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1 <html>
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2 <head>
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3 <title>
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4 Netlab Reference Manual metrop
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5 </title>
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6 </head>
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7 <body>
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8 <H1> metrop
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9 </H1>
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10 <h2>
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11 Purpose
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12 </h2>
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13 Markov Chain Monte Carlo sampling with Metropolis algorithm.
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14
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15 <p><h2>
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16 Synopsis
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17 </h2>
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18 <PRE>
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19
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20 samples = metrop(f, x, options)
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21 samples = metrop(f, x, options, [], P1, P2, ...)
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22 [samples, energies, diagn] = metrop(f, x, options)
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23 s = metrop('state')
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24 metrop('state', s)
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25 </PRE>
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26
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27
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28 <p><h2>
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29 Description
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30 </h2>
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31
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32 <CODE>samples = metrop(f, x, options)</CODE> uses
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33 the Metropolis algorithm to sample from the distribution
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34 <CODE>p ~ exp(-f)</CODE>, where <CODE>f</CODE> is the first argument to <CODE>metrop</CODE>.
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35 The Markov chain starts at the point <CODE>x</CODE> and each
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36 candidate state is picked from a Gaussian proposal distribution and
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37 accepted or rejected according to the Metropolis criterion.
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38
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39 <p><CODE>samples = metrop(f, x, options, [], p1, p2, ...)</CODE> allows
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40 additional arguments to be passed to <CODE>f()</CODE>. The fourth argument is
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41 ignored, but is included for compatibility with <CODE>hmc</CODE> and the
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42 optimisers.
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43
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44 <p><CODE>[samples, energies, diagn] = metrop(f, x, options)</CODE> also returns
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45 a log of the energy values (i.e. negative log probabilities) for the
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46 samples in <CODE>energies</CODE> and <CODE>diagn</CODE>, a structure containing
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47 diagnostic information (position and
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48 acceptance threshold) for each step of the chain in <CODE>diagn.pos</CODE> and
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49 <CODE>diagn.acc</CODE> respectively. All candidate states (including rejected
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50 ones) are stored in <CODE>diagn.pos</CODE>.
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51
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52 <p><CODE>s = metrop('state')</CODE> returns a state structure that contains the
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53 state of the two random number generators <CODE>rand</CODE> and <CODE>randn</CODE>.
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54 These are contained in fields
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55 <CODE>randstate</CODE>,
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56 <CODE>randnstate</CODE>.
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57
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58 <p><CODE>metrop('state', s)</CODE> resets the state to <CODE>s</CODE>. If <CODE>s</CODE> is an integer,
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59 then it is passed to <CODE>rand</CODE> and <CODE>randn</CODE>.
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60 If <CODE>s</CODE> is a structure returned by <CODE>metrop('state')</CODE> then
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61 it resets the generator to exactly the same state.
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62
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63 <p>The optional parameters in the <CODE>options</CODE> vector have the following
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64 interpretations.
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65
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66 <p><CODE>options(1)</CODE> is set to 1 to display the energy values and rejection
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67 threshold at each step of the Markov chain. If the value is 2, then the
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68 position vectors at each step are also displayed.
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69
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70 <p><CODE>options(14)</CODE> is the number of samples retained from the Markov chain;
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71 default 100.
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72
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73 <p><CODE>options(15)</CODE> is the number of samples omitted from the start of the
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74 chain; default 0.
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75
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76 <p><CODE>options(18)</CODE> is the variance of the proposal distribution; default 1.
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77
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78 <p><h2>
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79 Examples
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80 </h2>
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81 The following code fragment samples from the posterior distribution of
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82 weights for a neural network.
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83 <PRE>
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84
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85 w = mlppak(net);
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86 [samples, energies] = metrop('neterr', w, options, 'netgrad', net, x, t);
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87 </PRE>
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88
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89
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90 <p><h2>
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91 Algorithm
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92 </h2>
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93
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94 The algorithm follows the procedure outlined in Radford Neal's technical
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95 report CRG-TR-93-1 from the University of Toronto.
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96
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97 <p><h2>
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98 See Also
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99 </h2>
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100 <CODE><a href="hmc.htm">hmc</a></CODE><hr>
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101 <b>Pages:</b>
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102 <a href="index.htm">Index</a>
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103 <hr>
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104 <p>Copyright (c) Ian T Nabney (1996-9)
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105
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106
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107 </body>
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108 </html> |
