</CODE> is the step size used in leap-frogs; default 1/trajectory +length. + +<p><h2> +Examples +</h2> +The following code fragment samples from the posterior distribution of +weights for a neural network. +<PRE> + +w = mlppak(net); +[samples, energies] = hmc('neterr', w, options, 'netgrad', net, x, t); +</PRE> + + +<p><h2> +Algorithm +</h2> + +The algroithm follows the procedure outlined in Radford Neal's technical +report CRG-TR-93-1 from the University of Toronto. The stochastic update of +momenta samples from a zero mean unit covariance gaussian. + +<p><h2> +See Also +</h2> +<CODE><a href="metrop.htm">metrop</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/index.htm b/sourcecodes/bnt-master/nethelp3.3/index.htm new file mode 100644 index 00000000..816e24eb --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/index.htm @@ -0,0 +1,537 @@ +<html> +<head> +<title> +NETLAB Reference Documentation +</title> +</head> +<body> +<H1> NETLAB Online Reference Documentation </H1> +Welcome to the NETLAB online reference documentation. +The NETLAB simulation software is designed to provide all the tools necessary +for principled and theoretically well founded application development. The +NETLAB library is based on the approach and techniques described in <I>Neural +Networks for Pattern Recognition </I>(Bishop, 1995). The library includes software +implementations of a wide range of data analysis techniques, many of which are +not widely available, and are rarely, if ever, included in standard neural +network simulation packages. +<p>The online reference documentation provides direct hypertext links to specific Netlab function descriptions. +<p>If you have any comments or problems to report, please contact Ian Nabney (<a href="mailto:i.t.nabney@aston.ac.uk"><tt>i.t.nabney@aston.ac.uk</tt></a>) or Christopher Bishop (<a href="mailto:c.m.bishop@aston.ac.uk"><tt>c.m.bishop@aston.ac.uk</tt></a>).<H1> Index +</H1> +An alphabetic list of functions in Netlab.<p> +<DL> +<DT> +<CODE><a href="conffig.htm">conffig</a></CODE><DD> + Display a confusion matrix. +<DT> +<CODE><a href="confmat.htm">confmat</a></CODE><DD> + Compute a confusion matrix. +<DT> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE><DD> + Conjugate gradients optimization. +<DT> +<CODE><a href="consist.htm">consist</a></CODE><DD> + Check that arguments are consistent. +<DT> +<CODE><a href="convertoldnet.htm">convertoldnet</a></CODE><DD> + Convert pre-2.3 release MLP and MDN nets to new format +<DT> +<CODE><a href="datread.htm">datread</a></CODE><DD> + Read data from an ascii file. +<DT> +<CODE><a href="datwrite.htm">datwrite</a></CODE><DD> + Write data to ascii file. +<DT> +<CODE><a href="dem2ddat.htm">dem2ddat</a></CODE><DD> + Generates two dimensional data for demos. +<DT> +<CODE><a href="demard.htm">demard</a></CODE><DD> + Automatic relevance determination using the MLP. +<DT> +<CODE><a href="demev1.htm">demev1</a></CODE><DD> + Demonstrate Bayesian regression for the MLP. +<DT> +<CODE><a href="demev2.htm">demev2</a></CODE><DD> + Demonstrate Bayesian classification for the MLP. +<DT> +<CODE><a href="demev3.htm">demev3</a></CODE><DD> + Demonstrate Bayesian regression for the RBF. +<DT> +<CODE><a href="demgauss.htm">demgauss</a></CODE><DD> + Demonstrate sampling from Gaussian distributions. +<DT> +<CODE><a href="demglm1.htm">demglm1</a></CODE><DD> + Demonstrate simple classification using a generalized linear model. +<DT> +<CODE><a href="demglm2.htm">demglm2</a></CODE><DD> + Demonstrate simple classification using a generalized linear model. +<DT> +<CODE><a href="demgmm1.htm">demgmm1</a></CODE><DD> + Demonstrate density modelling with a Gaussian mixture model. +<DT> +<CODE><a href="demgmm3.htm">demgmm3</a></CODE><DD> + Demonstrate density modelling with a Gaussian mixture model. +<DT> +<CODE><a href="demgmm4.htm">demgmm4</a></CODE><DD> + Demonstrate density modelling with a Gaussian mixture model. +<DT> +<CODE><a href="demgmm5.htm">demgmm5</a></CODE><DD> + Demonstrate density modelling with a PPCA mixture model. +<DT> +<CODE><a href="demgp.htm">demgp</a></CODE><DD> + Demonstrate simple regression using a Gaussian Process. +<DT> +<CODE><a href="demgpard.htm">demgpard</a></CODE><DD> + Demonstrate ARD using a Gaussian Process. +<DT> +<CODE><a href="demgpot.htm">demgpot</a></CODE><DD> + Computes the gradient of the negative log likelihood for a mixture model. +<DT> +<CODE><a href="demgtm1.htm">demgtm1</a></CODE><DD> + Demonstrate EM for GTM. +<DT> +<CODE><a href="demgtm2.htm">demgtm2</a></CODE><DD> + Demonstrate GTM for visualisation. +<DT> +<CODE><a href="demhint.htm">demhint</a></CODE><DD> + Demonstration of Hinton diagram for 2-layer feed-forward network. +<DT> +<CODE><a href="demhmc1.htm">demhmc1</a></CODE><DD> + Demonstrate Hybrid Monte Carlo sampling on mixture of two Gaussians. +<DT> +<CODE><a href="demhmc2.htm">demhmc2</a></CODE><DD> + Demonstrate Bayesian regression with Hybrid Monte Carlo sampling. +<DT> +<CODE><a href="demhmc3.htm">demhmc3</a></CODE><DD> + Demonstrate Bayesian regression with Hybrid Monte Carlo sampling. +<DT> +<CODE><a href="demkmean.htm">demkmean</a></CODE><DD> + Demonstrate simple clustering model trained with K-means. +<DT> +<CODE><a href="demknn1.htm">demknn1</a></CODE><DD> + Demonstrate nearest neighbour classifier. +<DT> +<CODE><a href="demmdn1.htm">demmdn1</a></CODE><DD> + Demonstrate fitting a multi-valued function using a Mixture Density Network. +<DT> +<CODE><a href="demmet1.htm">demmet1</a></CODE><DD> + Demonstrate Markov Chain Monte Carlo sampling on a Gaussian. +<DT> +<CODE><a href="demmlp1.htm">demmlp1</a></CODE><DD> + Demonstrate simple regression using a multi-layer perceptron +<DT> +<CODE><a href="demmlp2.htm">demmlp2</a></CODE><DD> + Demonstrate simple classification using a multi-layer perceptron +<DT> +<CODE><a href="demnlab.htm">demnlab</a></CODE><DD> + A front-end Graphical User Interface to the demos +<DT> +<CODE><a href="demns1.htm">demns1</a></CODE><DD> + Demonstrate Neuroscale for visualisation. +<DT> +<CODE><a href="demolgd1.htm">demolgd1</a></CODE><DD> + Demonstrate simple MLP optimisation with on-line gradient descent +<DT> +<CODE><a href="demopt1.htm">demopt1</a></CODE><DD> + Demonstrate different optimisers on Rosenbrock's function. +<DT> +<CODE><a href="dempot.htm">dempot</a></CODE><DD> + Computes the negative log likelihood for a mixture model. +<DT> +<CODE><a href="demprgp.htm">demprgp</a></CODE><DD> + Demonstrate sampling from a Gaussian Process prior. +<DT> +<CODE><a href="demprior.htm">demprior</a></CODE><DD> + Demonstrate sampling from a multi-parameter Gaussian prior. +<DT> +<CODE><a href="demrbf1.htm">demrbf1</a></CODE><DD> + Demonstrate simple regression using a radial basis function network. +<DT> +<CODE><a href="demsom1.htm">demsom1</a></CODE><DD> + Demonstrate SOM for visualisation. +<DT> +<CODE><a href="demtrain.htm">demtrain</a></CODE><DD> + Demonstrate training of MLP network. +<DT> +<CODE><a href="dist2.htm">dist2</a></CODE><DD> + Calculates squared distance between two sets of points. +<DT> +<CODE><a href="eigdec.htm">eigdec</a></CODE><DD> + Sorted eigendecomposition +<DT> +<CODE><a href="errbayes.htm">errbayes</a></CODE><DD> + Evaluate Bayesian error function for network. +<DT> +<CODE><a href="evidence.htm">evidence</a></CODE><DD> + Re-estimate hyperparameters using evidence approximation. +<DT> +<CODE><a href="fevbayes.htm">fevbayes</a></CODE><DD> + Evaluate Bayesian regularisation for network forward propagation. +<DT> +<CODE><a href="gauss.htm">gauss</a></CODE><DD> + Evaluate a Gaussian distribution. +<DT> +<CODE><a href="gbayes.htm">gbayes</a></CODE><DD> + Evaluate gradient of Bayesian error function for network. +<DT> +<CODE><a href="glm.htm">glm</a></CODE><DD> + Create a generalized linear model. +<DT> +<CODE><a href="glmderiv.htm">glmderiv</a></CODE><DD> + Evaluate derivatives of GLM outputs with respect to weights. +<DT> +<CODE><a href="glmerr.htm">glmerr</a></CODE><DD> + Evaluate error function for generalized linear model. +<DT> +<CODE><a href="glmevfwd.htm">glmevfwd</a></CODE><DD> + Forward propagation with evidence for GLM +<DT> +<CODE><a href="glmfwd.htm">glmfwd</a></CODE><DD> + Forward propagation through generalized linear model. +<DT> +<CODE><a href="glmgrad.htm">glmgrad</a></CODE><DD> + Evaluate gradient of error function for generalized linear model. +<DT> +<CODE><a href="glmhess.htm">glmhess</a></CODE><DD> + Evaluate the Hessian matrix for a generalised linear model. +<DT> +<CODE><a href="glminit.htm">glminit</a></CODE><DD> + Initialise the weights in a generalized linear model. +<DT> +<CODE><a href="glmpak.htm">glmpak</a></CODE><DD> + Combines weights and biases into one weights vector. +<DT> +<CODE><a href="glmtrain.htm">glmtrain</a></CODE><DD> + Specialised training of generalized linear model +<DT> +<CODE><a href="glmunpak.htm">glmunpak</a></CODE><DD> + Separates weights vector into weight and bias matrices. +<DT> +<CODE><a href="gmm.htm">gmm</a></CODE><DD> + Creates a Gaussian mixture model with specified architecture. +<DT> +<CODE><a href="gmmactiv.htm">gmmactiv</a></CODE><DD> + Computes the activations of a Gaussian mixture model. +<DT> +<CODE><a href="gmmem.htm">gmmem</a></CODE><DD> + EM algorithm for Gaussian mixture model. +<DT> +<CODE><a href="gmminit.htm">gmminit</a></CODE><DD> + Initialises Gaussian mixture model from data +<DT> +<CODE><a href="gmmpak.htm">gmmpak</a></CODE><DD> + Combines all the parameters in a Gaussian mixture model into one vector. +<DT> +<CODE><a href="gmmpost.htm">gmmpost</a></CODE><DD> + Computes the class posterior probabilities of a Gaussian mixture model. +<DT> +<CODE><a href="gmmprob.htm">gmmprob</a></CODE><DD> + Computes the data probability for a Gaussian mixture model. +<DT> +<CODE><a href="gmmsamp.htm">gmmsamp</a></CODE><DD> + Sample from a Gaussian mixture distribution. +<DT> +<CODE><a href="gmmunpak.htm">gmmunpak</a></CODE><DD> + Separates a vector of Gaussian mixture model parameters into its components. +<DT> +<CODE><a href="gp.htm">gp</a></CODE><DD> + Create a Gaussian Process. +<DT> +<CODE><a href="gpcovar.htm">gpcovar</a></CODE><DD> + Calculate the covariance for a Gaussian Process. +<DT> +<CODE><a href="gpcovarf.htm">gpcovarf</a></CODE><DD> + Calculate the covariance function for a Gaussian Process. +<DT> +<CODE><a href="gpcovarp.htm">gpcovarp</a></CODE><DD> + Calculate the prior covariance for a Gaussian Process. +<DT> +<CODE><a href="gperr.htm">gperr</a></CODE><DD> + Evaluate error function for Gaussian Process. +<DT> +<CODE><a href="gpfwd.htm">gpfwd</a></CODE><DD> + Forward propagation through Gaussian Process. +<DT> +<CODE><a href="gpgrad.htm">gpgrad</a></CODE><DD> + Evaluate error gradient for Gaussian Process. +<DT> +<CODE><a href="gpinit.htm">gpinit</a></CODE><DD> + Initialise Gaussian Process model. +<DT> +<CODE><a href="gppak.htm">gppak</a></CODE><DD> + Combines GP hyperparameters into one vector. +<DT> +<CODE><a href="gpunpak.htm">gpunpak</a></CODE><DD> + Separates hyperparameter vector into components. +<DT> +<CODE><a href="gradchek.htm">gradchek</a></CODE><DD> + Checks a user-defined gradient function using finite differences. +<DT> +<CODE><a href="graddesc.htm">graddesc</a></CODE><DD> + Gradient descent optimization. +<DT> +<CODE><a href="gsamp.htm">gsamp</a></CODE><DD> + Sample from a Gaussian distribution. +<DT> +<CODE><a href="gtm.htm">gtm</a></CODE><DD> + Create a Generative Topographic Map. +<DT> +<CODE><a href="gtmem.htm">gtmem</a></CODE><DD> + EM algorithm for Generative Topographic Mapping. +<DT> +<CODE><a href="gtmfwd.htm">gtmfwd</a></CODE><DD> + Forward propagation through GTM. +<DT> +<CODE><a href="gtminit.htm">gtminit</a></CODE><DD> + Initialise the weights and latent sample in a GTM. +<DT> +<CODE><a href="gtmlmean.htm">gtmlmean</a></CODE><DD> + Mean responsibility for data in a GTM. +<DT> +<CODE><a href="gtmlmode.htm">gtmlmode</a></CODE><DD> + Mode responsibility for data in a GTM. +<DT> +<CODE><a href="gtmmag.htm">gtmmag</a></CODE><DD> + Magnification factors for a GTM +<DT> +<CODE><a href="gtmpost.htm">gtmpost</a></CODE><DD> + Latent space responsibility for data in a GTM. +<DT> +<CODE><a href="gtmprob.htm">gtmprob</a></CODE><DD> + Probability for data under a GTM. +<DT> +<CODE><a href="hbayes.htm">hbayes</a></CODE><DD> + Evaluate Hessian of Bayesian error function for network. +<DT> +<CODE><a href="hesschek.htm">hesschek</a></CODE><DD> + Use central differences to confirm correct evaluation of Hessian matrix. +<DT> +<CODE><a href="hintmat.htm">hintmat</a></CODE><DD> + Evaluates the coordinates of the patches for a Hinton diagram. +<DT> +<CODE><a href="hinton.htm">hinton</a></CODE><DD> + Plot Hinton diagram for a weight matrix. +<DT> +<CODE><a href="histp.htm">histp</a></CODE><DD> + Histogram estimate of 1-dimensional probability distribution. +<DT> +<CODE><a href="hmc.htm">hmc</a></CODE><DD> + Hybrid Monte Carlo sampling. +<DT> +<CODE><a href="kmeans.htm">kmeans</a></CODE><DD> + Trains a k means cluster model. +<DT> +<CODE><a href="knn.htm">knn</a></CODE><DD> + Creates a K-nearest-neighbour classifier. +<DT> +<CODE><a href="knnfwd.htm">knnfwd</a></CODE><DD> + Forward propagation through a K-nearest-neighbour classifier. +<DT> +<CODE><a href="linef.htm">linef</a></CODE><DD> + Calculate function value along a line. +<DT> +<CODE><a href="linemin.htm">linemin</a></CODE><DD> + One dimensional minimization. +<DT> +<CODE><a href="maxitmess.htm">maxitmess</a></CODE><DD> + Create a standard error message when training reaches max. iterations. +<DT> +<CODE><a href="mdn.htm">mdn</a></CODE><DD> + Creates a Mixture Density Network with specified architecture. +<DT> +<CODE><a href="mdn2gmm.htm">mdn2gmm</a></CODE><DD> + Converts an MDN mixture data structure to array of GMMs. +<DT> +<CODE><a href="mdndist2.htm">mdndist2</a></CODE><DD> + Calculates squared distance between centres of Gaussian kernels and data +<DT> +<CODE><a href="mdnerr.htm">mdnerr</a></CODE><DD> + Evaluate error function for Mixture Density Network. +<DT> +<CODE><a href="mdnfwd.htm">mdnfwd</a></CODE><DD> + Forward propagation through Mixture Density Network. +<DT> +<CODE><a href="mdngrad.htm">mdngrad</a></CODE><DD> + Evaluate gradient of error function for Mixture Density Network. +<DT> +<CODE><a href="mdninit.htm">mdninit</a></CODE><DD> + Initialise the weights in a Mixture Density Network. +<DT> +<CODE><a href="mdnpak.htm">mdnpak</a></CODE><DD> + Combines weights and biases into one weights vector. +<DT> +<CODE><a href="mdnpost.htm">mdnpost</a></CODE><DD> + Computes the posterior probability for each MDN mixture component. +<DT> +<CODE><a href="mdnprob.htm">mdnprob</a></CODE><DD> + Computes the data probability likelihood for an MDN mixture structure. +<DT> +<CODE><a href="mdnunpak.htm">mdnunpak</a></CODE><DD> + Separates weights vector into weight and bias matrices. +<DT> +<CODE><a href="metrop.htm">metrop</a></CODE><DD> + Markov Chain Monte Carlo sampling with Metropolis algorithm. +<DT> +<CODE><a href="minbrack.htm">minbrack</a></CODE><DD> + Bracket a minimum of a function of one variable. +<DT> +<CODE><a href="mlp.htm">mlp</a></CODE><DD> + Create a 2-layer feedforward network. +<DT> +<CODE><a href="mlpbkp.htm">mlpbkp</a></CODE><DD> + Backpropagate gradient of error function for 2-layer network. +<DT> +<CODE><a href="mlpderiv.htm">mlpderiv</a></CODE><DD> + Evaluate derivatives of network outputs with respect to weights. +<DT> +<CODE><a href="mlperr.htm">mlperr</a></CODE><DD> + Evaluate error function for 2-layer network. +<DT> +<CODE><a href="mlpevfwd.htm">mlpevfwd</a></CODE><DD> + Forward propagation with evidence for MLP +<DT> +<CODE><a href="mlpfwd.htm">mlpfwd</a></CODE><DD> + Forward propagation through 2-layer network. +<DT> +<CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><DD> + Evaluate gradient of error function for 2-layer network. +<DT> +<CODE><a href="mlphdotv.htm">mlphdotv</a></CODE><DD> + Evaluate the product of the data Hessian with a vector. +<DT> +<CODE><a href="mlphess.htm">mlphess</a></CODE><DD> + Evaluate the Hessian matrix for a multi-layer perceptron network. +<DT> +<CODE><a href="mlphint.htm">mlphint</a></CODE><DD> + Plot Hinton diagram for 2-layer feed-forward network. +<DT> +<CODE><a href="mlpinit.htm">mlpinit</a></CODE><DD> + Initialise the weights in a 2-layer feedforward network. +<DT> +<CODE><a href="mlppak.htm">mlppak</a></CODE><DD> + Combines weights and biases into one weights vector. +<DT> +<CODE><a href="mlpprior.htm">mlpprior</a></CODE><DD> + Create Gaussian prior for mlp. +<DT> +<CODE><a href="mlptrain.htm">mlptrain</a></CODE><DD> + Utility