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annotate code_tutoriel/SdA.py @ 578:61aae4fd2da5

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typo fixed, uploaded to CMT
author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Sun, 08 Aug 2010 08:16:21 -0400
parents 4bc5eeec6394
children
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1 """
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2 This tutorial introduces stacked denoising auto-encoders (SdA) using Theano.
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3
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4 Denoising autoencoders are the building blocks for SdA.
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5 They are based on auto-encoders as the ones used in Bengio et al. 2007.
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6 An autoencoder takes an input x and first maps it to a hidden representation
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7 y = f_{\theta}(x) = s(Wx+b), parameterized by \theta={W,b}. The resulting
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8 latent representation y is then mapped back to a "reconstructed" vector
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9 z \in [0,1]^d in input space z = g_{\theta'}(y) = s(W'y + b'). The weight
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10 matrix W' can optionally be constrained such that W' = W^T, in which case
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11 the autoencoder is said to have tied weights. The network is trained such
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12 that to minimize the reconstruction error (the error between x and z).
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13
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14 For the denosing autoencoder, during training, first x is corrupted into
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15 \tilde{x}, where \tilde{x} is a partially destroyed version of x by means
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16 of a stochastic mapping. Afterwards y is computed as before (using
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17 \tilde{x}), y = s(W\tilde{x} + b) and z as s(W'y + b'). The reconstruction
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18 error is now measured between z and the uncorrupted input x, which is
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19 computed as the cross-entropy :
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20 - \sum_{k=1}^d[ x_k \log z_k + (1-x_k) \log( 1-z_k)]
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21
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22
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23 References :
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24 - P. Vincent, H. Larochelle, Y. Bengio, P.A. Manzagol: Extracting and
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25 Composing Robust Features with Denoising Autoencoders, ICML'08, 1096-1103,
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26 2008
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27 - Y. Bengio, P. Lamblin, D. Popovici, H. Larochelle: Greedy Layer-Wise
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28 Training of Deep Networks, Advances in Neural Information Processing
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29 Systems 19, 2007
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30
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31 """
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32
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33 import numpy, time, cPickle, gzip
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34
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35 import theano
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36 import theano.tensor as T
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37 from theano.tensor.shared_randomstreams import RandomStreams
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38
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39 from logistic_sgd import LogisticRegression, load_data
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40 from mlp import HiddenLayer
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41 from dA import dA
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42
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43
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44
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45 class SdA(object):
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46 """Stacked denoising auto-encoder class (SdA)
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47
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48 A stacked denoising autoencoder model is obtained by stacking several
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49 dAs. The hidden layer of the dA at layer `i` becomes the input of
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50 the dA at layer `i+1`. The first layer dA gets as input the input of
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51 the SdA, and the hidden layer of the last dA represents the output.
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52 Note that after pretraining, the SdA is dealt with as a normal MLP,
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53 the dAs are only used to initialize the weights.
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54 """
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55
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56 def __init__(self, numpy_rng, theano_rng = None, n_ins = 784,
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57 hidden_layers_sizes = [500,500], n_outs = 10,
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58 corruption_levels = [0.1, 0.1]):
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59 """ This class is made to support a variable number of layers.
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60
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61 :type numpy_rng: numpy.random.RandomState
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62 :param numpy_rng: numpy random number generator used to draw initial
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63 weights
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64
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65 :type theano_rng: theano.tensor.shared_randomstreams.RandomStreams
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66 :param theano_rng: Theano random generator; if None is given one is
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67 generated based on a seed drawn from `rng`
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68
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69 :type n_ins: int
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70 :param n_ins: dimension of the input to the sdA
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71
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72 :type n_layers_sizes: list of ints
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73 :param n_layers_sizes: intermidiate layers size, must contain
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74 at least one value
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75
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76 :type n_outs: int
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77 :param n_outs: dimension of the output of the network
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78
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79 :type corruption_levels: list of float
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80 :param corruption_levels: amount of corruption to use for each
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81 layer
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82 """
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83
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84 self.sigmoid_layers = []
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85 self.dA_layers = []
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86 self.params = []
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87 self.n_layers = len(hidden_layers_sizes)
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88
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89 assert self.n_layers > 0
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90
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91 if not theano_rng:
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92 theano_rng = RandomStreams(numpy_rng.randint(2**30))
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93 # allocate symbolic variables for the data
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94 self.x = T.matrix('x') # the data is presented as rasterized images
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95 self.y = T.ivector('y') # the labels are presented as 1D vector of
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96 # [int] labels
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97
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98 # The SdA is an MLP, for which all weights of intermidiate layers
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99 # are shared with a different denoising autoencoders
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100 # We will first construct the SdA as a deep multilayer perceptron,
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101 # and when constructing each sigmoidal layer we also construct a
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102 # denoising autoencoder that shares weights with that layer
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103 # During pretraining we will train these autoencoders (which will
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104 # lead to chainging the weights of the MLP as well)
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105 # During finetunining we will finish training the SdA by doing
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106 # stochastich gradient descent on the MLP
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107
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108 for i in xrange( self.n_layers ):
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109 # construct the sigmoidal layer
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110
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111 # the size of the input is either the number of hidden units of
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112 # the layer below or the input size if we are on the first layer
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113 if i == 0 :
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114 input_size = n_ins
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115 else:
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116 input_size = hidden_layers_sizes[i-1]
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117
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118 # the input to this layer is either the activation of the hidden
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119 # layer below or the input of the SdA if you are on the first
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120 # layer
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121 if i == 0 :
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122 layer_input = self.x
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123 else:
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124 layer_input = self.sigmoid_layers[-1].output
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125
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126 sigmoid_layer = HiddenLayer(rng = numpy_rng,
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127 input = layer_input,
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128 n_in = input_size,
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129 n_out = hidden_layers_sizes[i],
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130 activation = T.nnet.sigmoid)
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131 # add the layer to our list of layers
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132 self.sigmoid_layers.append(sigmoid_layer)
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133 # its arguably a philosophical question...
