Mercurial > hg > camir-aes2014

annotate toolboxes/FullBNT-1.0.7/nethelp3.3/hmc.htm @ 0:e9a9cd732c1e tip

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
parents
children
rev   line source
wolffd@0 1 <html>
wolffd@0 2 <head>
wolffd@0 3 <title>
wolffd@0 4 Netlab Reference Manual hmc
wolffd@0 5 </title>
wolffd@0 6 </head>
wolffd@0 7 <body>
wolffd@0 8 <H1> hmc
wolffd@0 9 </H1>
wolffd@0 10 <h2>
wolffd@0 11 Purpose
wolffd@0 12 </h2>
wolffd@0 13 Hybrid Monte Carlo sampling.
wolffd@0 14
wolffd@0 15 <p><h2>
wolffd@0 16 Synopsis
wolffd@0 17 </h2>
wolffd@0 18 <PRE>
wolffd@0 19
wolffd@0 20 samples = hmc(f, x, options, gradf)
wolffd@0 21 samples = hmc(f, x, options, gradf, P1, P2, ...)
wolffd@0 22 [samples, energies, diagn] = hmc(f, x, options, gradf)
wolffd@0 23 s = hmc('state')
wolffd@0 24 hmc('state', s)
wolffd@0 25 </PRE>
wolffd@0 26
wolffd@0 27
wolffd@0 28 <p><h2>
wolffd@0 29 Description
wolffd@0 30 </h2>
wolffd@0 31 <CODE>samples = hmc(f, x, options, gradf)</CODE> uses a
wolffd@0 32 hybrid Monte Carlo algorithm to sample from the distribution <CODE>p ~ exp(-f)</CODE>,
wolffd@0 33 where <CODE>f</CODE> is the first argument to <CODE>hmc</CODE>.
wolffd@0 34 The Markov chain starts at the point <CODE>x</CODE>, and the function <CODE>gradf</CODE>
wolffd@0 35 is the gradient of the `energy' function <CODE>f</CODE>.
wolffd@0 36
wolffd@0 37 <p><CODE>hmc(f, x, options, gradf, p1, p2, ...)</CODE> allows
wolffd@0 38 additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>.
wolffd@0 39
wolffd@0 40 <p><CODE>[samples, energies, diagn] = hmc(f, x, options, gradf)</CODE> also returns
wolffd@0 41 a log of the energy values (i.e. negative log probabilities) for the
wolffd@0 42 samples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containing
wolffd@0 43 diagnostic information (position, momentum and
wolffd@0 44 acceptance threshold) for each step of the chain in <CODE>diagn.pos</CODE>,
wolffd@0 45 <CODE>diagn.mom</CODE> and
wolffd@0 46 <CODE>diagn.acc</CODE> respectively. All candidate states (including rejected ones)
wolffd@0 47 are stored in <CODE>diagn.pos</CODE>.
wolffd@0 48
wolffd@0 49 <p><CODE>[samples, energies, diagn] = hmc(f, x, options, gradf)</CODE> also returns the
wolffd@0 50 <CODE>energies</CODE> (i.e. negative log probabilities) corresponding to the samples.
wolffd@0 51 The <CODE>diagn</CODE> structure contains three fields:
wolffd@0 52
wolffd@0 53 <p><CODE>pos</CODE> the position vectors of the dynamic process.
wolffd@0 54
wolffd@0 55 <p><CODE>mom</CODE> the momentum vectors of the dynamic process.
wolffd@0 56
wolffd@0 57 <p><CODE>acc</CODE> the acceptance thresholds.
wolffd@0 58
wolffd@0 59 <p><CODE>s = hmc('state')</CODE> returns a state structure that contains the state of the
wolffd@0 60 two random number generators <CODE>rand</CODE> and <CODE>randn</CODE> and the momentum of
wolffd@0 61 the dynamic process. These are contained in fields
wolffd@0 62 <CODE>randstate</CODE>, <CODE>randnstate</CODE>
wolffd@0 63 and <CODE>mom</CODE> respectively. The momentum state is
wolffd@0 64 only used for a persistent momentum update.
wolffd@0 65
wolffd@0 66 <p><CODE>hmc('state', s)</CODE> resets the state to <CODE>s</CODE>. If <CODE>s</CODE> is an integer,
wolffd@0 67 then it is passed to <CODE>rand</CODE> and <CODE>randn</CODE> and the momentum variable
wolffd@0 68 is randomised. If <CODE>s</CODE> is a structure returned by <CODE>hmc('state')</CODE> then
wolffd@0 69 it resets the generator to exactly the same state.
wolffd@0 70
wolffd@0 71 <p>The optional parameters in the <CODE>options</CODE> vector have the following
wolffd@0 72 interpretations.
wolffd@0 73
wolffd@0 74 <p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejection
wolffd@0 75 threshold at each step of the Markov chain. If the value is 2, then the
wolffd@0 76 position vectors at each step are also displayed.
wolffd@0 77
wolffd@0 78 <p><CODE>options(5)</CODE> is set to 1 if momentum persistence is used; default 0, for
wolffd@0 79 complete replacement of momentum variables.
wolffd@0 80
wolffd@0 81 <p><CODE>options(7)</CODE> defines the trajectory length (i.e. the number of leap-frog
wolffd@0 82 steps at each iteration). Minimum value 1.
wolffd@0 83
wolffd@0 84 <p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function.
wolffd@0 85
wolffd@0 86 <p><CODE>options(14)</CODE> is the number of samples retained from the Markov chain;
wolffd@0 87 default 100.
wolffd@0 88
wolffd@0 89 <p><CODE>options(15)</CODE> is the number of samples omitted from the start of the
wolffd@0 90 chain; default 0.
wolffd@0 91
wolffd@0 92 <p><CODE>options(17)</CODE> defines the momentum used when a persistent update of
wolffd@0 93 (leap-frog) momentum is used. This is bounded to the interval [0, 1).
wolffd@0 94
wolffd@0 95 <p><CODE>options(18)</CODE> is the step size used in leap-frogs; default 1/trajectory
wolffd@0 96 length.
wolffd@0 97
wolffd@0 98 <p><h2>
wolffd@0 99 Examples
wolffd@0 100 </h2>
wolffd@0 101 The following code fragment samples from the posterior distribution of
wolffd@0 102 weights for a neural network.
wolffd@0 103 <PRE>
wolffd@0 104
wolffd@0 105 w = mlppak(net);
wolffd@0 106 [samples, energies] = hmc('neterr', w, options, 'netgrad', net, x, t);
wolffd@0 107 </PRE>
wolffd@0 108
wolffd@0 109
wolffd@0 110 <p><h2>
wolffd@0 111 Algorithm
wolffd@0 112 </h2>
wolffd@0 113
wolffd@0 114 The algroithm follows the procedure outlined in Radford Neal's technical
wolffd@0 115 report CRG-TR-93-1 from the University of Toronto. The stochastic update of
wolffd@0 116 momenta samples from a zero mean unit covariance gaussian.
wolffd@0 117
wolffd@0 118 <p><h2>
wolffd@0 119 See Also
wolffd@0 120 </h2>
wolffd@0 121 <CODE><a href="metrop.htm">metrop</a></CODE><hr>
wolffd@0 122 <b>Pages:</b>
wolffd@0 123 <a href="index.htm">Index</a>
wolffd@0 124 <hr>
wolffd@0 125 <p>Copyright (c) Ian T Nabney (1996-9)
wolffd@0 126
wolffd@0 127
wolffd@0 128 </body>
wolffd@0 129 </html>