to train an MLP network for demtrain +<DT> +<CODE><a href="mlpunpak.htm">mlpunpak</a></CODE><DD> + Separates weights vector into weight and bias matrices. +<DT> +<CODE><a href="netderiv.htm">netderiv</a></CODE><DD> + Evaluate derivatives of network outputs by weights generically. +<DT> +<CODE><a href="neterr.htm">neterr</a></CODE><DD> + Evaluate network error function for generic optimizers +<DT> +<CODE><a href="netevfwd.htm">netevfwd</a></CODE><DD> + Generic forward propagation with evidence for network +<DT> +<CODE><a href="netgrad.htm">netgrad</a></CODE><DD> + Evaluate network error gradient for generic optimizers +<DT> +<CODE><a href="nethess.htm">nethess</a></CODE><DD> + Evaluate network Hessian +<DT> +<CODE><a href="netinit.htm">netinit</a></CODE><DD> + Initialise the weights in a network. +<DT> +<CODE><a href="netopt.htm">netopt</a></CODE><DD> + Optimize the weights in a network model. +<DT> +<CODE><a href="netpak.htm">netpak</a></CODE><DD> + Combines weights and biases into one weights vector. +<DT> +<CODE><a href="netunpak.htm">netunpak</a></CODE><DD> + Separates weights vector into weight and bias matrices. +<DT> +<CODE><a href="olgd.htm">olgd</a></CODE><DD> + On-line gradient descent optimization. +<DT> +<CODE><a href="pca.htm">pca</a></CODE><DD> + Principal Components Analysis +<DT> +<CODE><a href="plotmat.htm">plotmat</a></CODE><DD> + Display a matrix. +<DT> +<CODE><a href="ppca.htm">ppca</a></CODE><DD> + Probabilistic Principal Components Analysis +<DT> +<CODE><a href="quasinew.htm">quasinew</a></CODE><DD> + Quasi-Newton optimization. +<DT> +<CODE><a href="rbf.htm">rbf</a></CODE><DD> + Creates an RBF network with specified architecture +<DT> +<CODE><a href="rbfbkp.htm">rbfbkp</a></CODE><DD> + Backpropagate gradient of error function for RBF network. +<DT> +<CODE><a href="rbfderiv.htm">rbfderiv</a></CODE><DD> + Evaluate derivatives of RBF network outputs with respect to weights. +<DT> +<CODE><a href="rbferr.htm">rbferr</a></CODE><DD> + Evaluate error function for RBF network. +<DT> +<CODE><a href="rbfevfwd.htm">rbfevfwd</a></CODE><DD> + Forward propagation with evidence for RBF +<DT> +<CODE><a href="rbffwd.htm">rbffwd</a></CODE><DD> + Forward propagation through RBF network with linear outputs. +<DT> +<CODE><a href="rbfgrad.htm">rbfgrad</a></CODE><DD> + Evaluate gradient of error function for RBF network. +<DT> +<CODE><a href="rbfhess.htm">rbfhess</a></CODE><DD> + Evaluate the Hessian matrix for RBF network. +<DT> +<CODE><a href="rbfjacob.htm">rbfjacob</a></CODE><DD> + Evaluate derivatives of RBF network outputs with respect to inputs. +<DT> +<CODE><a href="rbfpak.htm">rbfpak</a></CODE><DD> + Combines all the parameters in an RBF network into one weights vector. +<DT> +<CODE><a href="rbfprior.htm">rbfprior</a></CODE><DD> + Create Gaussian prior and output layer mask for RBF. +<DT> +<CODE><a href="rbfsetbf.htm">rbfsetbf</a></CODE><DD> + Set basis functions of RBF from data. +<DT> +<CODE><a href="rbfsetfw.htm">rbfsetfw</a></CODE><DD> + Set basis function widths of RBF. +<DT> +<CODE><a href="rbftrain.htm">rbftrain</a></CODE><DD> + Two stage training of RBF network. +<DT> +<CODE><a href="rbfunpak.htm">rbfunpak</a></CODE><DD> + Separates a vector of RBF weights into its components. +<DT> +<CODE><a href="rosegrad.htm">rosegrad</a></CODE><DD> + Calculate gradient of Rosenbrock's function. +<DT> +<CODE><a href="rosen.htm">rosen</a></CODE><DD> + Calculate Rosenbrock's function. +<DT> +<CODE><a href="scg.htm">scg</a></CODE><DD> + Scaled conjugate gradient optimization. +<DT> +<CODE><a href="som.htm">som</a></CODE><DD> + Creates a Self-Organising Map. +<DT> +<CODE><a href="somfwd.htm">somfwd</a></CODE><DD> + Forward propagation through a Self-Organising Map. +<DT> +<CODE><a href="sompak.htm">sompak</a></CODE><DD> + Combines node weights into one weights matrix. +<DT> +<CODE><a href="somtrain.htm">somtrain</a></CODE><DD> + Kohonen training algorithm for SOM. +<DT> +<CODE><a href="somunpak.htm">somunpak</a></CODE><DD> + Replaces node weights in SOM. +</DL> + +<hr> +<p>Copyright (c) Christopher M Bishop, Ian T Nabney (1996, 1997) +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/kmeans.htm b/sourcecodes/bnt-master/nethelp3.3/kmeans.htm new file mode 100644 index 00000000..092e51d3 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/kmeans.htm @@ -0,0 +1,89 @@ +<html> +<head> +<title> +Netlab Reference Manual kmeans +</title> +</head> +<body> +<H1> kmeans +</H1> +<h2> +Purpose +</h2> +Trains a k means cluster model. + +<p><h2> +Synopsis +</h2> +<PRE> +centres = kmeans(centres, data, options) +[centres, options] = kmeans(centres, data, options) +[centres, options, post, errlog] = kmeans(centres, data, options) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>centres = kmeans(centres, data, options)</CODE> +uses the batch K-means algorithm to set the centres of a cluster model. +The matrix <CODE>data</CODE> represents the data +which is being clustered, with each row corresponding to a vector. +The sum of squares error function is used. The point at which +a local minimum is achieved is returned as <CODE>centres</CODE>. The +error value at that point is returned in <CODE>options(8)</CODE>. + +<p><CODE>[centres, options, post, errlog] = kmeans(centres, data, options)</CODE> +also returns the cluster number (in a one-of-N encoding) for each data +point in <CODE>post</CODE> and a log of the error values after each cycle in +<CODE>errlog</CODE>. + +The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>. +If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value +of <CODE>centres</CODE> at the solution. If the absolute difference between +the values of <CODE>centres</CODE> between two successive steps is less than +<CODE>options(2)</CODE>, then this condition is satisfied. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the error +function at the solution. If the absolute difference between the +error functions between two successive steps is less than +<CODE>options(3)</CODE>, then this condition is satisfied. +Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p><h2> +Example +</h2> +<CODE>kmeans</CODE> can be used to initialise the centres of a Gaussian +mixture model that is then trained with the EM algorithm. +<PRE> + +[priors, centres, var] = gmmunpak(p, md); +centres = kmeans(centres, data, options); +p = gmmpak(priors, centres, var); +p = gmmem(p, md, data, options); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="gmminit.htm">gmminit</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/knn.htm b/sourcecodes/bnt-master/nethelp3.3/knn.htm new file mode 100644 index 00000000..31f032bc --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/knn.htm @@ -0,0 +1,54 @@ +<html> +<head> +<title> +Netlab Reference Manual knn +</title> +</head> +<body> +<H1> knn +</H1> +<h2> +Purpose +</h2> +Creates a K-nearest-neighbour classifier. + +<p><h2> +Synopsis +</h2> +<PRE> + +net = knn(nin, nout, k, tr_in, tr_targets) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = knn(nin, nout, k, tr_in, tr_targets)</CODE> creates a KNN model <CODE>net</CODE> +with input dimension <CODE>nin</CODE>, output dimension <CODE>nout</CODE> and <CODE>k</CODE> +neighbours. The training data is also stored in the data structure and the +targets are assumed to be using a 1-of-N coding. + +<p>The fields in <CODE>net</CODE> are +<PRE> + + type = 'knn' + nin = number of inputs + nout = number of outputs + tr_in = training input data + tr_targets = training target data +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="kmeans.htm">kmeans</a></CODE>, <CODE><a href="knnfwd.htm">knnfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/knnfwd.htm b/sourcecodes/bnt-master/nethelp3.3/knnfwd.htm new file mode 100644 index 00000000..6670920f --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/knnfwd.htm @@ -0,0 +1,66 @@ +<html> +<head> +<title> +Netlab Reference Manual knnfwd +</title> +</head> +<body> +<H1> knnfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through a K-nearest-neighbour classifier. + +<p><h2> +Synopsis +</h2> +<PRE> + +[y, l] = knnfwd(net, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>[y, l] = knnfwd(net, x)</CODE> takes a matrix <CODE>x</CODE> +of input vectors (one vector per row) + and uses the <CODE>k</CODE>-nearest-neighbour rule on the training data contained +in <CODE>net</CODE> to +produce +a matrix <CODE>y</CODE> of outputs and a matrix <CODE>l</CODE> of classification +labels. +The nearest neighbours are determined using Euclidean distance. +The <CODE>ij</CODE>th entry of <CODE>y</CODE> counts the number of occurrences that +an example from class <CODE>j</CODE> is among the <CODE>k</CODE> closest training +examples to example <CODE>i</CODE> from <CODE>x</CODE>. +The matrix <CODE>l</CODE> contains the predicted class labels +as an index 1..N, not as 1-of-N coding. + +<p><h2> +Example +</h2> +<PRE> + +net = knn(size(xtrain, 2), size(t_train, 2), 3, xtrain, t_train); +y = knnfwd(net, xtest); +conffig(y, t_test); +</PRE> + +Creates a 3 nearest neighbour model <CODE>net</CODE> and then applies it to +the data <CODE>xtest</CODE>. The results are plotted as a confusion matrix with +<CODE>conffig</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="kmeans.htm">kmeans</a></CODE>, <CODE><a href="knn.htm">knn</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/linef.htm b/sourcecodes/bnt-master/nethelp3.3/linef.htm new file mode 100644 index 00000000..c6eb9188 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/linef.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual linef +</title> +</head> +<body> +<H1> linef +</H1> +<h2> +Purpose +</h2> +Calculate function value along a line. + +<p><h2> +Description +</h2> +<CODE>linef(lambda, fn, x, d)</CODE> calculates the value of the function +<CODE>fn</CODE> at the point <CODE>x+lambda*d</CODE>. Here <CODE>x</CODE> is a row vector +and <CODE>lambda</CODE> is a scalar. + +<p><CODE>linef(lambda, fn, x, d, p1, p2, ...)</CODE> allows additional +arguments to be passed to <CODE>fn()</CODE>. +This function is used for convenience in some of the optimisation routines. + +<p><h2> +Examples +</h2> +An example of +the use of this function can be found in the function <CODE>linemin</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gradchek.htm">gradchek</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/linemin.htm b/sourcecodes/bnt-master/nethelp3.3/linemin.htm new file mode 100644 index 00000000..e4d7a8b9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/linemin.htm @@ -0,0 +1,74 @@ +<html> +<head> +<title> +Netlab Reference Manual linemin +</title> +</head> +<body> +<H1> linemin +</H1> +<h2> +Purpose +</h2> +One dimensional minimization. + +<p><h2> +Description +</h2> +<CODE>[x, options] = linemin(f, pt, dir, fpt, options)</CODE> uses Brent's +algorithm to find the minimum of the function <CODE>f(x)</CODE> along the +line <CODE>dir</CODE> through the point <CODE>pt</CODE>. The function value at the +starting point is <CODE>fpt</CODE>. The point at which <CODE>f</CODE> has a local minimum +is returned as <CODE>x</CODE>. The function value at that point is returned +in <CODE>options(8)</CODE>. + +<p><CODE>linemin(f, pt, dir, fpt, options, p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE>. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values. + +<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value +of <CODE>x</CODE> at the solution. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p><h2> +Examples +</h2> +An example of the use of this function to find the minimum of a function +<CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>conjgrad</CODE> +<PRE> + +x = linemin(f, xold, sd, fold, lineoptions); +</PRE> + + +<p><h2> +Algorithm +</h2> + +Brent's algorithm uses a mixture of quadratic interpolation and golden +section search to find the minimum of a function of a single variable once +it has been bracketed (which is done with <CODE>minbrack</CODE>). This is adapted +to minimize a function along a line. +This implementation +is based on that in Numerical Recipes. + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/maxitmess.htm b/sourcecodes/bnt-master/nethelp3.3/maxitmess.htm new file mode 100644 index 00000000..a42b1f8b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/maxitmess.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual maxitmess +</title> +</head> +<body> +<H1> maxitmess +</H1> +<h2> +Purpose +</h2> +Create a standard error message when training reaches max. iterations. + +<p><h2> +Synopsis +</h2> +<PRE> +s = maxitmess +</PRE> + + +<p><h2> +Description +</h2> +<CODE>s = maxitmess</CODE> returns a standard string that it used by training +algorithms when the maximum number of iterations (as specified in +<CODE>options(14)</CODE> is reached. + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="glmtrain.htm">glmtrain</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE>, <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="gtmem.htm">gtmem</a></CODE>, <CODE><a href="kmeans.htm">kmeans</a></CODE>, <CODE><a href="olgd.htm">olgd</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdn.htm b/sourcecodes/bnt-master/nethelp3.3/mdn.htm new file mode 100644 index 00000000..5e5b83a8 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdn.htm @@ -0,0 +1,84 @@ +<html> +<head> +<title> +Netlab Reference Manual mdn +</title> +</head> +<body> +<H1> mdn +</H1> +<h2> +Purpose +</h2> +Creates a Mixture Density Network with specified architecture. + +<p><h2> +Synopsis +</h2> +<PRE> +net = mdn(nin, nhidden, ncentres, dimtarget) +net = mdn(nin, nhidden, ncentres, dimtarget, mixtype, ... + prior, beta) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = mdn(nin, nhidden, ncentres, dimtarget)</CODE> takes the number of +inputs, +hidden units for a 2-layer feed-forward +network and the number of centres and target dimension for the +mixture model whose parameters are set from the outputs of the neural network. +The fifth argument <CODE>mixtype</CODE> is used to define the type of mixture +model. (Currently there is only one type supported: a mixture of Gaussians with +a single covariance parameter for each component.) For this model, +the mixture coefficients are computed from a group of softmax outputs, +the centres are equal to a group of linear outputs, and the variances are +obtained by applying the exponential function to a third group of outputs. + +<p>The network is initialised by a call to <CODE>mlp</CODE>, and the arguments +<CODE>prior</CODE>, and <CODE>beta</CODE> have the same role as for that function. +Weight initialisation uses the Matlab function <CODE>randn</CODE> + and so the seed for the random weight initialization can be +set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the seed value. +A specialised data structure (rather than <CODE>gmm</CODE>) +is used for the mixture model outputs to improve +the efficiency of error and gradient calculations in network training. +The fields are described in <CODE>mdnfwd</CODE> where they are set up. + +<p>The fields in <CODE>net</CODE> are +<PRE> + + type = 'mdn' + nin = number of input variables + nout = dimension of target space (not number of network outputs) + nwts = total number of weights and biases + mdnmixes = data structure for mixture model output + mlp = data structure for MLP network +</PRE> + + +<p><h2> +Example +</h2> +<PRE> + +net = mdn(2, 4, 3, 1, 'spherical'); +</PRE> + +This creates a Mixture Density Network with 2 inputs and 4 hidden units. +The mixture model has 3 components and the target space has dimension 1. + +<p><h2> +See Also +</h2> +<CODE><a href="mdnfwd.htm">mdnfwd</a></CODE>, <CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdn2gmm.htm">mdn2gmm</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE>, <CODE><a href="mdnpak.htm">mdnpak</a></CODE>, <CODE><a href="mdnunpak.htm">mdnunpak</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdn2gmm.htm b/sourcecodes/bnt-master/nethelp3.3/mdn2gmm.htm new file mode 100644 index 00000000..51369a50 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdn2gmm.htm @@ -0,0 +1,58 @@ +<html> +<head> +<title> +Netlab Reference Manual mdn2gmm +</title> +</head> +<body> +<H1> mdn2gmm +</H1> +<h2> +Purpose +</h2> +Converts an MDN mixture data structure to array of GMMs. + +<p><h2> +Synopsis +</h2> +<PRE> +gmmmixes = mdn2gmm(mdnmixes) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>gmmmixes = mdn2gmm(mdnmixes)</CODE> takes an MDN mixture data structure +<CODE>mdnmixes</CODE> +containing three matrices (for priors, centres and variances) where each +row represents the corresponding parameter values for a different mixture model +and creates an array of GMMs. These can then be used with the standard +Netlab Gaussian mixture model functions. + +<p><h2> +Example +</h2> +<PRE> + +mdnmixes = mdnfwd(net, x); +mixes = mdn2gmm(mdnmixes); +p = gmmprob(mixes(1), y); +</PRE> + +This creates an array GMM mixture models (one for each data point in +<CODE>x</CODE>). The vector <CODE>p</CODE> is then filled with the conditional +probabilities of the values <CODE>y</CODE> given <CODE>x(1,:)</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="gmm.htm">gmm</a></CODE>, <CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdnfwd.htm">mdnfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdndist2.htm b/sourcecodes/bnt-master/nethelp3.3/mdndist2.htm new file mode 100644 index 00000000..76713ae4 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdndist2.