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134 # but we are going to only declare that the parameters of the
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135 # sigmoid_layers are parameters of the StackedDAA
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136 # the visible biases in the dA are parameters of those
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137 # dA, but not the SdA
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138 self.params.extend(sigmoid_layer.params)
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139
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140 # Construct a denoising autoencoder that shared weights with this
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141 # layer
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142 dA_layer = dA(numpy_rng = numpy_rng, theano_rng = theano_rng, input = layer_input,
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143 n_visible = input_size,
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144 n_hidden = hidden_layers_sizes[i],
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145 W = sigmoid_layer.W, bhid = sigmoid_layer.b)
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146 self.dA_layers.append(dA_layer)
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147
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148
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149 # We now need to add a logistic layer on top of the MLP
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150 self.logLayer = LogisticRegression(\
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151 input = self.sigmoid_layers[-1].output,\
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152 n_in = hidden_layers_sizes[-1], n_out = n_outs)
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153
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154 self.params.extend(self.logLayer.params)
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155 # construct a function that implements one step of finetunining
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156
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157 # compute the cost for second phase of training,
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158 # defined as the negative log likelihood
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159 self.finetune_cost = self.logLayer.negative_log_likelihood(self.y)
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160 # compute the gradients with respect to the model parameters
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161 # symbolic variable that points to the number of errors made on the
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162 # minibatch given by self.x and self.y
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163 self.errors = self.logLayer.errors(self.y)
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164
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165 def pretraining_functions(self, train_set_x, batch_size):
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166 ''' Generates a list of functions, each of them implementing one
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167 step in trainnig the dA corresponding to the layer with same index.
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168 The function will require as input the minibatch index, and to train
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169 a dA you just need to iterate, calling the corresponding function on
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170 all minibatch indexes.
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171
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172 :type train_set_x: theano.tensor.TensorType
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173 :param train_set_x: Shared variable that contains all datapoints used
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174 for training the dA
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175
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176 :type batch_size: int
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177 :param batch_size: size of a [mini]batch
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178
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179 :type learning_rate: float
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180 :param learning_rate: learning rate used during training for any of
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181 the dA layers
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182 '''
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183
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184 # index to a [mini]batch
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185 index = T.lscalar('index') # index to a minibatch
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186 corruption_level = T.scalar('corruption') # amount of corruption to use
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187 learning_rate = T.scalar('lr') # learning rate to use
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188 # number of batches
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189 n_batches = train_set_x.value.shape[0] / batch_size
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190 # begining of a batch, given `index`
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191 batch_begin = index * batch_size
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192 # ending of a batch given `index`
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193 batch_end = batch_begin+batch_size
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194
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195 pretrain_fns = []
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196 for dA in self.dA_layers:
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197 # get the cost and the updates list
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198 cost,updates = dA.get_cost_updates( corruption_level, learning_rate)
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199 # compile the theano function
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200 fn = theano.function( inputs = [index,
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201 theano.Param(corruption_level, default = 0.2),
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202 theano.Param(learning_rate, default = 0.1)],
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203 outputs = cost,
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204 updates = updates,
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205 givens = {self.x :train_set_x[batch_begin:batch_end]})
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206 # append `fn` to the list of functions
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207 pretrain_fns.append(fn)
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208
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209 return pretrain_fns
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210
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211
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212 def build_finetune_functions(self, datasets, batch_size, learning_rate):
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213 '''Generates a function `train` that implements one step of
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214 finetuning, a function `validate` that computes the error on
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215 a batch from the validation set, and a function `test` that
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216 computes the error on a batch from the testing set
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217
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218 :type datasets: list of pairs of theano.tensor.TensorType
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219 :param datasets: It is a list that contain all the datasets;
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220 the has to contain three pairs, `train`,
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221 `valid`, `test` in this order, where each pair
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222 is formed of two Theano variables, one for the
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223 datapoints, the other for the labels
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224
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225 :type batch_size: int
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226 :param batch_size: size of a minibatch
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227
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228 :type learning_rate: float
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229 :param learning_rate: learning rate used during finetune stage
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230 '''
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231
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232 (train_set_x, train_set_y) = datasets[0]
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233 (valid_set_x, valid_set_y) = datasets[1]
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234 (test_set_x , test_set_y ) = datasets[2]
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235
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236 # compute number of minibatches for training, validation and testing
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237 n_valid_batches = valid_set_x.value.shape[0] / batch_size
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238 n_test_batches = test_set_x.value.shape[0] / batch_size
