Mercurial > ift6266

annotate code_tutoriel/rbm.py @ 225:eb78a695ad7a

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author fsavard
date Thu, 11 Mar 2010 16:29:39 -0500
parents 4bc5eeec6394
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165
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1 """This tutorial introduces restricted boltzmann machines (RBM) using Theano.
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2
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3 Boltzmann Machines (BMs) are a particular form of energy-based model which
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4 contain hidden variables. Restricted Boltzmann Machines further restrict BMs
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5 to those without visible-visible and hidden-hidden connections.
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6 """
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7
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8
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9 import numpy, time, cPickle, gzip, PIL.Image
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10
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11 import theano
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12 import theano.tensor as T
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13 import os
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14
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15 from theano.tensor.shared_randomstreams import RandomStreams
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16
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17 from utils import tile_raster_images
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18 from logistic_sgd import load_data
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19
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20 class RBM(object):
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21 """Restricted Boltzmann Machine (RBM) """
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22 def __init__(self, input=None, n_visible=784, n_hidden=500, \
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23 W = None, hbias = None, vbias = None, numpy_rng = None,
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24 theano_rng = None):
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25 """
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26 RBM constructor. Defines the parameters of the model along with
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27 basic operations for inferring hidden from visible (and vice-versa),
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28 as well as for performing CD updates.
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29
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30 :param input: None for standalone RBMs or symbolic variable if RBM is
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31 part of a larger graph.
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32
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33 :param n_visible: number of visible units
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34
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35 :param n_hidden: number of hidden units
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36
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37 :param W: None for standalone RBMs or symbolic variable pointing to a
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38 shared weight matrix in case RBM is part of a DBN network; in a DBN,
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39 the weights are shared between RBMs and layers of a MLP
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40
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41 :param hbias: None for standalone RBMs or symbolic variable pointing
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42 to a shared hidden units bias vector in case RBM is part of a
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43 different network
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44
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45 :param vbias: None for standalone RBMs or a symbolic variable
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46 pointing to a shared visible units bias
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47 """
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48
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49 self.n_visible = n_visible
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50 self.n_hidden = n_hidden
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51
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52
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53 if W is None :
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54 # W is initialized with `initial_W` which is uniformely sampled
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55 # from -6./sqrt(n_visible+n_hidden) and 6./sqrt(n_hidden+n_visible)
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56 # the output of uniform if converted using asarray to dtype
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57 # theano.config.floatX so that the code is runable on GPU
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58 initial_W = numpy.asarray( numpy.random.uniform(
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59 low = -numpy.sqrt(6./(n_hidden+n_visible)),
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60 high = numpy.sqrt(6./(n_hidden+n_visible)),
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61 size = (n_visible, n_hidden)),
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62 dtype = theano.config.floatX)
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63 # theano shared variables for weights and biases
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64 W = theano.shared(value = initial_W, name = 'W')
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65
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66 if hbias is None :
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67 # create shared variable for hidden units bias
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68 hbias = theano.shared(value = numpy.zeros(n_hidden,
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69 dtype = theano.config.floatX), name='hbias')
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70
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71 if vbias is None :
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72 # create shared variable for visible units bias
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73 vbias = theano.shared(value =numpy.zeros(n_visible,
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74 dtype = theano.config.floatX),name='vbias')
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75
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76 if numpy_rng is None:
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77 # create a number generator
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78 numpy_rng = numpy.random.RandomState(1234)
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79
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80 if theano_rng is None :
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81 theano_rng = RandomStreams(numpy_rng.randint(2**30))
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82
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83
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84 # initialize input layer for standalone RBM or layer0 of DBN
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85 self.input = input if input else T.dmatrix('input')
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86
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87 self.W = W
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88 self.hbias = hbias
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89 self.vbias = vbias
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90 self.theano_rng = theano_rng
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91 # **** WARNING: It is not a good idea to put things in this list
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92 # other than shared variables created in this function.