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual mdndist2 +</title> +</head> +<body> +<H1> mdndist2 +</H1> +<h2> +Purpose +</h2> +Calculates squared distance between centres of Gaussian kernels and data + +<p><h2> +Synopsis +</h2> +<PRE> +n2 = mdndist2(mixparams, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>n2 = mdndist2(mixparams, t)</CODE> takes takes the centres of the Gaussian +contained in + <CODE>mixparams</CODE> and the target data matrix, <CODE>t</CODE>, and computes the squared +Euclidean distance between them. If <CODE>t</CODE> has <CODE>m</CODE> rows and <CODE>n</CODE> +columns, then the <CODE>centres</CODE> field in +the <CODE>mixparams</CODE> structure should have <CODE>m</CODE> rows and +<CODE>n*mixparams.ncentres</CODE> columns: the centres in each row relate to +the corresponding row in <CODE>t</CODE>. +The result has <CODE>m</CODE> rows and <CODE>mixparams.ncentres</CODE> columns. +The <CODE>i, j</CODE>th entry is the +squared distance from the <CODE>i</CODE>th row of <CODE>x</CODE> to the <CODE>j</CODE>th +centre in the <CODE>i</CODE>th row of <CODE>mixparams.centres</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mdnfwd.htm">mdnfwd</a></CODE>, <CODE><a href="mdnprob.htm">mdnprob</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdnerr.htm b/sourcecodes/bnt-master/nethelp3.3/mdnerr.htm new file mode 100644 index 00000000..41d2f260 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdnerr.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual mdnerr +</title> +</head> +<body> +<H1> mdnerr +</H1> +<h2> +Purpose +</h2> +Evaluate error function for Mixture Density Network. + +<p><h2> +Synopsis +</h2> +<PRE> +e = mdnerr(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>e = mdnerr(net, x, t)</CODE> takes a mixture density network data +structure <CODE>net</CODE>, a matrix <CODE>x</CODE> of input vectors and a matrix +<CODE>t</CODE> of target vectors, and evaluates the error function +<CODE>e</CODE>. The error function is the negative log likelihood of the +target data under the conditional density given by the mixture model +parameterised by the MLP. Each row of <CODE>x</CODE> corresponds to one +input vector and each row of <CODE>t</CODE> corresponds to one target vector. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdnfwd.htm">mdnfwd</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdnfwd.htm b/sourcecodes/bnt-master/nethelp3.3/mdnfwd.htm new file mode 100644 index 00000000..67c5c5d3 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdnfwd.htm @@ -0,0 +1,71 @@ +<html> +<head> +<title> +Netlab Reference Manual mdnfwd +</title> +</head> +<body> +<H1> mdnfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through Mixture Density Network. + +<p><h2> +Synopsis +</h2> +<PRE> +mixparams = mdnfwd(net, x) +[mixparams, y, z] = mdnfwd(net, x) +[mixparams, y, z, a] = mdnfwd(net, x) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>mixparams = mdnfwd(net, x)</CODE> takes a mixture density network data +structure <CODE>net</CODE> and a matrix <CODE>x</CODE> of input vectors, and forward +propagates the inputs through the network to generate a structure +<CODE>mixparams</CODE> which contains the parameters of several mixture models. +Each row of <CODE>x</CODE> represents +one input vector and the corresponding row of the matrices in <CODE>mixparams</CODE> +represents the parameters of a mixture model for the conditional probability +of target vectors given the input vector. This is not represented as an array +of <CODE>gmm</CODE> structures to improve the efficiency of MDN training. + +<p>The fields in <CODE>mixparams</CODE> are +<PRE> + + type = 'mdnmixes' + ncentres = number of mixture components + dimtarget = dimension of target space + mixcoeffs = mixing coefficients + centres = means of Gaussians: stored as one row per pattern + covars = covariances of Gaussians + nparams = number of parameters +</PRE> + + +<p><CODE>[mixparams, y, z] = mdnfwd(net, x)</CODE> also generates a matrix <CODE>y</CODE> of +the outputs of the MLP and a matrix <CODE>z</CODE> of the hidden +unit activations where each row corresponds to one pattern. + +<p><CODE>[mixparams, y, z, a] = mlpfwd(net, x)</CODE> also returns a matrix <CODE>a</CODE> +giving the summed inputs to each output unit, where each row +corresponds to one pattern. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdn2gmm.htm">mdn2gmm</a></CODE>, <CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdngrad.htm b/sourcecodes/bnt-master/nethelp3.3/mdngrad.htm new file mode 100644 index 00000000..b3842991 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdngrad.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual mdngrad +</title> +</head> +<body> +<H1> mdngrad +</H1> +<h2> +Purpose +</h2> +Evaluate gradient of error function for Mixture Density Network. + +<p><h2> +Synopsis +</h2> +<PRE> + +g = mdngrad(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>g = mdngrad(net, x, t)</CODE> takes a mixture density network data +structure <CODE>net</CODE>, a matrix <CODE>x</CODE> of input vectors and a matrix +<CODE>t</CODE> of target vectors, and evaluates the gradient <CODE>g</CODE> of the +error function with respect to the network weights. The error function +is negative log likelihood of the target data. Each row of <CODE>x</CODE> +corresponds to one input vector and each row of <CODE>t</CODE> corresponds to +one target vector. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdnfwd.htm">mdnfwd</a></CODE>, <CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdnprob.htm">mdnprob</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdninit.htm b/sourcecodes/bnt-master/nethelp3.3/mdninit.htm new file mode 100644 index 00000000..9e205c51 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdninit.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual mdninit +</title> +</head> +<body> +<H1> mdninit +</H1> +<h2> +Purpose +</h2> +Initialise the weights in a Mixture Density Network. + +<p><h2> +Synopsis +</h2> +<PRE> +net = mdninit(net, prior) +net = mdninit(net, prior, t, options) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = mdninit(net, prior)</CODE> takes a Mixture Density Network +<CODE>net</CODE> and sets the weights and biases by sampling from a Gaussian +distribution. It calls <CODE>mlpinit</CODE> for the MLP component of <CODE>net</CODE>. + +<p><CODE>net = mdninit(net, prior, t, options)</CODE> uses the target data <CODE>t</CODE> to +initialise the biases for the output units after initialising the +other weights as above. It calls <CODE>gmminit</CODE>, with <CODE>t</CODE> and <CODE>options</CODE> +as arguments, to obtain a model of the unconditional density of <CODE>t</CODE>. The +biases are then set so that <CODE>net</CODE> will output the values in the Gaussian +mixture model. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlpinit.htm">mlpinit</a></CODE>, <CODE><a href="gmminit.htm">gmminit</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdnpak.htm b/sourcecodes/bnt-master/nethelp3.3/mdnpak.htm new file mode 100644 index 00000000..d5e39033 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdnpak.htm @@ -0,0 +1,41 @@ +<html> +<head> +<title> +Netlab Reference Manual mdnpak +</title> +</head> +<body> +<H1> mdnpak +</H1> +<h2> +Purpose +</h2> +Combines weights and biases into one weights vector. + +<p><h2> +Synopsis +</h2> +<PRE> +w = mdnpak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>w = mdnpak(net)</CODE> takes a mixture density +network data structure <CODE>net</CODE> and +combines the network weights into a single row vector <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdnunpak.htm">mdnunpak</a></CODE>, <CODE><a href="mdnfwd.htm">mdnfwd</a></CODE>, <CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdnpost.htm b/sourcecodes/bnt-master/nethelp3.3/mdnpost.htm new file mode 100644 index 00000000..3ae071a0 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdnpost.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual mdnpost +</title> +</head> +<body> +<H1> mdnpost +</H1> +<h2> +Purpose +</h2> +Computes the posterior probability for each MDN mixture component. + +<p><h2> +Synopsis +</h2> +<PRE> +post = mdnpost(mixparams, t) +[post, a] = mdnpost(mixparams, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>post = mdnpost(mixparams, t)</CODE> computes the posterior +probability <CODE>p(j|t)</CODE> of each +data vector in <CODE>t</CODE> under the Gaussian mixture model represented by the +corresponding entries in <CODE>mixparams</CODE>. Each row of <CODE>t</CODE> represents a +single vector. + +<p><CODE>[post, a] = mdnpost(mixparams, t)</CODE> also computes the activations +<CODE>a</CODE> (i.e. the probability <CODE>p(t|j)</CODE> of the data conditioned on +each component density) for a Gaussian mixture model. + +<p><h2> +See Also +</h2> +<CODE><a href="mdngrad.htm">mdngrad</a></CODE>, <CODE><a href="mdnprob.htm">mdnprob</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdnprob.htm b/sourcecodes/bnt-master/nethelp3.3/mdnprob.htm new file mode 100644 index 00000000..cffa2517 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdnprob.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual mdnprob +</title> +</head> +<body> +<H1> mdnprob +</H1> +<h2> +Purpose +</h2> +Computes the data probability likelihood for an MDN mixture structure. + +<p><h2> +Synopsis +</h2> +<PRE> +prob = mdnprob(mixparams, t) +[prob, a] = mdnprob(mixparams, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>prob = mdnprob(mixparams, t)</CODE> computes the probability <CODE>p(t)</CODE> of each +data vector in <CODE>t</CODE> under the Gaussian mixture model represented by the +corresponding entries in <CODE>mixparams</CODE>. Each row of <CODE>t</CODE> represents a +single vector. + +<p><CODE>[prob, a] = mdnprob(mixparams, t)</CODE> also computes the activations +<CODE>a</CODE> (i.e. the probability <CODE>p(t|j)</CODE> of the data conditioned on +each component density) for a Gaussian mixture model. + +<p><h2> +See Also +</h2> +<CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdnpost.htm">mdnpost</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mdnunpak.htm b/sourcecodes/bnt-master/nethelp3.3/mdnunpak.htm new file mode 100644 index 00000000..de6d2610 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mdnunpak.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual mdnunpak +</title> +</head> +<body> +<H1> mdnunpak +</H1> +<h2> +Purpose +</h2> +Separates weights vector into weight and bias matrices. + +<p><h2> +Synopsis +</h2> +<PRE> +net = mdnunpak(net, w) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = mdnunpak(net, w)</CODE> takes an mdn network data structure <CODE>net</CODE> and +a weight vector <CODE>w</CODE>, and returns a network data structure identical to +the input network, except that the weights in the MLP sub-structure are +set to the corresponding elements of <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mdn.htm">mdn</a></CODE>, <CODE><a href="mdnpak.htm">mdnpak</a></CODE>, <CODE><a href="mdnfwd.htm">mdnfwd</a></CODE>, <CODE><a href="mdnerr.htm">mdnerr</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) +<p>David J Evans (1998) + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/metrop.htm b/sourcecodes/bnt-master/nethelp3.3/metrop.htm new file mode 100644 index 00000000..93c3ed49 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/metrop.htm @@ -0,0 +1,108 @@ +<html> +<head> +<title> +Netlab Reference Manual metrop +</title> +</head> +<body> +<H1> metrop +</H1> +<h2> +Purpose +</h2> +Markov Chain Monte Carlo sampling with Metropolis algorithm. + +<p><h2> +Synopsis +</h2> +<PRE> + +samples = metrop(f, x, options) +samples = metrop(f, x, options, [], P1, P2, ...) +[samples, energies, diagn] = metrop(f, x, options) +s = metrop('state') +metrop('state', s) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>samples = metrop(f, x, options)</CODE> uses +the Metropolis algorithm to sample from the distribution +<CODE>p ~ exp(-f)</CODE>, where <CODE>f</CODE> is the first argument to <CODE>metrop</CODE>. +The Markov chain starts at the point <CODE>x</CODE> and each +candidate state is picked from a Gaussian proposal distribution and +accepted or rejected according to the Metropolis criterion. + +<p><CODE>samples = metrop(f, x, options, [], p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE>. The fourth argument is +ignored, but is included for compatibility with <CODE>hmc</CODE> and the +optimisers. + +<p><CODE>[samples, energies, diagn] = metrop(f, x, options)</CODE> also returns +a log of the energy values (i.e. negative log probabilities) for the +samples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containing +diagnostic information (position and +acceptance threshold) for each step of the chain in <CODE>diagn.pos</CODE> and +<CODE>diagn.acc</CODE> respectively. All candidate states (including rejected +ones) are stored in <CODE>diagn.pos</CODE>. + +<p><CODE>s = metrop('state')</CODE> returns a state structure that contains the +state of the two random number generators <CODE>rand</CODE> and <CODE>randn</CODE>. +These are contained in fields +<CODE>randstate</CODE>, +<CODE>randnstate</CODE>. + +<p><CODE>metrop('state', s)</CODE> resets the state to <CODE>s</CODE>. If <CODE>s</CODE> is an integer, +then it is passed to <CODE>rand</CODE> and <CODE>randn</CODE>. +If <CODE>s</CODE> is a structure returned by <CODE>metrop('state')</CODE> then +it resets the generator to exactly the same state. + +<p>The optional parameters in the <CODE>options</CODE> vector have the following +interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejection +threshold at each step of the Markov chain. If the value is 2, then the +position vectors at each step are also displayed. + +<p><CODE>options(14)</CODE> is the number of samples retained from the Markov chain; +default 100. + +<p><CODE>options(15)</CODE> is the number of samples omitted from the start of the +chain; default 0. + +<p><CODE>options(18)</CODE> is the variance of the proposal distribution; default 1. + +<p><h2> +Examples +</h2> +The following code fragment samples from the posterior distribution of +weights for a neural network. +<PRE> + +w = mlppak(net); +[samples, energies] = metrop('neterr', w, options, 'netgrad', net, x, t); +</PRE> + + +<p><h2> +Algorithm +</h2> + +The algorithm follows the procedure outlined in Radford Neal's technical +report CRG-TR-93-1 from the University of Toronto. + +<p><h2> +See Also +</h2> +<CODE><a href="hmc.htm">hmc</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/minbrack.htm b/sourcecodes/bnt-master/nethelp3.3/minbrack.htm new file mode 100644 index 00000000..f49d18f5 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/minbrack.htm @@ -0,0 +1,65 @@ +<html> +<head> +<title> +Netlab Reference Manual minbrack +</title> +</head> +<body> +<H1> minbrack +</H1> +<h2> +Purpose +</h2> +Bracket a minimum of a function of one variable. + +<p><h2> +Description +</h2> +<CODE>brmin, brmid, brmax, numevals] = minbrack(f, a, b, fa)</CODE> +finds a bracket of three points around a local minimum of +<CODE>f</CODE>. The function <CODE>f</CODE> must have a one dimensional domain. +<CODE>a < b</CODE> is an initial guess at the minimum and maximum points +of a bracket, but <CODE>minbrack</CODE> will search outside this interval if +necessary. The bracket consists of three points (in increasing order) +such that <CODE>f(brmid) < f(brmin)</CODE> and <CODE>f(brmid) < f(brmax)</CODE>. +<CODE>fa</CODE> is the value of the function at <CODE>a</CODE>: it is included to +avoid unnecessary function evaluations in the optimization routines. +The return value <CODE>numevals</CODE> is the number of function evaluations +in <CODE>minbrack</CODE>. + +<p><CODE>minbrack(f, a, b, fa, p1, p2, ...)