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)