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93 self.params = [self.W, self.hbias, self.vbias]
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94 self.batch_size = self.input.shape[0]
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95
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96 def free_energy(self, v_sample):
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97 ''' Function to compute the free energy '''
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98 wx_b = T.dot(v_sample, self.W) + self.hbias
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99 vbias_term = T.sum(T.dot(v_sample, self.vbias))
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100 hidden_term = T.sum(T.log(1+T.exp(wx_b)))
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101 return -hidden_term - vbias_term
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102
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103 def sample_h_given_v(self, v0_sample):
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104 ''' This function infers state of hidden units given visible units '''
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105 # compute the activation of the hidden units given a sample of the visibles
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106 h1_mean = T.nnet.sigmoid(T.dot(v0_sample, self.W) + self.hbias)
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107 # get a sample of the hiddens given their activation
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108 h1_sample = self.theano_rng.binomial(size = h1_mean.shape, n = 1, prob = h1_mean)
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109 return [h1_mean, h1_sample]
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110
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111 def sample_v_given_h(self, h0_sample):
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112 ''' This function infers state of visible units given hidden units '''
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113 # compute the activation of the visible given the hidden sample
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114 v1_mean = T.nnet.sigmoid(T.dot(h0_sample, self.W.T) + self.vbias)
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115 # get a sample of the visible given their activation
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116 v1_sample = self.theano_rng.binomial(size = v1_mean.shape,n = 1,prob = v1_mean)
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117 return [v1_mean, v1_sample]
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118
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119 def gibbs_hvh(self, h0_sample):
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120 ''' This function implements one step of Gibbs sampling,
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121 starting from the hidden state'''
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122 v1_mean, v1_sample = self.sample_v_given_h(h0_sample)
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123 h1_mean, h1_sample = self.sample_h_given_v(v1_sample)
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124 return [v1_mean, v1_sample, h1_mean, h1_sample]
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125
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126 def gibbs_vhv(self, v0_sample):
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127 ''' This function implements one step of Gibbs sampling,
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128 starting from the visible state'''
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129 h1_mean, h1_sample = self.sample_h_given_v(v0_sample)
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130 v1_mean, v1_sample = self.sample_v_given_h(h1_sample)
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131 return [h1_mean, h1_sample, v1_mean, v1_sample]
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132
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133 def cd(self, lr = 0.1, persistent=None):
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134 """
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135 This functions implements one step of CD-1 or PCD-1
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136
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137 :param lr: learning rate used to train the RBM
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138 :param persistent: None for CD. For PCD, shared variable containing old state
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139 of Gibbs chain. This must be a shared variable of size (batch size, number of
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140 hidden units).
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141
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142 Returns the updates dictionary. The dictionary contains the update rules for weights
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143 and biases but also an update of the shared variable used to store the persistent
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144 chain, if one is used.