</CODE> allows additional +arguments to be passed to <CODE>f</CODE> + +<p><h2> +Examples +</h2> +An example of the use of this function to bracket the minimum of a function +<CODE>f</CODE> in the direction <CODE>sd</CODE> can be found in <CODE>linemin</CODE> +<PRE> + +[min, mid, max, nevals]] = minbrack('linef', 0.0, 1.0, fa, f, pt, dir); +</PRE> + +where the function <CODE>linef</CODE> is used to turn a general function <CODE>f</CODE> +into a one dimensional one. + +<p><h2> +Algorithm +</h2> + +Quadratic extrapolation with a limit to the maximum step size is +used to find the outside points of the bracket. This implementation +is based on that in Numerical Recipes. + +<p><h2> +See Also +</h2> +<CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="linef.htm">linef</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlp.htm b/sourcecodes/bnt-master/nethelp3.3/mlp.htm new file mode 100644 index 00000000..b8237991 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlp.htm @@ -0,0 +1,94 @@ +<html> +<head> +<title> +Netlab Reference Manual mlp +</title> +</head> +<body> +<H1> mlp +</H1> +<h2> +Purpose +</h2> +Create a 2-layer feedforward network. + +<p><h2> +Synopsis +</h2> +<PRE> +net = mlp(nin, nhidden, nout, func) +net = mlp(nin, nhidden, nout, func, prior) +net = mlp(nin, nhidden, nout, func, prior, beta) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = mlp(nin, nhidden, nout, func)</CODE> takes the number of inputs, +hidden units and output units for a 2-layer feed-forward network, +together with a string <CODE>func</CODE> which specifies the output unit +activation function, and returns a data structure <CODE>net</CODE>. The +weights are drawn from a zero mean, unit variance isotropic Gaussian, +with varianced scaled by the fan-in of the hidden or output units as +appropriate. This makes use of the Matlab function +<CODE>randn</CODE> and so the seed for the random weight initialization can be +set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the seed value. +The hidden units use the <CODE>tanh</CODE> activation function. + +<p>The fields in <CODE>net</CODE> are +<PRE> + + type = 'mlp' + nin = number of inputs + nhidden = number of hidden units + nout = number of outputs + nwts = total number of weights and biases + actfn = string describing the output unit activation function: + 'linear' + 'logistic + 'softmax' + w1 = first-layer weight matrix + b1 = first-layer bias vector + w2 = second-layer weight matrix + b2 = second-layer bias vector +</PRE> + +Here <CODE>w1</CODE> has dimensions <CODE>nin</CODE> times <CODE>nhidden</CODE>, <CODE>b1</CODE> has +dimensions <CODE>1</CODE> times <CODE>nhidden</CODE>, <CODE>w2</CODE> has +dimensions <CODE>nhidden</CODE> times <CODE>nout</CODE>, and <CODE>b2</CODE> has +dimensions <CODE>1</CODE> times <CODE>nout</CODE>. + +<p><CODE>net = mlp(nin, nhidden, nout, func, prior)</CODE>, in which <CODE>prior</CODE> is +a scalar, allows the field <CODE>net.alpha</CODE> in the data structure +<CODE>net</CODE> to be set, corresponding to a zero-mean isotropic Gaussian +prior with inverse variance with value <CODE>prior</CODE>. Alternatively, +<CODE>prior</CODE> can consist of a data structure with fields <CODE>alpha</CODE> +and <CODE>index</CODE>, allowing individual Gaussian priors to be set over +groups of weights in the network. Here <CODE>alpha</CODE> is a column vector +in which each element corresponds to a separate group of weights, +which need not be mutually exclusive. The membership of the groups is +defined by the matrix <CODE>indx</CODE> in which the columns correspond to +the elements of <CODE>alpha</CODE>. Each column has one element for each +weight in the matrix, in the order defined by the function +<CODE>mlppak</CODE>, and each element is 1 or 0 according to whether the +weight is a member of the corresponding group or not. A utility +function <CODE>mlpprior</CODE> is provided to help in setting up the +<CODE>prior</CODE> data structure. + +<p><CODE>net = mlp(nin, nhidden, nout, func, prior, beta)</CODE> also sets the +additional field <CODE>net.beta</CODE> in the data structure <CODE>net</CODE>, where +beta corresponds to the inverse noise variance. + +<p><h2> +See Also +</h2> +<CODE><a href="mlpprior.htm">mlpprior</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpbkp.htm b/sourcecodes/bnt-master/nethelp3.3/mlpbkp.htm new file mode 100644 index 00000000..00fd6846 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpbkp.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpbkp +</title> +</head> +<body> +<H1> mlpbkp +</H1> +<h2> +Purpose +</h2> +Backpropagate gradient of error function for 2-layer network. + +<p><h2> +Synopsis +</h2> +<PRE> +g = mlpbkp(net, x, z, deltas)</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = mlpbkp(net, x, z, deltas)</CODE> takes a network data structure +<CODE>net</CODE> together with a matrix <CODE>x</CODE> of input vectors, a matrix +<CODE>z</CODE> of hidden unit activations, and a matrix <CODE>deltas</CODE> of the +gradient of the error function with respect to the values of the +output units (i.e. the summed inputs to the output units, before the +activation function is applied). The return value is the gradient +<CODE>g</CODE> of the error function with respect to the network +weights. Each row of <CODE>x</CODE> corresponds to one input vector. + +<p>This function is provided so that the common backpropagation algorithm +can be used by multi-layer perceptron network models to compute +gradients for mixture density networks as well as standard error +functions. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE>, <CODE><a href="mlpderiv.htm">mlpderiv</a></CODE>, <CODE><a href="mdngrad.htm">mdngrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpderiv.htm b/sourcecodes/bnt-master/nethelp3.3/mlpderiv.htm new file mode 100644 index 00000000..514dafc6 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpderiv.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpderiv +</title> +</head> +<body> +<H1> mlpderiv +</H1> +<h2> +Purpose +</h2> +Evaluate derivatives of network outputs with respect to weights. + +<p><h2> +Synopsis +</h2> +<PRE> +g = mlpderiv(net, x)</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = mlpderiv(net, x)</CODE> takes a network data structure <CODE>net</CODE> +and a matrix of input vectors <CODE>x</CODE> and returns a three-index matrix +<CODE>g</CODE> whose <CODE>i</CODE>, <CODE>j</CODE>, <CODE>k</CODE> element contains the +derivative of network output <CODE>k</CODE> with respect to weight or bias +parameter <CODE>j</CODE> for input pattern <CODE>i</CODE>. The ordering of the +weight and bias parameters is defined by <CODE>mlpunpak</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlperr.htm b/sourcecodes/bnt-master/nethelp3.3/mlperr.htm new file mode 100644 index 00000000..33d748da --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlperr.htm @@ -0,0 +1,49 @@ +<html> +<head> +<title> +Netlab Reference Manual mlperr +</title> +</head> +<body> +<H1> mlperr +</H1> +<h2> +Purpose +</h2> +Evaluate error function for 2-layer network. + +<p><h2> +Synopsis +</h2> +<PRE> +e = mlperr(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>e = mlperr(net, x, t)</CODE> takes a network data structure <CODE>net</CODE> together +with a matrix <CODE>x</CODE> of input vectors and a matrix <CODE>t</CODE> of target +vectors, and evaluates the error function <CODE>e</CODE>. The choice of error +function corresponds to the output unit activation function. Each row +of <CODE>x</CODE> corresponds to one input vector and each row of <CODE>t</CODE> +corresponds to one target vector. + +<p><CODE>[e, edata, eprior] = mlperr(net, x, t)</CODE> additionally returns the +data and prior components of the error, assuming a zero mean Gaussian +prior on the weights with inverse variance parameters <CODE>alpha</CODE> and +<CODE>beta</CODE> taken from the network data structure <CODE>net</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpevfwd.htm b/sourcecodes/bnt-master/nethelp3.3/mlpevfwd.htm new file mode 100644 index 00000000..1cf75307 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpevfwd.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpevfwd +</title> +</head> +<body> +<H1> mlpevfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation with evidence for MLP + +<p><h2> +Synopsis +</h2> +<PRE> + +[y, extra] = mlpevfwd(net, x, t, x_test) +[y, extra, invhess] = mlpevfwd(net, x, t, x_test, invhess) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = mlpevfwd(net, x, t, x_test)</CODE> takes a network data structure +<CODE>net</CODE> together with the input <CODE>x</CODE> and target <CODE>t</CODE> training data +and input test data <CODE>x_test</CODE>. +It returns the normal forward propagation through the network <CODE>y</CODE> +together with a matrix <CODE>extra</CODE> which consists of error bars (variance) +for a regression problem or moderated outputs for a classification problem. +The optional argument (and return value) +<CODE>invhess</CODE> is the inverse of the network Hessian +computed on the training data inputs and targets. Passing it in avoids +recomputing it, which can be a significant saving for large training sets. + +<p><h2> +See Also +</h2> +<CODE><a href="fevbayes.htm">fevbayes</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpfwd.htm b/sourcecodes/bnt-master/nethelp3.3/mlpfwd.htm new file mode 100644 index 00000000..2f2be47a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpfwd.htm @@ -0,0 +1,52 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpfwd +</title> +</head> +<body> +<H1> mlpfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through 2-layer network. + +<p><h2> +Synopsis +</h2> +<PRE> +y = mlpfwd(net, x) +[y, z] = mlpfwd(net, x) +[y, z, a] = mlpfwd(net, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = mlpfwd(net, x)</CODE> takes a network data structure <CODE>net</CODE> together with +a matrix <CODE>x</CODE> of input vectors, and forward propagates the inputs +through the network to generate a matrix <CODE>y</CODE> of output +vectors. Each row of <CODE>x</CODE> corresponds to one input vector and each +row of <CODE>y</CODE> corresponds to one output vector. + +<p><CODE>[y, z] = mlpfwd(net, x)</CODE> also generates a matrix <CODE>z</CODE> of the hidden +unit activations where each row corresponds to one pattern. + +<p><CODE>[y, z, a] = mlpfwd(net, x)</CODE> also returns a matrix <CODE>a</CODE> +giving the summed inputs to each output unit, where each row +corresponds to one pattern. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpgrad.htm b/sourcecodes/bnt-master/nethelp3.3/mlpgrad.htm new file mode 100644 index 00000000..08943cc9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpgrad.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpgrad +</title> +</head> +<body> +<H1> mlpgrad +</H1> +<h2> +Purpose +</h2> +Evaluate gradient of error function for 2-layer network. + +<p><h2> +Synopsis +</h2> +<PRE> + +g = mlpgrad(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = mlpgrad(net, x, t)</CODE> takes a network data structure <CODE>net</CODE> +together with a matrix <CODE>x</CODE> of input vectors and a matrix <CODE>t</CODE> +of target vectors, and evaluates the gradient <CODE>g</CODE> of the error +function with respect to the network weights. The error funcion +corresponds to the choice of output unit activation function. Each row +of <CODE>x</CODE> corresponds to one input vector and each row of <CODE>t</CODE> +corresponds to one target vector. + +<p><CODE>[g, gdata, gprior] = mlpgrad(net, x, t)</CODE> also returns separately +the data and prior contributions to the gradient. In the case of +multiple groups in the prior, <CODE>gprior</CODE> is a matrix with a row +for each group and a column for each weight parameter. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlphdotv.htm b/sourcecodes/bnt-master/nethelp3.3/mlphdotv.htm new file mode 100644 index 00000000..7ecf2765 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlphdotv.htm @@ -0,0 +1,45 @@ +<html> +<head> +<title> +Netlab Reference Manual mlphdotv +</title> +</head> +<body> +<H1> mlphdotv +</H1> +<h2> +Purpose +</h2> +Evaluate the product of the data Hessian with a vector. + +<p><h2> +Synopsis +</h2> +<PRE> +hdv = mlphdotv(net, x, t, v)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>hdv = mlphdotv(net, x, t, v)</CODE> takes an MLP network data structure +<CODE>net</CODE>, together with the matrix <CODE>x</CODE> of input vectors, the +matrix <CODE>t</CODE> of target vectors and an arbitrary row vector <CODE>v</CODE> +whose length equals the number of parameters in the network, and +returns the product of the data-dependent contribution to the Hessian +matrix with <CODE>v</CODE>. The implementation is based on the R-propagation +algorithm of Pearlmutter. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlphess.htm">mlphess</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlphess.htm b/sourcecodes/bnt-master/nethelp3.3/mlphess.htm new file mode 100644 index 00000000..59a6ec91 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlphess.htm @@ -0,0 +1,73 @@ +<html> +<head> +<title> +Netlab Reference Manual mlphess +</title> +</head> +<body> +<H1> mlphess +</H1> +<h2> +Purpose +</h2> +Evaluate the Hessian matrix for a multi-layer perceptron network. + +<p><h2> +Synopsis +</h2> +<PRE> +h = mlphess(net, x, t) +[h, hdata] = mlphess(net, x, t) +h = mlphess(net, x, t, hdata) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>h = mlphess(net, x, t)</CODE> takes an MLP network data structure <CODE>net</CODE>, +a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of target +values and returns the full Hessian matrix <CODE>h</CODE> corresponding to +the second derivatives of the negative log posterior distribution, +evaluated for the current weight and bias values as defined by +<CODE>net</CODE>. + +<p><CODE>[h, hdata] = mlphess(net, x, t)</CODE> returns both the Hessian matrix +<CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependent +term in the Hessian. + +<p><CODE>h = mlphess(net, x, t, hdata)</CODE> takes a network data structure +<CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of +target values, together with the contribution <CODE>hdata</CODE> arising from +the data dependent term in the Hessian, and returns the full Hessian +matrix <CODE>h</CODE> corresponding to the second derivatives of the negative +log posterior distribution. This version saves computation time if +<CODE>hdata</CODE> has already been evaluated for the current weight and bias +values. + +<p><h2> +Example +</h2> +For the standard regression framework with a Gaussian conditional +distribution of target values given input values, and a simple +Gaussian prior over weights, the Hessian takes the form +<PRE> + + h = beta*hd + alpha*I +</PRE> + +where the contribution <CODE>hd</CODE> is evaluated by calls to <CODE>mlphdotv</CODE> and +<CODE>h</CODE> is the full Hessian. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE>, <CODE><a href="mlphdotv.htm">mlphdotv</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlphint.htm b/sourcecodes/bnt-master/nethelp3.3/mlphint.htm new file mode 100644 index 00000000..82411403 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlphint.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual mlphint +</title> +</head> +<body> +<H1> mlphint +</H1> +<h2> +Purpose +</h2> +Plot Hinton diagram for 2-layer feed-forward network. + +<p><h2> +Synopsis +</h2> +<PRE> +mlphint(net) +[h1, h2] = mlphint(net)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>mlphint(net)</CODE> takes a network structure <CODE>net</CODE> +and plots the Hinton diagram comprised of two +figure windows, one displaying the first-layer weights and biases, and +one displaying the second-layer weights and biases. + +<p><CODE>[h1, h2] = mlphint(net)</CODE> also returns handles <CODE>h1</CODE> and +<CODE>h2</CODE> to the figures which can be used, for instance, to delete the +figures when they are no longer needed. + +<p>To print the figure correctly, you should call +<CODE>set(h, 'InvertHardCopy', 'on')</CODE> before printing. + +<p><h2> +See Also +</h2> +<CODE><a href="demhint.htm">demhint</a></CODE>, <CODE><a href="hintmat.htm">hintmat</a></CODE>, <CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpinit.htm b/sourcecodes/bnt-master/nethelp3.3/mlpinit.htm new file mode 100644 index 00000000..2f7dbd4e --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpinit.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpinit +</title> +</head> +<body> +<H1> mlpinit +</H1> +<h2> +Purpose +</h2> +Initialise the weights in a 2-layer feedforward network. + +<p><h2> +Synopsis +</h2> +<PRE> +net = mlpinit(net, prior) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = mlpinit(net, prior)</CODE> takes a 2-layer feedforward network +<CODE>net</CODE> and sets the weights and biases by sampling from a Gaussian +distribution. If <CODE>prior</CODE> is a scalar, then all of the parameters +(weights and biases) are sampled from a single isotropic Gaussian with +inverse variance equal to <CODE>prior</CODE>. If <CODE>prior</CODE> is a data +structure of the kind generated by <CODE>mlpprior</CODE>, then the parameters +are sampled from multiple Gaussians according to their groupings +(defined by the <CODE>index</CODE> field) with corresponding variances +(defined by the <CODE>alpha</CODE> field). + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlpprior.htm">mlpprior</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlppak.htm b/sourcecodes/bnt-master/nethelp3.3/mlppak.htm new file mode 100644 index 00000000..aa038f46 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlppak.htm @@ -0,0 +1,55 @@ +<html> +<head> +<title> +Netlab Reference Manual mlppak +</title> +</head> +<body> +<H1> mlppak +</H1> +<h2> +Purpose +</h2> +Combines weights and biases into one weights vector. + +<p><h2> +Synopsis +</h2> +<PRE> +w = mlppak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>w = mlppak(net)</CODE> takes a network data structure <CODE>net</CODE> and +combines the component weight matrices bias vectors into a single row +vector <CODE>w</CODE>. The facility to switch between these two +representations for the network parameters is useful, for example, in +training a network by error function minimization, since a single +vector of parameters can be handled by general-purpose optimization +routines. + +<p>The ordering of the paramters in <CODE>w</CODE> is defined by +<PRE> + + w = [net.w1(:)', net.b1, net.w2(:)', net.b2]; +</PRE> + +where <CODE>w1</CODE> is the first-layer weight matrix, <CODE>b1</CODE> is the +first-layer bias vector, <CODE>w2</CODE> is the second-layer weight matrix, +and <CODE>b2</CODE> is the second-layer bias vector. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlpunpak.htm">mlpunpak</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpprior.htm b/sourcecodes/bnt-master/nethelp3.3/mlpprior.htm new file mode 100644 index 00000000..1821e919 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpprior.htm @@ -0,0 +1,58 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpprior +</title> +</head> +<body> +<H1> mlpprior +</H1> +<h2> +Purpose +</h2> +Create Gaussian prior for mlp. + +<p><h2> +Synopsis +</h2> +<PRE> +prior = mlpprior(nin, nhidden, nout, aw1, ab1, aw2, ab2)</PRE> + + +<p><h2> +Description +</h2> +<CODE>prior = mlpprior(nin, nhidden, nout, aw1, ab1, aw2, ab2)</CODE> +generates a data structure +<CODE>prior</CODE>, with fields <CODE>prior.alpha</CODE> and <CODE>prior.index</CODE>, which +specifies a Gaussian prior distribution for the network weights in a +two-layer feedforward network. Two different cases are possible. In +the first case, <CODE>aw1</CODE>, <CODE>ab1</CODE>, <CODE>aw2</CODE> and <CODE>ab2</CODE> are all +scalars and represent the regularization coefficients for four groups +of parameters in the network corresponding to first-layer weights, +first-layer biases, second-layer weights, and second-layer biases +respectively. Then <CODE>prior.alpha</CODE> represents a column vector of +length 4 containing the parameters, and <CODE>prior.index</CODE> is a matrix +specifying which weights belong in each group. Each column has one +element for each weight in the matrix, using the standard ordering as +defined in <CODE>mlppak</CODE>, and each element is 1 or 0 according to +whether the weight is a member of the corresponding group or not. In +the second case the parameter <CODE>aw1</CODE> is a vector of length equal to +the number of inputs in the network, and the corresponding matrix +<CODE>prior.index</CODE> now partitions the first-layer weights into groups +corresponding to the weights fanning out of each input unit. This +prior is appropriate for the technique of automatic relevance +determination. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlptrain.htm b/sourcecodes/bnt-master/nethelp3.3/mlptrain.htm new file mode 100644 index 00000000..ad89786b --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlptrain.htm @@ -0,0 +1,35 @@ +<html> +<head> +<title> +Netlab Reference Manual mlptrain +</title> +</head> +<body> +<H1> mlptrain +</H1> +<h2> +Purpose +</h2> +Utility to train an MLP network for demtrain + +<p><h2> +Description +</h2> + +<p><CODE>[net, error] = mlptrain(net, x, t, its)</CODE> trains a network data +structure <CODE>net</CODE> using the scaled conjugate gradient algorithm +for <CODE>its</CODE> cycles with +input data <CODE>x</CODE>, target data <CODE>t</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="demtrain.htm">demtrain</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE>, <CODE><a href="netopt.htm">netopt</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/mlpunpak.htm b/sourcecodes/bnt-master/nethelp3.3/mlpunpak.htm new file mode 100644 index 00000000..3c6bba21 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/mlpunpak.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual mlpunpak +</title> +</head> +<body> +<H1> mlpunpak +</H1> +<h2> +Purpose +</h2> +Separates weights vector into weight and bias matrices. + +<p><h2> +Synopsis +</h2> +<PRE> +net = mlpunpak(net, w) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = mlpunpak(net, w)</CODE> takes an mlp network data structure <CODE>net</CODE> and +a weight vector <CODE>w</CODE>, and returns a network data structure identical to +the input network, except that the first-layer weight matrix +<CODE>w1</CODE>, the first-layer bias vector <CODE>b1</CODE>, the second-layer +weight matrix <CODE>w2</CODE> and the second-layer bias vector <CODE>b2</CODE> have all +been set to the corresponding elements of <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="mlppak.htm">mlppak</a></CODE>, <CODE><a href="mlpfwd.htm">mlpfwd</a></CODE>, <CODE><a href="mlperr.htm">mlperr</a></CODE>, <CODE><a href="mlpbkp.htm">mlpbkp</a></CODE>, <CODE><a href="mlpgrad.htm">mlpgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netderiv.htm b/sourcecodes/bnt-master/nethelp3.3/netderiv.htm new file mode 100644 index 00000000..3275eced --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netderiv.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual netderiv +</title> +</head> +<body> +<H1> netderiv +</H1> +<h2> +Purpose +</h2> +Evaluate derivatives of network outputs by weights generically. + +<p><h2> +Synopsis +</h2> +<PRE> +g = netderiv(w, net, x)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>g = netderiv(w, net, x)</CODE> takes a weight vector <CODE>w</CODE> and a network +data structure <CODE>net</CODE>, together with the matrix <CODE>x</CODE> of input +vectors, and returns the +gradient of the outputs with respect to the weights evaluated at <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="netevfwd.htm">netevfwd</a></CODE>, <CODE><a href="netopt.htm">netopt</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/neterr.htm b/sourcecodes/bnt-master/nethelp3.3/neterr.htm new file mode 100644 index 00000000..2ec53e61 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/neterr.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual neterr +</title> +</head> +<body> +<H1> neterr +</H1> +<h2> +Purpose +</h2> +Evaluate network error function for generic optimizers + +<p><h2> +Synopsis +</h2> +<PRE> +e = neterr(w, net, x, t) +[e, varargout] = neterr(w, net, x, t) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>e = neterr(w, net, x, t)</CODE> takes a weight vector <CODE>w</CODE> and a network +data structure <CODE>net</CODE>, together with the matrix <CODE>x</CODE> of input +vectors and the matrix <CODE>t</CODE> of target vectors, and returns the +value of the error function evaluated at <CODE>w</CODE>. + +<p><CODE>[e, varargout] = neterr(w, net, x, t)</CODE> also returns any additional +return values from the error function. + +<p><h2> +See Also +</h2> +<CODE><a href="netgrad.htm">netgrad</a></CODE>, <CODE><a href="nethess.htm">nethess</a></CODE>, <CODE><a href="netopt.htm">netopt</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netevfwd.htm b/sourcecodes/bnt-master/nethelp3.3/netevfwd.htm new file mode 100644 index 00000000..ea876bb2 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netevfwd.htm @@ -0,0 +1,52 @@ +<html> +<head> +<title> +Netlab Reference Manual netevfwd +</title> +</head> +<body> +<H1> netevfwd +</H1> +<h2> +Purpose +</h2> +Generic forward propagation with evidence for network + +<p><h2> +Synopsis +</h2> +<PRE> + +[y, extra] = netevfwd(w, net, x, t, x_test) +[y, extra, invhess] = netevfwd(w, net, x, t, x_test, invhess) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>[y, extra] = netevfwd(w, net, x, t, x_test)</CODE> takes a network data +structure +<CODE>net</CODE> together with the input <CODE>x</CODE> and target <CODE>t</CODE> training data +and input test data <CODE>x_test</CODE>. +It returns the normal forward propagation through the network <CODE>y</CODE> +together with a matrix <CODE>extra</CODE> which consists of error bars (variance) +for a regression problem or moderated outputs for a classification problem. + +<p>The optional argument (and return value) +<CODE>invhess</CODE> is the inverse of the network Hessian +computed on the training data inputs and targets. Passing it in avoids +recomputing it, which can be a significant saving for large training sets. + +<p><h2> +See Also +</h2> +<CODE><a href="mlpevfwd.htm">mlpevfwd</a></CODE>, <CODE><a href="rbfevfwd.htm">rbfevfwd</a></CODE>, <CODE><a href="glmevfwd.htm">glmevfwd</a></CODE>, <CODE><a href="fevbayes.htm">fevbayes</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netgrad.htm b/sourcecodes/bnt-master/nethelp3.3/netgrad.htm new file mode 100644 index 00000000..a9ce1571 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netgrad.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual netgrad +</title> +</head> +<body> +<H1> netgrad +</H1> +<h2> +Purpose +</h2> +Evaluate network error gradient for generic optimizers + +<p><h2> +Synopsis +</h2> +<PRE> +g = netgrad(w, net, x, t)</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>g = netgrad(w, net, x, t)</CODE> takes a weight vector <CODE>w</CODE> and a network +data structure <CODE>net</CODE>, together with the matrix <CODE>x</CODE> of input +vectors and the matrix <CODE>t</CODE> of target vectors, and returns the +gradient of the error function evaluated at <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="mlp.htm">mlp</a></CODE>, <CODE><a href="neterr.htm">neterr</a></CODE>, <CODE><a href="netopt.htm">netopt</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/nethelp3.3.zip b/sourcecodes/bnt-master/nethelp3.3/nethelp3.3.zip new file mode 100644 index 00000000..5c316a1d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/nethelp3.3.zip Binary files differdiff --git a/sourcecodes/bnt-master/nethelp3.3/nethess.htm b/sourcecodes/bnt-master/nethelp3.3/nethess.htm new file mode 100644 index 00000000..b918fe0a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/nethess.htm @@ -0,0 +1,66 @@ +<html> +<head> +<title> +Netlab Reference Manual nethess +</title> +</head> +<body> +<H1> nethess +</H1> +<h2> +Purpose +</h2> +Evaluate network Hessian + +<p><h2> +Synopsis +</h2> +<PRE> +h = neterr(w, net, x, t) +[h, varargout] = neterr(w, net, x, t, varargin) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>h = nethess(w, net, x, t)</CODE> takes a weight vector <CODE>w</CODE> and a network +data structure <CODE>net</CODE>, together with the matrix <CODE>x</CODE> of input +vectors and the matrix <CODE>t</CODE> of target vectors, and returns the +value of the Hessian evaluated at <CODE>w</CODE>. + +<p><CODE>[e, varargout] = nethess(w, net, x, t, varargin)</CODE> also returns any additional +return values from the network Hessian function, and passes additional arguments +to that function. + +<p><h2> +Example +</h2> + +<p>In <CODE>evidence</CODE>, this function is called once to compute the +data contribution to the Hessian +<PRE> + +[h, dh] = nethess(w, net, x, t, dh); +</PRE> + +and again to update the Hessian for new values of the hyper-parameters +<PRE> + +h = nethess(w, net, x, t, dh); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="neterr.htm">neterr</a></CODE>, <CODE><a href="netgrad.htm">netgrad</a></CODE>, <CODE><a href="netopt.htm">netopt</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netinit.htm b/sourcecodes/bnt-master/nethelp3.3/netinit.htm new file mode 100644 index 00000000..3612b574 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netinit.htm @@ -0,0 +1,48 @@ +<html> +<head> +<title> +Netlab Reference Manual netinit +</title> +</head> +<body> +<H1> netinit +</H1> +<h2> +Purpose +</h2> +Initialise the weights in a network. + +<p><h2> +Synopsis +</h2> +<PRE> +net = netinit(net, prior) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>net = netinit(net, prior)</CODE> takes a network data structure +<CODE>net</CODE> and sets the weights and biases by sampling from a Gaussian +distribution. If <CODE>prior</CODE> is a scalar, then all of the parameters +(weights and biases) are sampled from a single isotropic Gaussian with +inverse variance equal to <CODE>prior</CODE>. If <CODE>prior</CODE> is a data +structure of the kind generated by <CODE>mlpprior</CODE>, then the parameters +are sampled from multiple Gaussians according to their groupings +(defined by the <CODE>index</CODE> field) with corresponding variances +(defined by the <CODE>alpha</CODE> field). + +<p><h2> +See Also +</h2> +<CODE><a href="mlpprior.htm">mlpprior</a></CODE>, <CODE><a href="netunpak.htm">netunpak</a></CODE>, <CODE><a href="rbfprior.htm">rbfprior</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netopt.htm b/sourcecodes/bnt-master/nethelp3.3/netopt.htm new file mode 100644 index 00000000..369c959c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netopt.htm @@ -0,0 +1,75 @@ +<html> +<head> +<title> +Netlab Reference Manual netopt +</title> +</head> +<body> +<H1> netopt +</H1> +<h2> +Purpose +</h2> +Optimize the weights in a network model. + +<p><h2> +Synopsis +</h2> +<PRE> +[net, options] = netopt(net, options, x, t, alg) +[net, options, varargout] = netopt(net, options, x, t, alg) +</PRE> + + +<p><h2> +Description +</h2> + +<p><CODE>netopt</CODE> is a helper function which facilitates the training of +networks using the general purpose optimizers as well as sampling from the +posterior distribution of parameters using general purpose Markov chain +Monte Carlo sampling algorithms. It can be used with any function that +searches in parameter space using error and gradient functions. + +<p><CODE>[net, options] = netopt(net, options, x, t, alg)</CODE> takes a network +data structure <CODE>net</CODE>, together with a vector <CODE>options</CODE> of +parameters governing the behaviour of the optimization algorithm, a +matrix <CODE>x</CODE> of input vectors and a matrix <CODE>t</CODE> of target +vectors, and returns the trained network as well as an updated +<CODE>options</CODE> vector. The string <CODE>alg</CODE> determines which optimization +algorithm (<CODE>conjgrad</CODE>, <CODE>quasinew</CODE>, <CODE>scg</CODE>, etc.) or Monte +Carlo algorithm (such as <CODE>hmc</CODE>) will be used. + +<p><CODE>[net, options, varargout] = netopt(net, options, x, t, alg)</CODE> +also returns any additional return values from the optimisation algorithm. + +<p><h2> +Examples +</h2> +Suppose we create a 4-input, 3 hidden unit, 2-output feed-forward +network using <CODE>net = mlp(4, 3, 2, 'linear')</CODE>. We can then train +the network with the scaled conjugate gradient algorithm by using +<CODE>net = netopt(net, options, x, t, 'scg')</CODE> where <CODE>x</CODE> and +<CODE>t</CODE> are the input and target data matrices respectively, and the +options vector is set appropriately for <CODE>scg</CODE>. + +<p>If we also wish to plot the learning curve, we can use the additional +return value <CODE>errlog</CODE> given by <CODE>scg</CODE>: +<PRE> + +[net, options, errlog] = netopt(net, options, x, t, 'scg'); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="netgrad.htm">netgrad</a></CODE>, <CODE><a href="bfgs.htm">bfgs</a></CODE>, <CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="hmc.htm">hmc</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netpak.htm b/sourcecodes/bnt-master/nethelp3.3/netpak.htm new file mode 100644 index 00000000..29286b7d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netpak.htm @@ -0,0 +1,47 @@ +<html> +<head> +<title> +Netlab Reference Manual netpak +</title> +</head> +<body> +<H1> netpak +</H1> +<h2> +Purpose +</h2> +Combines weights and biases into one weights vector. + +<p><h2> +Synopsis +</h2> +<PRE> +w = netpak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>w = netpak(net)</CODE> takes a network data structure <CODE>net</CODE> and +combines the component weight matrices into a single row +vector <CODE>w</CODE>. The facility to switch between these two +representations for the network parameters is useful, for example, in +training a network by error function minimization, since a single +vector of parameters can be handled by general-purpose optimization +routines. This function also takes into account a <CODE>mask</CODE> defined +as a field in <CODE>net</CODE> by removing any weights that correspond to +entries of 0 in the mask. + +<p><h2> +See Also +</h2> +<CODE><a href="net.htm">net</a></CODE>, <CODE><a href="netunpak.htm">netunpak</a></CODE>, <CODE><a href="netfwd.htm">netfwd</a></CODE>, <CODE><a href="neterr.htm">neterr</a></CODE>, <CODE><a href="netgrad.htm">netgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/netunpak.htm b/sourcecodes/bnt-master/nethelp3.3/netunpak.htm new file mode 100644 index 00000000..fef34ed7 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/netunpak.