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239
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240 index = T.lscalar('index') # index to a [mini]batch
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241
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242 # compute the gradients with respect to the model parameters
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243 gparams = T.grad(self.finetune_cost, self.params)
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244
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245 # compute list of fine-tuning updates
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246 updates = {}
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247 for param, gparam in zip(self.params, gparams):
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248 updates[param] = param - gparam*learning_rate
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249
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250 train_fn = theano.function(inputs = [index],
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251 outputs = self.finetune_cost,
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252 updates = updates,
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253 givens = {
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254 self.x : train_set_x[index*batch_size:(index+1)*batch_size],
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255 self.y : train_set_y[index*batch_size:(index+1)*batch_size]})
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256
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257 test_score_i = theano.function([index], self.errors,
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258 givens = {
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259 self.x: test_set_x[index*batch_size:(index+1)*batch_size],
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260 self.y: test_set_y[index*batch_size:(index+1)*batch_size]})
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261
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262 valid_score_i = theano.function([index], self.errors,
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263 givens = {
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264 self.x: valid_set_x[index*batch_size:(index+1)*batch_size],
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265 self.y: valid_set_y[index*batch_size:(index+1)*batch_size]})
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266
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267 # Create a function that scans the entire validation set
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268 def valid_score():
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269 return [valid_score_i(i) for i in xrange(n_valid_batches)]
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270
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271 # Create a function that scans the entire test set
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272 def test_score():
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273 return [test_score_i(i) for i in xrange(n_test_batches)]
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274
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275 return train_fn, valid_score, test_score
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276
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277
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278
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279
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280
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281
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282 def test_SdA( finetune_lr = 0.1, pretraining_epochs = 15, \
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283 pretrain_lr = 0.1, training_epochs = 1000, \
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284 dataset='mnist.pkl.gz'):
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285 """
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286 Demonstrates how to train and test a stochastic denoising autoencoder.
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287
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288 This is demonstrated on MNIST.
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289
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290 :type learning_rate: float
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291 :param learning_rate: learning rate used in the finetune stage
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292 (factor for the stochastic gradient)
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293
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294 :type pretraining_epochs: int
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295 :param pretraining_epochs: number of epoch to do pretraining
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296
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297 :type pretrain_lr: float
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298 :param pretrain_lr: learning rate to be used during pre-training
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299
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300 :type n_iter: int
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301 :param n_iter: maximal number of iterations ot run the optimizer
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302
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303 :type dataset: string
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304 :param dataset: path the the pickled dataset
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305
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306 """
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307
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308 datasets = load_data(dataset)
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309
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310 train_set_x, train_set_y = datasets[0]
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311 valid_set_x, valid_set_y = datasets[1]
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312 test_set_x , test_set_y = datasets[2]
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313
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314
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315 batch_size = 20 # size of the minibatch
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316
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317 # compute number of minibatches for training, validation and testing
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318 n_train_batches = train_set_x.value.shape[0] / batch_size
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319
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320 # numpy random generator
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321 numpy_rng = numpy.random.RandomState(123)
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322 print '... building the model'
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323 # construct the stacked denoising autoencoder class
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324 sda = SdA( numpy_rng = numpy_rng, n_ins = 28*28,
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325 hidden_layers_sizes = [1000,1000,1000],
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326 n_outs = 10)
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327
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328
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329 #########################
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330 # PRETRAINING THE MODEL #
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331 #########################
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332 print '... getting the pretraining functions'
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333 pretraining_fns = sda.pretraining_functions(
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334 train_set_x = train_set_x,
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335 batch_size = batch_size )
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336
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337 print '... pre-training the model'
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338 start_time = time.clock()
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339 ## Pre-train layer-wise
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340 for i in xrange(sda.n_layers):
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341 # go through pretraining epochs
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342 for epoch in xrange(pretraining_epochs):
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343 # go through the training set
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344 c = []
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345 for batch_index in xrange(n_train_batches):
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346 c.append( pretraining_fns[i](index = batch_index,
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347 corruption = 0.2, lr = pretrain_lr ) )
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348 print 'Pre-training layer %i, epoch %d, cost '%(i,epoch),numpy.mean(c)
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349
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350 end_time = time.clock()
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351
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352 print ('Pretraining took %f minutes' %((end_time-start_time)/60.))