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145 """
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146
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147 # compute positive phase
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148 ph_mean, ph_sample = self.sample_h_given_v(self.input)
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149
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150 # decide how to initialize persistent chain:
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151 # for CD, we use the newly generate hidden sample
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152 # for PCD, we initialize from the old state of the chain
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153 if persistent is None:
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154 chain_start = ph_sample
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155 else:
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156 chain_start = persistent
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157
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158 # perform actual negative phase
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159 [nv_mean, nv_sample, nh_mean, nh_sample] = self.gibbs_hvh(chain_start)
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160
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161 # determine gradients on RBM parameters
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162 g_vbias = T.sum( self.input - nv_mean, axis = 0)/self.batch_size
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163 g_hbias = T.sum( ph_mean - nh_mean, axis = 0)/self.batch_size
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164 g_W = T.dot(ph_mean.T, self.input )/ self.batch_size - \
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165 T.dot(nh_mean.T, nv_mean )/ self.batch_size
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166
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167 gparams = [g_W.T, g_hbias, g_vbias]
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168
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169 # constructs the update dictionary
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170 updates = {}
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171 for gparam, param in zip(gparams, self.params):
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172 updates[param] = param + gparam * lr
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173
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174 if persistent:
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175 # Note that this works only if persistent is a shared variable
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176 updates[persistent] = T.cast(nh_sample, dtype=theano.config.floatX)
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177 # pseudo-likelihood is a better proxy for PCD
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178 cost = self.get_pseudo_likelihood_cost(updates)
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179 else:
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180 # reconstruction cross-entropy is a better proxy for CD
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181 cost = self.get_reconstruction_cost(updates, nv_mean)
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182
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183 return cost, updates
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184
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185 def get_pseudo_likelihood_cost(self, updates):
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186 """Stochastic approximation to the pseudo-likelihood"""
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187
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188 # index of bit i in expression p(x_i | x_{\i})
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189 bit_i_idx = theano.shared(value=0, name = 'bit_i_idx')
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190
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191 # binarize the input image by rounding to nearest integer
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192 xi = T.iround(self.input)
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193
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194 # calculate free energy for the given bit configuration
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195 fe_xi = self.free_energy(xi)
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196
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197 # flip bit x_i of matrix xi and preserve all other bits x_{\i}
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198 # Equivalent to xi[:,bit_i_idx] = 1-xi[:, bit_i_idx]
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199 # NB: slice(start,stop,step) is the python object used for
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200 # slicing, e.g. to index matrix x as follows: x[start:stop:step]
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201 xi_flip = T.setsubtensor(xi, 1-xi[:, bit_i_idx],
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202 idx_list=(slice(None,None,None),bit_i_idx))
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203
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204 # calculate free energy with bit flipped
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205 fe_xi_flip = self.free_energy(xi_flip)
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206
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207 # equivalent to e^(-FE(x_i)) / (e^(-FE(x_i)) + e^(-FE(x_{\i})))
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208 cost = self.n_visible * T.log(T.nnet.sigmoid(fe_xi_flip - fe_xi))
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209
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210 # increment bit_i_idx % number as part of updates
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211 updates[bit_i_idx] = (bit_i_idx + 1) % self.n_visible
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212
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213 return cost
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214
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215 def get_reconstruction_cost(self, updates, nv_mean):
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216 """Approximation to the reconstruction error"""
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217
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218 cross_entropy = T.mean(
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219 T.sum(self.input*T.log(nv_mean) +
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220 (1 - self.input)*T.log(1-nv_mean), axis = 1))
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221
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222 return cross_entropy
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223
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224
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225
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226 def test_rbm(learning_rate=0.1, training_epochs = 15,
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227 dataset='mnist.pkl.gz'):
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228 """
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229 Demonstrate ***
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230
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231 This is demonstrated on MNIST.
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232
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233 :param learning_rate: learning rate used for training the RBM
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234
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235 :param training_epochs: number of epochs used for training
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236
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237 :param dataset: path the the pickled dataset
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238
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239 """
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240 datasets = load_data(dataset)
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241
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242 train_set_x, train_set_y = datasets[0]
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243 test_set_x , test_set_y = datasets[2]
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244
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245
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246 batch_size = 20 # size of the minibatch
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247
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248 # compute number of minibatches for training, validation and testing
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249 n_train_batches = train_set_x.value.shape[0] / batch_size
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250
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251 # allocate symbolic variables for the data
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252 index = T.lscalar() # index to a [mini]batch
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253 x = T.matrix('x') # the data is presented as rasterized images
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254
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255 rng = numpy.random.RandomState(123)
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256 theano_rng = RandomStreams( rng.randint(2**30))
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257
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258 # initialize storage fot the persistent chain (state = hidden layer of chain)
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259 persistent_chain = theano.shared(numpy.zeros((batch_size, 500)))
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260
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261 # construct the RBM class
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262 rbm = RBM( input = x, n_visible=28*28, \
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263 n_hidden = 500,numpy_rng = rng, theano_rng = theano_rng)
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264
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265 # get the cost and the gradient corresponding to one step of CD
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266 cost, updates = rbm.cd(lr=learning_rate, persistent=persistent_chain)
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267
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268
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269 #################################
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270 # Training the RBM #
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271 #################################
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272 dirname = 'lr=%.5f'%learning_rate
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273 os.makedirs(dirname)
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274 os.chdir(dirname)
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275
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276 # it is ok for a theano function to have no output
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277 # the purpose of train_rbm is solely to update the RBM parameters
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278 train_rbm = theano.function([index], cost,
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279 updates = updates,
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280 givens = { x: train_set_x[index*batch_size:(index+1)*batch_size]})
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281
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282 plotting_time = 0.