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual netunpak +</title> +</head> +<body> +<H1> netunpak +</H1> +<h2> +Purpose +</h2> +Separates weights vector into weight and bias matrices. + +<p><h2> +Synopsis +</h2> +<PRE> +net = netunpak(net, w) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = netunpak(net, w)</CODE> takes an net network data structure <CODE>net</CODE> and +a weight vector <CODE>w</CODE>, and returns a network data structure identical to +the input network, except that the componenet weight matrices have all +been set to the corresponding elements of <CODE>w</CODE>. If there is +a <CODE>mask</CODE> field in the <CODE>net</CODE> data structure, then the weights in +<CODE>w</CODE> are placed in locations corresponding to non-zero entries in the +mask (so <CODE>w</CODE> should have the same length as the number of non-zero +entries in the <CODE>mask</CODE>). + +<p><h2> +See Also +</h2> +<CODE><a href="netpak.htm">netpak</a></CODE>, <CODE><a href="netfwd.htm">netfwd</a></CODE>, <CODE><a href="neterr.htm">neterr</a></CODE>, <CODE><a href="netgrad.htm">netgrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/olgd.htm b/sourcecodes/bnt-master/nethelp3.3/olgd.htm new file mode 100644 index 00000000..15417b70 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/olgd.htm @@ -0,0 +1,101 @@ +<html> +<head> +<title> +Netlab Reference Manual olgd +</title> +</head> +<body> +<H1> olgd +</H1> +<h2> +Purpose +</h2> +On-line gradient descent optimization. + +<p><h2> +Description +</h2> +<CODE>[net, options, errlog, pointlog] = olgd(net, options, x, t)</CODE> uses +on-line gradient descent to find a local minimum of the error function for the +network +<CODE>net</CODE> computed on the input data <CODE>x</CODE> and target values +<CODE>t</CODE>. A log of the error values +after each cycle is (optionally) returned in <CODE>errlog</CODE>, and a log +of the points visited is (optionally) returned in <CODE>pointlog</CODE>. +Because the gradient is computed on-line (i.e. after each pattern) +this can be quite inefficient in Matlab. + +<p>The error function value at final weight vector is returned +in <CODE>options(8)</CODE>. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>, and the points visited +in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is the precision required for the value +of <CODE>x</CODE> at the solution. If the absolute difference between +the values of <CODE>x</CODE> between two successive steps is less than +<CODE>options(2)</CODE>, then this condition is satisfied. + +<p><CODE>options(3)</CODE> is the precision required of the objective +function at the solution. If the absolute difference between the +error functions between two successive steps is less than +<CODE>options(3)</CODE>, then this condition is satisfied. +Both this and the previous condition must be +satisfied for termination. Note that testing the function value at each +iteration roughly halves the speed of the algorithm. + +<p><CODE>options(5)</CODE> determines whether the patterns are sampled randomly +with replacement. If it is 0 (the default), then patterns are sampled +in order. + +<p><CODE>options(6)</CODE> determines if the learning rate decays. If it is 1 +then the learning rate decays at a rate of <CODE>1/t</CODE>. If it is 0 +(the default) then the learning rate is constant. + +<p><CODE>options(9)</CODE> should be set to 1 to check the user defined gradient +function. + +<p><CODE>options(10)</CODE> returns the total number of function evaluations (including +those in any line searches). + +<p><CODE>options(11)</CODE> returns the total number of gradient evaluations. + +<p><CODE>options(14)</CODE> is the maximum number of iterations (passes through +the complete pattern set); default 100. + +<p><CODE>options(17)</CODE> is the momentum; default 0.5. + +<p><CODE>options(18)</CODE> is the learning rate; default 0.01. + +<p><h2> +Examples +</h2> +The following example performs on-line gradient descent on an MLP with +random sampling from the pattern set. +<PRE> + +net = mlp(5, 3, 1, 'linear'); +options = foptions; +options(18) = 0.01; +options(5) = 1; +net = olgd(net, options, x, t); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="graddesc.htm">graddesc</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/pca.htm b/sourcecodes/bnt-master/nethelp3.3/pca.htm new file mode 100644 index 00000000..84fe3e38 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/pca.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual pca +</title> +</head> +<body> +<H1> pca +</H1> +<h2> +Purpose +</h2> +Principal Components Analysis + +<p><h2> +Synopsis +</h2> +<PRE> +PCcoeff = pca(data) +PCcoeff = pca(data, N) +[PCcoeff, PCvec] = pca(data) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>PCcoeff = pca(data)</CODE> computes the eigenvalues of the covariance +matrix of the dataset <CODE>data</CODE> and returns them as <CODE>PCcoeff</CODE>. These +coefficients give the variance of <CODE>data</CODE> along the corresponding +principal components. + +<p><CODE>PCcoeff = pca(data, N)</CODE> returns the largest <CODE>N</CODE> eigenvalues. + +<p><CODE>[PCcoeff, PCvec] = pca(data)</CODE> returns the principal components as +well as the coefficients. This is considerably more computationally +demanding than just computing the eigenvalues. + +<p><h2> +See Also +</h2> +<CODE><a href="eigdec.htm">eigdec</a></CODE>, <CODE><a href="gtminit.htm">gtminit</a></CODE>, <CODE><a href="ppca.htm">ppca</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/plotmat.htm b/sourcecodes/bnt-master/nethelp3.3/plotmat.htm new file mode 100644 index 00000000..a9a38cc9 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/plotmat.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual plotmat +</title> +</head> +<body> +<H1> plotmat +</H1> +<h2> +Purpose +</h2> +Display a matrix. + +<p><h2> +Synopsis +</h2> +<PRE> +plotmat(matrix, textcolour, gridcolour, fontsize)</PRE> + + +<p><h2> +Description +</h2> +<CODE>plotmat(matrix, textcolour, gridcolour, fontsize)</CODE> displays the matrix +<CODE>matrix</CODE> on the current figure. The <CODE>textcolour</CODE> and <CODE>gridcolour</CODE> +arguments control the colours of the numbers and grid labels respectively and +should follow the usual Matlab specification. +The parameter <CODE>fontsize</CODE> should be an integer. + +<p><h2> +See Also +</h2> +<CODE><a href="conffig.htm">conffig</a></CODE>, <CODE><a href="demmlp2.htm">demmlp2</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/ppca.htm b/sourcecodes/bnt-master/nethelp3.3/ppca.htm new file mode 100644 index 00000000..b55a61c4 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/ppca.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual ppca +</title> +</head> +<body> +<H1> ppca +</H1> +<h2> +Purpose +</h2> +Probabilistic Principal Components Analysis + +<p><h2> +Synopsis +</h2> +<PRE> +[var, U, lambda] = pca(x, ppca_dim) +</PRE> + + +<p><h2> +Description +</h2> + +<CODE>[var, U, lambda] = ppca(x, ppca_dim)</CODE> computes the principal component +subspace <CODE>U</CODE> of dimension <CODE>ppca_dim</CODE> using a centred +covariance matrix <CODE>x</CODE>. The variable <CODE>var</CODE> contains +the off-subspace variance (which is assumed to be spherical), while the +vector <CODE>lambda</CODE> contains the variances of each of the principal +components. This is computed using the eigenvalue and eigenvector +decomposition of <CODE>x</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="eigdec.htm">eigdec</a></CODE>, <CODE><a href="pca.htm">pca</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/quasinew.htm b/sourcecodes/bnt-master/nethelp3.3/quasinew.htm new file mode 100644 index 00000000..528ecb1d --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/quasinew.htm @@ -0,0 +1,99 @@ +<html> +<head> +<title> +Netlab Reference Manual quasinew +</title> +</head> +<body> +<H1> quasinew +</H1> +<h2> +Purpose +</h2> +Quasi-Newton optimization. + +<p><h2> +Description +</h2> +<CODE>[x, options, flog, pointlog] = quasinew(f, x, options, gradf)</CODE> +uses a quasi-Newton +algorithm to find a local minimum of the function <CODE>f(x)</CODE> whose +gradient is given by <CODE>gradf(x)</CODE>. Here <CODE>x</CODE> is a row vector +and <CODE>f</CODE> returns a scalar value. +The point at which <CODE>f</CODE> has a local minimum +is returned as <CODE>x</CODE>. The function value at that point is returned +in <CODE>options(8)</CODE>. A log of the function values +after each cycle is (optionally) returned in <CODE>flog</CODE>, and a log +of the points visited is (optionally) returned in <CODE>pointlog</CODE>. + +<p><CODE>quasinew(f, x, options, gradf, p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>, and the points visited +in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value +of <CODE>x</CODE> at the solution. If the absolute difference between +the values of <CODE>x</CODE> between two successive steps is less than +<CODE>options(2)</CODE>, then this condition is satisfied. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. If the absolute difference between the +objective function values between two successive steps is less than +<CODE>options(3)</CODE>, then this condition is satisfied. +Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(9)</CODE> should be set to 1 to check the user defined gradient +function. + +<p><CODE>options(10)</CODE> returns the total number of function evaluations (including +those in any line searches). + +<p><CODE>options(11)</CODE> returns the total number of gradient evaluations. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p><CODE>options(15)</CODE> is the precision in parameter space of the line search; +default <CODE>1e-2</CODE>. + +<p><h2> +Examples +</h2> +An example of +the use of the additional arguments is the minimization of an error +function for a neural network: +<PRE> + +w = quasinew('neterr', w, options, 'netgrad', net, x, t); +</PRE> + + +<p><h2> +Algorithm +</h2> + +The quasi-Newton algorithm builds up an +approximation to the inverse Hessian over a number of steps. The +method requires order W squared storage, where W is the number of function +parameters. The Broyden-Fletcher-Goldfarb-Shanno formula for the +inverse Hessian updates is used. The line searches are carried out to +a relatively low precision (1.0e-2). + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbf.htm b/sourcecodes/bnt-master/nethelp3.3/rbf.htm new file mode 100644 index 00000000..97a7f925 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbf.htm @@ -0,0 +1,114 @@ +<html> +<head> +<title> +Netlab Reference Manual rbf +</title> +</head> +<body> +<H1> rbf +</H1> +<h2> +Purpose +</h2> +Creates an RBF network with specified architecture + +<p><h2> +Synopsis +</h2> +<PRE> + +net = rbf(nin, nhidden, nout, rbfunc) +net = rbf(nin, nhidden, nout, rbfunc, outfunc) +net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = rbf(nin, nhidden, nout, rbfunc)</CODE> constructs and initialises +a radial basis function network returning a data structure <CODE>net</CODE>. +The weights are all initialised with a zero mean, unit variance normal +distribution, with the exception of the variances, which are set to one. +This makes use of the Matlab function +<CODE>randn</CODE> and so the seed for the random weight initialization can be +set using <CODE>randn('state', s)</CODE> where <CODE>s</CODE> is the seed value. The +activation functions are defined in terms of the distance between +the data point and the corresponding centre. Note that the functions are +computed to a convenient constant multiple: for example, the Gaussian +is not normalised. (Normalisation is not needed as the function outputs +are linearly combined in the next layer.) + +<p>The fields in <CODE>net</CODE> are +<PRE> + + type = 'rbf' + nin = number of inputs + nhidden = number of hidden units + nout = number of outputs + nwts = total number of weights and biases + actfn = string defining hidden unit activation function: + 'gaussian' for a radially symmetric Gaussian function. + 'tps' for r^2 log r, the thin plate spline function. + 'r4logr' for r^4 log r. + outfn = string defining output error function: + 'linear' for linear outputs (default) and SoS error. + 'neuroscale' for Sammon stress measure. + c = centres + wi = squared widths (null for rlogr and tps) + w2 = second layer weight matrix + b2 = second layer bias vector +</PRE> + + +<p><CODE>net = rbf(nin, nhidden, nout, rbfund, outfunc)</CODE> allows the user to +specify the type of error function to be used. The field <CODE>outfn</CODE> +is set to the value of this string. Linear outputs (for regression problems) +and Neuroscale outputs (for topographic mappings) are supported. + +<p><CODE>net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)</CODE>, +in which <CODE>prior</CODE> is +a scalar, allows the field <CODE>net.alpha</CODE> in the data structure +<CODE>net</CODE> to be set, corresponding to a zero-mean isotropic Gaussian +prior with inverse variance with value <CODE>prior</CODE>. Alternatively, +<CODE>prior</CODE> can consist of a data structure with fields <CODE>alpha</CODE> +and <CODE>index</CODE>, allowing individual Gaussian priors to be set over +groups of weights in the network. Here <CODE>alpha</CODE> is a column vector +in which each element corresponds to a separate group of weights, +which need not be mutually exclusive. The membership of the groups is +defined by the matrix <CODE>indx</CODE> in which the columns correspond to +the elements of <CODE>alpha</CODE>. Each column has one element for each +weight in the matrix, in the order defined by the function +<CODE>rbfpak</CODE>, and each element is 1 or 0 according to whether the +weight is a member of the corresponding group or not. A utility +function <CODE>rbfprior</CODE> is provided to help in setting up the +<CODE>prior</CODE> data structure. + +<p><CODE>net = rbf(nin, nhidden, nout, func, prior, beta)</CODE> also sets the +additional field <CODE>net.beta</CODE> in the data structure <CODE>net</CODE>, where +beta corresponds to the inverse noise variance. + +<p><h2> +Example +</h2> +The following code constructs an RBF network with 1 input and output node +and 5 hidden nodes and then propagates some data <CODE>x</CODE> through it. +<PRE> + +net = rbf(1, 5, 1, 'tps'); +[y, act] = rbffwd(net, x); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="rbferr.htm">rbferr</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfunpak.htm">rbfunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfbkp.htm b/sourcecodes/bnt-master/nethelp3.3/rbfbkp.htm new file mode 100644 index 00000000..cf3a9d52 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfbkp.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfbkp +</title> +</head> +<body> +<H1> rbfbkp +</H1> +<h2> +Purpose +</h2> +Backpropagate gradient of error function for RBF network. + +<p><h2> +Synopsis +</h2> +<PRE> +g = rbfbkp(net, x, z, n2, deltas)</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = rbfbkp(net, x, z, n2, deltas)</CODE> takes a network data structure +<CODE>net</CODE> together with a matrix <CODE>x</CODE> of input vectors, a matrix +<CODE>z</CODE> of hidden unit activations, a matrix <CODE>n2</CODE> of the squared +distances between centres and inputs, and a matrix <CODE>deltas</CODE> of the +gradient of the error function with respect to the values of the +output units (i.e. the summed inputs to the output units, before the +activation function is applied). The return value is the gradient +<CODE>g</CODE> of the error function with respect to the network +weights. Each row of <CODE>x</CODE> corresponds to one input vector. + +<p>This function is provided so that the common backpropagation algorithm +can be used by RBF network models to compute +gradients for the output values (in <CODE>rbfderiv</CODE>) as well as standard error +functions. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfderiv.htm">rbfderiv</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfderiv.htm b/sourcecodes/bnt-master/nethelp3.3/rbfderiv.htm new file mode 100644 index 00000000..f9c0438a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfderiv.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfderiv +</title> +</head> +<body> +<H1> rbfderiv +</H1> +<h2> +Purpose +</h2> +Evaluate derivatives of RBF network outputs with respect to weights. + +<p><h2> +Synopsis +</h2> +<PRE> +g = rbfderiv(net, x)</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = rbfderiv(net, x)</CODE> takes a network data structure <CODE>net</CODE> +and a matrix of input vectors <CODE>x</CODE> and returns a three-index matrix +<CODE>g</CODE> whose <CODE>i</CODE>, <CODE>j</CODE>, <CODE>k</CODE> element contains the +derivative of network output <CODE>k</CODE> with respect to weight or bias +parameter <CODE>j</CODE> for input pattern <CODE>i</CODE>. The ordering of the +weight and bias parameters is defined by <CODE>rbfunpak</CODE>. This +function also takes into account any mask in the network data structure. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfbkp.htm">rbfbkp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbferr.htm b/sourcecodes/bnt-master/nethelp3.3/rbferr.htm new file mode 100644 index 00000000..5a97de46 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbferr.htm @@ -0,0 +1,50 @@ +<html> +<head> +<title> +Netlab Reference Manual rbferr +</title> +</head> +<body> +<H1> rbferr +</H1> +<h2> +Purpose +</h2> +Evaluate error function for RBF network. + +<p><h2> +Synopsis +</h2> +<PRE> +e = rbferr(net, x, t) +[e, edata, eprior] = rbferr(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>e = rbferr(net, x, t)</CODE> takes a network data structure <CODE>net</CODE> together +with a matrix <CODE>x</CODE> of input +vectors and a matrix <CODE>t</CODE> of target vectors, and evaluates the +appropriate error function <CODE>e</CODE> depending on <CODE>net.outfn</CODE>. +Each row of <CODE>x</CODE> corresponds to one +input vector and each row of <CODE>t</CODE> contains the corresponding target vector. + +<p><CODE>[e, edata, eprior] = rbferr(net, x, t)</CODE> additionally returns the +data and prior components of the error, assuming a zero mean Gaussian +prior on the weights with inverse variance parameters <CODE>alpha</CODE> and +<CODE>beta</CODE> taken from the network data structure <CODE>net</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfunpak.htm">rbfunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfevfwd.htm b/sourcecodes/bnt-master/nethelp3.3/rbfevfwd.htm new file mode 100644 index 00000000..21513c59 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfevfwd.htm @@ -0,0 +1,51 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfevfwd +</title> +</head> +<body> +<H1> rbfevfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation with evidence for RBF + +<p><h2> +Synopsis +</h2> +<PRE> + +[y, extra] = rbfevfwd(net, x, t, x_test) +[y, extra, invhess] = rbfevfwd(net, x, t, x_test, invhess) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = rbfevfwd(net, x, t, x_test)</CODE> takes a network data structure +<CODE>net</CODE> together with the input <CODE>x</CODE> and target <CODE>t</CODE> training data +and input test data <CODE>x_test</CODE>. +It returns the normal forward propagation through the network <CODE>y</CODE> +together with a matrix <CODE>extra</CODE> which consists of error bars (variance) +for a regression problem or moderated outputs for a classification problem. + +<p>The optional argument (and return value) +<CODE>invhess</CODE> is the inverse of the network Hessian +computed on the training data inputs and targets. Passing it in avoids +recomputing it, which can be a significant saving for large training sets. + +<p><h2> +See Also +</h2> +<CODE><a href="fevbayes.htm">fevbayes</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbffwd.htm b/sourcecodes/bnt-master/nethelp3.3/rbffwd.htm new file mode 100644 index 00000000..02e56931 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbffwd.htm @@ -0,0 +1,67 @@ +<html> +<head> +<title> +Netlab Reference Manual rbffwd +</title> +</head> +<body> +<H1> rbffwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through RBF network with linear outputs. + +<p><h2> +Synopsis +</h2> +<PRE> +a = rbffwd(net, x) +function [a, z, n2] = rbffwd(net, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>a = rbffwd(net, x)</CODE> takes a network data structure +<CODE>net</CODE> and a matrix <CODE>x</CODE> of input +vectors and forward propagates the inputs through the network to generate +a matrix <CODE>a</CODE> of output vectors. Each row of <CODE>x</CODE> corresponds to one +input vector and each row of <CODE>a</CODE> contains the corresponding output vector. +The activation function that is used is determined by <CODE>net.actfn</CODE>. + +<p><CODE>[a, z, n2] = rbffwd(net, x)</CODE> also generates a matrix <CODE>z</CODE> of +the hidden unit activations where each row corresponds to one pattern. +These hidden unit activations represent the <CODE>design matrix</CODE> for +the RBF. The matrix <CODE>n2</CODE> is the squared distances between each +basis function centre and each pattern in which each row corresponds +to a data point. + +<p><h2> +Examples +</h2> +<PRE> + +[a, z] = rbffwd(net, x); + +<p>temp = pinv([z ones(size(x, 1), 1)]) * t; +net.w2 = temp(1: nd(2), :); +net.b2 = temp(size(x, nd(2)) + 1, :); +</PRE> + +Here <CODE>x</CODE> is the input data, <CODE>t</CODE> are the target values, and we use the +pseudo-inverse to find the output weights and biases. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbferr.htm">rbferr</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfunpak.htm">rbfunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfgrad.htm b/sourcecodes/bnt-master/nethelp3.3/rbfgrad.htm new file mode 100644 index 00000000..30759dfe --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfgrad.htm @@ -0,0 +1,55 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfgrad +</title> +</head> +<body> +<H1> rbfgrad +</H1> +<h2> +Purpose +</h2> +Evaluate gradient of error function for RBF network. + +<p><h2> +Synopsis +</h2> +<PRE> + +g = rbfgrad(net, x, t) +[g, gdata, gprior] = rbfgrad(net, x, t) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = rbfgrad(net, x, t)</CODE> takes a network data structure <CODE>net</CODE> +together with a matrix <CODE>x</CODE> of input +vectors and a matrix <CODE>t</CODE> of target vectors, and evaluates the gradient +<CODE>g</CODE> of the error function with respect to the network weights (i.e. +including the hidden unit parameters). The error +function is sum of squares. +Each row of <CODE>x</CODE> corresponds to one +input vector and each row of <CODE>t</CODE> contains the corresponding target vector. +If the output function is <CODE>'neuroscale'</CODE> then the gradient is only +computed for the output layer weights and biases. + +<p><CODE>[g, gdata, gprior] = rbfgrad(net, x, t)</CODE> also returns separately +the data and prior contributions to the gradient. In the case of +multiple groups in the prior, <CODE>gprior</CODE> is a matrix with a row +for each group and a column for each weight parameter. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE>, <CODE><a href="rbferr.htm">rbferr</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbfunpak.htm">rbfunpak</a></CODE>, <CODE><a href="rbfbkp.htm">rbfbkp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfhess.htm b/sourcecodes/bnt-master/nethelp3.3/rbfhess.htm new file mode 100644 index 00000000..a9c6be79 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfhess.htm @@ -0,0 +1,72 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfhess +</title> +</head> +<body> +<H1> rbfhess +</H1> +<h2> +Purpose +</h2> +Evaluate the Hessian matrix for RBF network. + +<p><h2> +Synopsis +</h2> +<PRE> +h = rbfhess(net, x, t) +[h, hdata] = rbfhess(net, x, t) +h = rbfhess(net, x, t, hdata) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>h = rbfhess(net, x, t)</CODE> takes an RBF network data structure <CODE>net</CODE>, +a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of target +values and returns the full Hessian matrix <CODE>h</CODE> corresponding to +the second derivatives of the negative log posterior distribution, +evaluated for the current weight and bias values as defined by +<CODE>net</CODE>. Currently, the implementation only computes the +Hessian for the output layer weights. + +<p><CODE>[h, hdata] = rbfhess(net, x, t)</CODE> returns both the Hessian matrix +<CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependent +term in the Hessian. + +<p><CODE>h = rbfhess(net, x, t, hdata)</CODE> takes a network data structure +<CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of +target values, together with the contribution <CODE>hdata</CODE> arising from +the data dependent term in the Hessian, and returns the full Hessian +matrix <CODE>h</CODE> corresponding to the second derivatives of the negative +log posterior distribution. This version saves computation time if +<CODE>hdata</CODE> has already been evaluated for the current weight and bias +values. + +<p><h2> +Example +</h2> +For the standard regression framework with a Gaussian conditional +distribution of target values given input values, and a simple +Gaussian prior over weights, the Hessian takes the form +<PRE> + + h = beta*hdata + alpha*I +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="mlphess.htm">mlphess</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfjacob.htm b/sourcecodes/bnt-master/nethelp3.3/rbfjacob.htm new file mode 100644 index 00000000..853e59a3 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfjacob.htm @@ -0,0 +1,42 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfjacob +</title> +</head> +<body> +<H1> rbfjacob +</H1> +<h2> +Purpose +</h2> +Evaluate derivatives of RBF network outputs with respect to inputs. + +<p><h2> +Synopsis +</h2> +<PRE> +g = rbfjacob(net, x)</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = rbfjacob(net, x)</CODE> takes a network data structure <CODE>net</CODE> +and a matrix of input vectors <CODE>x</CODE> and returns a three-index matrix +<CODE>g</CODE> whose <CODE>i</CODE>, <CODE>j</CODE>, <CODE>k</CODE> element contains the +derivative of network output <CODE>k</CODE> with respect to input +parameter <CODE>j</CODE> for input pattern <CODE>i</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfbkp.htm">rbfbkp</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfpak.htm b/sourcecodes/bnt-master/nethelp3.3/rbfpak.htm new file mode 100644 index 00000000..08769b16 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfpak.htm @@ -0,0 +1,40 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfpak +</title> +</head> +<body> +<H1> rbfpak +</H1> +<h2> +Purpose +</h2> +Combines all the parameters in an RBF network into one weights vector. + +<p><h2> +Synopsis +</h2> +<PRE> +w = rbfpak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>w = rbfpak(net)</CODE> takes a network data structure <CODE>net</CODE> and combines +the component parameter matrices into a single row vector <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="rbfunpak.htm">rbfunpak</a></CODE>, <CODE><a href="rbf.htm">rbf</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfprior.htm b/sourcecodes/bnt-master/nethelp3.3/rbfprior.htm new file mode 100644 index 00000000..202bdde7 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfprior.htm @@ -0,0 +1,59 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfprior +</title> +</head> +<body> +<H1> rbfprior +</H1> +<h2> +Purpose +</h2> +Create Gaussian prior and output layer mask for RBF. + +<p><h2> +Synopsis +</h2> +<PRE> +[mask, prior] = rbfprior(rbfunc, nin, nhidden, nout, aw2, ab2)</PRE> + + +<p><h2> +Description +</h2> +<CODE>[mask, prior] = rbfprior(rbfunc, nin, nhidden, nout, aw2, ab2)</CODE> +generates a vector +<CODE>mask</CODE> that selects only the output +layer weights. This is because most uses of RBF networks in a Bayesian +context have fixed basis functions with the output layer as the only +adjustable parameters. In particular, the Neuroscale output error function +is designed to work only with this mask. + +<p>The return value +<CODE>prior</CODE> is a data structure, +with fields <CODE>prior.alpha</CODE> and <CODE>prior.index</CODE>, which +specifies a Gaussian prior distribution for the network weights in an +RBF network. The parameters <CODE>aw2</CODE> and <CODE>ab2</CODE> are all +scalars and represent the regularization coefficients for two groups +of parameters in the network corresponding to + second-layer weights, and second-layer biases +respectively. Then <CODE>prior.alpha</CODE> represents a column vector of +length 2 containing the parameters, and <CODE>prior.index</CODE> is a matrix +specifying which weights belong in each group. Each column has one +element for each weight in the matrix, using the standard ordering as +defined in <CODE>rbfpak</CODE>, and each element is 1 or 0 according to +whether the weight is a member of the corresponding group or not. + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbferr.htm">rbferr</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfsetbf.htm b/sourcecodes/bnt-master/nethelp3.3/rbfsetbf.htm new file mode 100644 index 00000000..c4fbf443 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfsetbf.htm @@ -0,0 +1,43 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfsetbf +</title> +</head> +<body> +<H1> rbfsetbf +</H1> +<h2> +Purpose +</h2> +Set basis functions of RBF from data. + +<p><h2> +Synopsis +</h2> +<PRE> +net = rbfsetbf(net, options, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = rbfsetbf(net, options, x)</CODE> sets the basis functions of the +RBF network <CODE>net</CODE> so that they model the unconditional density of the +dataset <CODE>x</CODE>. This is done by training a GMM with spherical covariances +using <CODE>gmmem</CODE>. The <CODE>options</CODE> vector is passed to <CODE>gmmem</CODE>. +The widths of the functions are set by a call to <CODE>rbfsetfw</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfsetfw.htm">rbfsetfw</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfsetfw.htm b/sourcecodes/bnt-master/nethelp3.3/rbfsetfw.htm new file mode 100644 index 00000000..ae3fab56 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfsetfw.htm @@ -0,0 +1,46 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfsetfw +</title> +</head> +<body> +<H1> rbfsetfw +</H1> +<h2> +Purpose +</h2> +Set basis function widths of RBF. + +<p><h2> +Synopsis +</h2> +<PRE> +net = rbfsetfw(net, scale) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = rbfsetfw(net, scale)</CODE> sets the widths of +the basis functions of the +RBF network <CODE>net</CODE>. +If Gaussian basis functions are used, then the variances are set to +the largest squared distance between centres if <CODE>scale</CODE> is non-positive +and <CODE>scale</CODE> times the mean distance of each centre to its nearest +neighbour if <CODE>scale</CODE> is positive. Non-Gaussian basis functions do +not have a width. + +<p><h2> +See Also +</h2> +<CODE><a href="rbftrain.htm">rbftrain</a></CODE>, <CODE><a href="rbfsetbf.htm">rbfsetbf</a></CODE>, <CODE><a href="gmmem.htm">gmmem</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbftrain.htm b/sourcecodes/bnt-master/nethelp3.3/rbftrain.htm new file mode 100644 index 00000000..04c2bef5 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbftrain.htm @@ -0,0 +1,90 @@ +<html> +<head> +<title> +Netlab Reference Manual rbftrain +</title> +</head> +<body> +<H1> rbftrain +</H1> +<h2> +Purpose +</h2> +Two stage training of RBF network. + +<p><h2> +Description +</h2> +<CODE>net = rbftrain(net, options, x, t)</CODE> uses a +two stage training +algorithm to set the weights in the RBF model structure <CODE>net</CODE>. +Each row of <CODE>x</CODE> corresponds to one +input vector and each row of <CODE>t</CODE> contains the corresponding target vector. +The centres are determined by fitting a Gaussian mixture model +with circular covariances using the EM algorithm through a call to +<CODE>rbfsetbf</CODE>. (The mixture model is +initialised using a small number of iterations of the K-means algorithm.) +If the activation functions are Gaussians, then the basis function widths +are then set to the maximum inter-centre squared distance. + +<p>For linear outputs, +the hidden to output +weights that give rise to the least squares solution +can then be determined using the pseudo-inverse. For neuroscale outputs, +the hidden to output weights are determined using the iterative shadow +targets algorithm. + Although this two stage +procedure may not give solutions with as low an error as using general +purpose non-linear optimisers, it is much faster. + +<p>The options vector may have two rows: if this is the case, then the second row +is passed to <CODE>rbfsetbf</CODE>, which allows the user to specify a different +number iterations for RBF and GMM training. +The optional parameters to <CODE>rbftrain</CODE> have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values during EM training. + +<p><CODE>options(2)</CODE> is a measure of the precision required for the value +of the weights <CODE>w</CODE> at the solution. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(5)</CODE> is set to 1 if the basis functions parameters should remain +unchanged; default 0. + +<p><CODE>options(6)</CODE> is set to 1 if the output layer weights should be should +set using PCA. This is only relevant for Neuroscale outputs; default 0. + +<p><CODE>options(14)</CODE> is the maximum number of iterations for the shadow +targets algorithm; +default 100. + +<p><h2> +Example +</h2> +The following example creates an RBF network and then trains it: +<PRE> + +net = rbf(1, 4, 1, 'gaussian'); +options(1, :) = foptions; +options(2, :) = foptions; +options(2, 14) = 10; % 10 iterations of EM +options(2, 5) = 1; % Check for covariance collapse in EM +net = rbftrain(net, options, x, t); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="rbf.htm">rbf</a></CODE>, <CODE><a href="rbferr.htm">rbferr</a></CODE>, <CODE><a href="rbffwd.htm">rbffwd</a></CODE>, <CODE><a href="rbfgrad.htm">rbfgrad</a></CODE>, <CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbfunpak.htm">rbfunpak</a></CODE>, <CODE><a href="rbfsetbf.htm">rbfsetbf</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rbfunpak.htm b/sourcecodes/bnt-master/nethelp3.3/rbfunpak.htm new file mode 100644 index 00000000..20464916 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rbfunpak.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual rbfunpak +</title> +</head> +<body> +<H1> rbfunpak +</H1> +<h2> +Purpose +</h2> +Separates a vector of RBF weights into its components. + +<p><h2> +Synopsis +</h2> +<PRE> +net = rbfunpak(net, w) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = rbfunpak(net, w)</CODE> takes an RBF network data structure <CODE>net</CODE> and +a weight vector <CODE>w</CODE>, and returns a network data structure identical to +the input network, except that the centres +<CODE>c</CODE>, the widths <CODE>wi</CODE>, the second-layer +weight matrix <CODE>w2</CODE> and the second-layer bias vector <CODE>b2</CODE> have all +been set to the corresponding elements of <CODE>w</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="rbfpak.htm">rbfpak</a></CODE>, <CODE><a href="rbf.htm">rbf</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rosegrad.htm b/sourcecodes/bnt-master/nethelp3.3/rosegrad.htm new file mode 100644 index 00000000..fc4fa9d6 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rosegrad.htm @@ -0,0 +1,40 @@ +<html> +<head> +<title> +Netlab Reference Manual rosegrad +</title> +</head> +<body> +<H1> rosegrad +</H1> +<h2> +Purpose +</h2> +Calculate gradient of Rosenbrock's function. + +<p><h2> +Synopsis +</h2> +<PRE> +g = rosegrad(x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>g = rosegrad(x)</CODE> computes the gradient of Rosenbrock's function +at each row of <CODE>x</CODE>, which should have two columns. + +<p><h2> +See Also +</h2> +<CODE><a href="demopt1.htm">demopt1</a></CODE>, <CODE><a href="rosen.htm">rosen</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/rosen.htm b/sourcecodes/bnt-master/nethelp3.3/rosen.htm new file mode 100644 index 00000000..2b8f37aa --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/rosen.htm @@ -0,0 +1,40 @@ +<html> +<head> +<title> +Netlab Reference Manual rosen +</title> +</head> +<body> +<H1> rosen +</H1> +<h2> +Purpose +</h2> +Calculate Rosenbrock's function. + +<p><h2> +Synopsis +</h2> +<PRE> +y = rosen(x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>y = rosen(x)</CODE> computes the value of Rosenbrock's function +at each row of <CODE>x</CODE>, which should have two columns. + +<p><h2> +See Also +</h2> +<CODE><a href="demopt1.htm">demopt1</a></CODE>, <CODE><a href="rosegrad.htm">rosegrad</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/scg.htm b/sourcecodes/bnt-master/nethelp3.3/scg.htm new file mode 100644 index 00000000..e2e512e2 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/scg.htm @@ -0,0 +1,97 @@ +<html> +<head> +<title> +Netlab Reference Manual scg +</title> +</head> +<body> +<H1> scg +</H1> +<h2> +Purpose +</h2> +Scaled conjugate gradient optimization. + +<p><h2> +Description +</h2> +<CODE>[x, options] = scg(f, x, options, gradf)</CODE> uses a scaled conjugate +gradients +algorithm to find a local minimum of the function <CODE>f(x)</CODE> whose +gradient is given by <CODE>gradf(x)</CODE>. Here <CODE>x</CODE> is a row vector +and <CODE>f</CODE> returns a scalar value. +The point at which <CODE>f</CODE> has a local minimum +is returned as <CODE>x</CODE>. The function value at that point is returned +in <CODE>options(8)</CODE>. + +<p><CODE>[x, options, flog, pointlog, scalelog] = scg(f, x, options, gradf)</CODE> +also returns (optionally) a log of the function values +after each cycle in <CODE>flog</CODE>, a log +of the points visited in <CODE>pointlog</CODE>, and a log of the scale values +in the algorithm in <CODE>scalelog</CODE>. + +<p><CODE>scg(f, x, options, gradf, p1, p2, ...)</CODE> allows +additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. + +The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error +values in the return argument <CODE>errlog</CODE>, and the points visited +in the return argument <CODE>pointslog</CODE>. If <CODE>options(1)</CODE> is set to 0, +then only warning messages are displayed. If <CODE>options(1)</CODE> is -1, +then nothing is displayed. + +<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value +of <CODE>x</CODE> at the solution. If the absolute difference between +the values of <CODE>x</CODE> between two successive steps is less than +<CODE>options(2)</CODE>, then this condition is satisfied. + +<p><CODE>options(3)</CODE> is a measure of the precision required of the objective +function at the solution. If the absolute difference between the +objective function values between two successive steps is less than +<CODE>options(3)</CODE>, then this condition is satisfied. +Both this and the previous condition must be +satisfied for termination. + +<p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function. + +<p><CODE>options(10)</CODE> returns the total number of function evaluations (including +those in any line searches). + +<p><CODE>options(11)</CODE> returns the total number of gradient evaluations. + +<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100. + +<p><h2> +Examples +</h2> +An example of +the use of the additional arguments is the minimization of an error +function for a neural network: +<PRE> + +w = scg('neterr', w, options, 'netgrad', net, x, t); +</PRE> + + +<p><h2> +Algorithm +</h2> +The search direction is re-started after every <CODE>nparams</CODE> +successful weight updates where <CODE>nparams</CODE> is the total number of +parameters in <CODE>x</CODE>. The algorithm is based on that given by Williams +(1991), with a simplified procedure for updating <CODE>lambda</CODE> when +<CODE>rho < 0.25</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/som.htm b/sourcecodes/bnt-master/nethelp3.3/som.htm new file mode 100644 index 00000000..637e752a --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/som.htm @@ -0,0 +1,58 @@ +<html> +<head> +<title> +Netlab Reference Manual som +</title> +</head> +<body> +<H1> som +</H1> +<h2> +Purpose +</h2> +Creates a Self-Organising Map. + +<p><h2> +Synopsis +</h2> +<PRE> + +net = som(nin, map_size) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = som(nin, map_size)</CODE> creates a SOM <CODE>net</CODE> +with input dimension (i.e. data dimension) <CODE>nin</CODE> and map dimensions +<CODE>map_size</CODE>. Only two-dimensional maps are currently implemented. + +<p>The fields in <CODE>net</CODE> are +<PRE> + + type = 'som' + nin = number of inputs + map_dim = dimension of map (constrained to be 2) + map_size = grid size: number of nodes in each dimension + num_nodes = number of nodes: the product of values in map_size + map = map_dim+1 dimensional array containing nodes + inode_dist = map of inter-node distances using Manhatten metric +</PRE> + + +<p>The map contains the node vectors arranged column-wise in the first +dimension of the array. + +<p><h2> +See Also +</h2> +<CODE><a href="kmeans.htm">kmeans</a></CODE>, <CODE><a href="somfwd.htm">somfwd</a></CODE>, <CODE><a href="somtrain.htm">somtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/somfwd.htm b/sourcecodes/bnt-master/nethelp3.3/somfwd.htm new file mode 100644 index 00000000..82102b4c --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/somfwd.htm @@ -0,0 +1,59 @@ +<html> +<head> +<title> +Netlab Reference Manual somfwd +</title> +</head> +<body> +<H1> somfwd +</H1> +<h2> +Purpose +</h2> +Forward propagation through a Self-Organising Map. + +<p><h2> +Synopsis +</h2> +<PRE> + +d2 = somfwd(net, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>d2 = somfwd(net, x)</CODE> propagates the data matrix <CODE>x</CODE> through + a SOM <CODE>net</CODE>, returning the squared distance matrix <CODE>d2</CODE> with +dimension <CODE>nin</CODE> by <CODE>num_nodes</CODE>. The $i$th row represents the +squared Euclidean distance to each of the nodes of the SOM. + +<p><CODE>[d2, win_nodes] = somfwd(net, x)</CODE> also returns the indices of the +winning nodes for each pattern. + +<p><h2> +Example +</h2> + +<p>The following code fragment creates a SOM with a $5times 5$ map for an +8-dimensional data space. It then applies the test data to the map. +<PRE> + +net = som(8, [5, 5]); +[d2, wn] = somfwd(net, test_data); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="som.htm">som</a></CODE>, <CODE><a href="somtrain.htm">somtrain</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/sompak.htm b/sourcecodes/bnt-master/nethelp3.3/sompak.htm new file mode 100644 index 00000000..902ef52e --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/sompak.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual sompak +</title> +</head> +<body> +<H1> sompak +</H1> +<h2> +Purpose +</h2> +Combines node weights into one weights matrix. + +<p><h2> +Synopsis +</h2> +<PRE> +c = sompak(net) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>c = sompak(net)</CODE> takes a SOM data structure <CODE>net</CODE> and +combines the node weights into a matrix of centres +<CODE>c</CODE> where each row represents the node vector. + +<p>The ordering of the parameters in <CODE>w</CODE> is defined by the indexing of the +multi-dimensional array <CODE>net.map</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="som.htm">som</a></CODE>, <CODE><a href="somunpak.htm">somunpak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/somtrain.htm b/sourcecodes/bnt-master/nethelp3.3/somtrain.htm new file mode 100644 index 00000000..ecf4e2cb --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/somtrain.htm @@ -0,0 +1,104 @@ +<html> +<head> +<title> +Netlab Reference Manual somtrain +</title> +</head> +<body> +<H1> somtrain +</H1> +<h2> +Purpose +</h2> +Kohonen training algorithm for SOM. + +<p><h2> +Synopsis +</h2> +<PRE> + +net = somtrain{net, options, x) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = somtrain{net, options, x)</CODE> uses Kohonen's algorithm to +train a SOM. Both on-line and batch algorithms are implemented. +The learning rate (for on-line) and neighbourhood size decay linearly. +There is no error function minimised during training (so there is +no termination criterion other than the number of epochs), but the +sum-of-squares is computed and returned in <CODE>options(8)</CODE>. + +<p>The optional parameters have the following interpretations. + +<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs learning +rate <CODE>alpha</CODE> and neighbourhood size <CODE>nsize</CODE>. +Otherwise nothing is displayed. + +<p><CODE>options(5)</CODE> determines whether the patterns are sampled randomly +with replacement. If it is 0 (the default), then patterns are sampled +in order. This is only relevant to the on-line algorithm. + +<p><CODE>options(6)</CODE> determines if the on-line or batch algorithm is +used. If it is 1 +then the batch algorithm is used. If it is 0 +(the default) then the on-line algorithm is used. + +<p><CODE>options(14)</CODE> is the maximum number of iterations (passes through +the complete pattern set); default 100. + +<p><CODE>options(15)</CODE> is the final neighbourhood size; default value is the +same as the initial neighbourhood size. + +<p><CODE>options(16)</CODE> is the final learning rate; default value is the same +as the initial learning rate. + +<p><CODE>options(17)</CODE> is the initial neighbourhood size; default 0.5*maximum +map size. + +<p><CODE>options(18)</CODE> is the initial learning rate; default 0.9. This parameter +must be positive. + +<p><h2> +Examples +</h2> +The following example performs on-line training on a SOM in two stages: +ordering and convergence. +<PRE> + +net = som(nin, [8, 7]); +options = foptions; + +<p>% Ordering phase +options(1) = 1; +options(14) = 50; +options(18) = 0.9; % Initial learning rate +options(16) = 0.05; % Final learning rate +options(17) = 8; % Initial neighbourhood size +options(15) = 1; % Final neighbourhood size +net2 = somtrain(net, options, x); + +<p>% Convergence phase +options(14) = 400; +options(18) = 0.05; +options(16) = 0.01; +options(17) = 0; +options(15) = 0; +net3 = somtrain(net2, options, x); +</PRE> + + +<p><h2> +See Also +</h2> +<CODE><a href="kmeans.htm">kmeans</a></CODE>, <CODE><a href="som.htm">som</a></CODE>, <CODE><a href="somfwd.htm">somfwd</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file diff --git a/sourcecodes/bnt-master/nethelp3.3/somunpak.htm b/sourcecodes/bnt-master/nethelp3.3/somunpak.htm new file mode 100644 index 00000000..68032339 --- /dev/null +++ b/sourcecodes/bnt-master/nethelp3.3/somunpak.htm @@ -0,0 +1,44 @@ +<html> +<head> +<title> +Netlab Reference Manual somunpak +</title> +</head> +<body> +<H1> somunpak +</H1> +<h2> +Purpose +</h2> +Replaces node weights in SOM. + +<p><h2> +Synopsis +</h2> +<PRE> +net = somunpak(net, w) +</PRE> + + +<p><h2> +Description +</h2> +<CODE>net = somunpak(net, w)</CODE> takes a SOM data structure <CODE>net</CODE> and +weight matrix <CODE>w</CODE> (each node represented by a row) and +puts the nodes back into the multi-dimensional array <CODE>net.map</CODE>. + +<p>The ordering of the parameters in <CODE>w</CODE> is defined by the indexing of the +multi-dimensional array <CODE>net.map</CODE>. + +<p><h2> +See Also +</h2> +<CODE><a href="som.htm">som</a></CODE>, <CODE><a href="sompak.htm">sompak</a></CODE><hr> +<b>Pages:</b> +<a href="index.htm">Index</a> +<hr> +<p>Copyright (c) Ian T Nabney (1996-9) + + +</body> +</html> \ No newline at end of file |