1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
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>
|