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283 start_time = time.clock()
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284
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285
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286 # go through training epochs
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287 for epoch in xrange(training_epochs):
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288
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289 # go through the training set
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290 mean_cost = []
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291 for batch_index in xrange(n_train_batches):
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292 mean_cost += [train_rbm(batch_index)]
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293
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294 print 'Training epoch %d, cost is '%epoch, numpy.mean(mean_cost)
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295
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296 # Plot filters after each training epoch
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297 plotting_start = time.clock()
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298 # Construct image from the weight matrix
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299 image = PIL.Image.fromarray(tile_raster_images( X = rbm.W.value.T,
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300 img_shape = (28,28),tile_shape = (10,10),
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301 tile_spacing=(1,1)))
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302 image.save('filters_at_epoch_%i.png'%epoch)
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303 plotting_stop = time.clock()
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304 plotting_time += (plotting_stop - plotting_start)
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305
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306 end_time = time.clock()
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307
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308 pretraining_time = (end_time - start_time) - plotting_time
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309
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310 print ('Training took %f minutes' %(pretraining_time/60.))
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311
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312
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313 #################################
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314 # Sampling from the RBM #
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315 #################################
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316
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317 # find out the number of test samples
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318 number_of_test_samples = test_set_x.value.shape[0]
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319
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320 # pick random test examples, with which to initialize the persistent chain
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321 test_idx = rng.randint(number_of_test_samples-20)
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322 persistent_vis_chain = theano.shared(test_set_x.value[test_idx:test_idx+20])
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323
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324 # define one step of Gibbs sampling (mf = mean-field)
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325 [hid_mf, hid_sample, vis_mf, vis_sample] = rbm.gibbs_vhv(persistent_vis_chain)
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326
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327 # the sample at the end of the channel is returned by ``gibbs_1`` as
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328 # its second output; note that this is computed as a binomial draw,
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329 # therefore it is formed of ints (0 and 1) and therefore needs to
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330 # be converted to the same dtype as ``persistent_vis_chain``
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331 vis_sample = T.cast(vis_sample, dtype=theano.config.floatX)
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332
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333 # construct the function that implements our persistent chain
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334 # we generate the "mean field" activations for plotting and the actual samples for
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335 # reinitializing the state of our persistent chain
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336 sample_fn = theano.function([], [vis_mf, vis_sample],
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337 updates = { persistent_vis_chain:vis_sample})
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338
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339 # sample the RBM, plotting every `plot_every`-th sample; do this
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340 # until you plot at least `n_samples`
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341 n_samples = 10
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342 plot_every = 1000
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343
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344 for idx in xrange(n_samples):
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345
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346 # do `plot_every` intermediate samplings of which we do not care
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347 for jdx in xrange(plot_every):
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348 vis_mf, vis_sample = sample_fn()
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349
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350 # construct image
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351 image = PIL.Image.fromarray(tile_raster_images(
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352 X = vis_mf,
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353 img_shape = (28,28),
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354 tile_shape = (10,10),
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355 tile_spacing = (1,1) ) )
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356 print ' ... plotting sample ', idx
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357 image.save('sample_%i_step_%i.png'%(idx,idx*jdx))
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358
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359 if __name__ == '__main__':
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360 test_rbm()