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353
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354 ########################
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355 # FINETUNING THE MODEL #
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356 ########################
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357
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358 # get the training, validation and testing function for the model
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359 print '... getting the finetuning functions'
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360 train_fn, validate_model, test_model = sda.build_finetune_functions (
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361 datasets = datasets, batch_size = batch_size,
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362 learning_rate = finetune_lr)
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363
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364 print '... finetunning the model'
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365 # early-stopping parameters
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366 patience = 10000 # look as this many examples regardless
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367 patience_increase = 2. # wait this much longer when a new best is
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368 # found
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369 improvement_threshold = 0.995 # a relative improvement of this much is
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370 # considered significant
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371 validation_frequency = min(n_train_batches, patience/2)
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372 # go through this many
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373 # minibatche before checking the network
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374 # on the validation set; in this case we
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375 # check every epoch
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376
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377
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378 best_params = None
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379 best_validation_loss = float('inf')
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380 test_score = 0.
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381 start_time = time.clock()
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382
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383 done_looping = False
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384 epoch = 0
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385
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386 while (epoch < training_epochs) and (not done_looping):
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387 epoch = epoch + 1
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388 for minibatch_index in xrange(n_train_batches):
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389
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390 minibatch_avg_cost = train_fn(minibatch_index)
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391 iter = epoch * n_train_batches + minibatch_index
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392
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393 if (iter+1) % validation_frequency == 0:
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394
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395 validation_losses = validate_model()
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396 this_validation_loss = numpy.mean(validation_losses)
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Dumitru Erhan <dumitru.erhan@gmail.com>
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397 print('epoch %i, minibatch %i/%i, validation error %f %%' % \
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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398 (epoch, minibatch_index+1, n_train_batches, \
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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399 this_validation_loss*100.))
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Dumitru Erhan <dumitru.erhan@gmail.com>
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400
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Dumitru Erhan <dumitru.erhan@gmail.com>
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401
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Dumitru Erhan <dumitru.erhan@gmail.com>
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402 # if we got the best validation score until now
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Dumitru Erhan <dumitru.erhan@gmail.com>
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403 if this_validation_loss < best_validation_loss:
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Dumitru Erhan <dumitru.erhan@gmail.com>
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404
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Dumitru Erhan <dumitru.erhan@gmail.com>
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405 #improve patience if loss improvement is good enough
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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406 if this_validation_loss < best_validation_loss * \
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Dumitru Erhan <dumitru.erhan@gmail.com>
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407 improvement_threshold :
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Dumitru Erhan <dumitru.erhan@gmail.com>
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408 patience = max(patience, iter * patience_increase)
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Dumitru Erhan <dumitru.erhan@gmail.com>
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409
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Dumitru Erhan <dumitru.erhan@gmail.com>
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410 # save best validation score and iteration number
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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411 best_validation_loss = this_validation_loss
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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412 best_iter = iter
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Dumitru Erhan <dumitru.erhan@gmail.com>
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413
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Dumitru Erhan <dumitru.erhan@gmail.com>
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414 # test it on the test set
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Dumitru Erhan <dumitru.erhan@gmail.com>
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415 test_losses = test_model()
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Dumitru Erhan <dumitru.erhan@gmail.com>
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416 test_score = numpy.mean(test_losses)
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Dumitru Erhan <dumitru.erhan@gmail.com>
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417 print((' epoch %i, minibatch %i/%i, test error of best '
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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418 'model %f %%') %
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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419 (epoch, minibatch_index+1, n_train_batches,
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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420 test_score*100.))
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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421
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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422
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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423 if patience <= iter :
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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424 done_looping = True
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Dumitru Erhan <dumitru.erhan@gmail.com>
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425 break
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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426
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Dumitru Erhan <dumitru.erhan@gmail.com>
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427 end_time = time.clock()
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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428 print(('Optimization complete with best validation score of %f %%,'
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
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429 'with test performance %f %%') %
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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430 (best_validation_loss * 100., test_score*100.))
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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431 print ('The code ran for %f minutes' % ((end_time-start_time)/60.))
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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432
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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433
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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434
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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435
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
diff changeset
436
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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437
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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438 if __name__ == '__main__':
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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439 test_SdA()
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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440
4bc5eeec6394 Updating the tutorial code to the latest revisions.
Dumitru Erhan <dumitru.erhan@gmail.com>
parents:
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441