+
+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)
+
+
+
+samples = hmc(f, x, options, gradf) uses a
+hybrid Monte Carlo algorithm to sample from the distribution p ~ exp(-f),
+where f is the first argument to hmc.
+The Markov chain starts at the point x, and the function gradf
+is the gradient of the `energy' function f.
+
+hmc(f, x, options, gradf, p1, p2, ...) allows
+additional arguments to be passed to f() and gradf().
+
+
[samples, energies, diagn] = hmc(f, x, options, gradf) also returns
+a log of the energy values (i.e. negative log probabilities) for the
+samples in energies and diagn, a structure containing
+diagnostic information (position, momentum and
+acceptance threshold) for each step of the chain in diagn.pos,
+diagn.mom and
+diagn.acc respectively. All candidate states (including rejected ones)
+are stored in diagn.pos.
+
+
[samples, energies, diagn] = hmc(f, x, options, gradf) also returns the
+energies (i.e. negative log probabilities) corresponding to the samples.
+The diagn structure contains three fields:
+
+
pos the position vectors of the dynamic process.
+
+
mom the momentum vectors of the dynamic process.
+
+
acc the acceptance thresholds.
+
+
s = hmc('state') returns a state structure that contains the state of the
+two random number generators rand and randn and the momentum of
+the dynamic process. These are contained in fields
+randstate, randnstate
+and mom respectively. The momentum state is
+only used for a persistent momentum update.
+
+
hmc('state', s) resets the state to s. If s is an integer,
+then it is passed to rand and randn and the momentum variable
+is randomised. If s is a structure returned by hmc('state') then
+it resets the generator to exactly the same state.
+
+
The optional parameters in the options vector have the following
+interpretations.
+
+
options(1) 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.
+
+
options(5) is set to 1 if momentum persistence is used; default 0, for
+complete replacement of momentum variables.
+
+
options(7) defines the trajectory length (i.e. the number of leap-frog
+steps at each iteration). Minimum value 1.
+
+
options(9) is set to 1 to check the user defined gradient function.
+
+
options(14) is the number of samples retained from the Markov chain;
+default 100.
+
+
options(15) is the number of samples omitted from the start of the
+chain; default 0.
+
+
options(17) defines the momentum used when a persistent update of
+(leap-frog) momentum is used. This is bounded to the interval [0, 1).
+
+
options(18) is the step size used in leap-frogs; default 1/trajectory
+length.
+
+
+
+w = mlppak(net);
+[samples, energies] = hmc('neterr', w, options, 'netgrad', net, x, t);
+
+
+
+metropCopyright (c) Ian T Nabney (1996-9) + + + + \ No newline at end of file -- cgit 1.4.1