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<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> allowsadditional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>. <p><CODE>[samples, energies, diagn] = hmc(f, x, options, gradf)</CODE> also returnsa log of the energy values (i.e. negative log probabilities) for thesamples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containingdiagnostic information (position, momentum andacceptance 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 thetwo 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 isonly 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 variableis randomised. If <CODE>s</CODE> is a structure returned by <CODE>hmc('state')</CODE> thenit resets the generator to exactly the same state.<p>The optional parameters in the <CODE>options</CODE> vector have the followinginterpretations.<p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejectionthreshold at each step of the Markov chain. If the value is 2, then theposition vectors at each step are also displayed.<p><CODE>options(5)</CODE> is set to 1 if momentum persistence is used; default 0, forcomplete replacement of momentum variables.<p><CODE>options(7)</CODE> defines the trajectory length (i.e. the number of leap-frogsteps 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 thechain; 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/trajectorylength.<p><h2>Examples</h2>The following code fragment samples from the posterior distribution ofweights 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 technicalreport CRG-TR-93-1 from the University of Toronto. The stochastic update ofmomenta 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>⌨️ 快捷键说明
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