annotate code_tutoriel/dA.py @ 645:9455871d4703

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author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Thu, 07 Apr 2011 13:32:39 -0400
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1 """
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2 This tutorial introduces denoising auto-encoders (dA) 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 load_data
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40 from utils import tile_raster_images
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41
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42 import PIL.Image
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43
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44
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45 class dA(object):
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46 """Denoising Auto-Encoder class (dA)
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47
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48 A denoising autoencoders tries to reconstruct the input from a corrupted
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49 version of it by projecting it first in a latent space and reprojecting
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50 it afterwards back in the input space. Please refer to Vincent et al.,2008
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51 for more details. If x is the input then equation (1) computes a partially
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52 destroyed version of x by means of a stochastic mapping q_D. Equation (2)
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53 computes the projection of the input into the latent space. Equation (3)
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54 computes the reconstruction of the input, while equation (4) computes the
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55 reconstruction error.
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56
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57 .. math::
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58
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59 \tilde{x} ~ q_D(\tilde{x}|x) (1)
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60
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61 y = s(W \tilde{x} + b) (2)
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62
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63 x = s(W' y + b') (3)
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64
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65 L(x,z) = -sum_{k=1}^d [x_k \log z_k + (1-x_k) \log( 1-z_k)] (4)
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66
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67 """
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68
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69 def __init__(self, numpy_rng, theano_rng = None, input = None, n_visible= 784, n_hidden= 500,
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70 W = None, bhid = None, bvis = None):
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71 """
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72 Initialize the dA class by specifying the number of visible units (the
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73 dimension d of the input ), the number of hidden units ( the dimension
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74 d' of the latent or hidden space ) and the corruption level. The
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75 constructor also receives symbolic variables for the input, weights and
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76 bias. Such a symbolic variables are useful when, for example the input is
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77 the result of some computations, or when weights are shared between the
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78 dA and an MLP layer. When dealing with SdAs this always happens,
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79 the dA on layer 2 gets as input the output of the dA on layer 1,
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80 and the weights of the dA are used in the second stage of training
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81 to construct an MLP.
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82
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83 :type numpy_rng: numpy.random.RandomState
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84 :param numpy_rng: number random generator used to generate weights
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85
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86 :type theano_rng: theano.tensor.shared_randomstreams.RandomStreams
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87 :param theano_rng: Theano random generator; if None is given one is generated
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88 based on a seed drawn from `rng`
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89
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90 :type input: theano.tensor.TensorType
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91 :paran input: a symbolic description of the input or None for standalone
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92 dA
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93
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94 :type n_visible: int
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95 :param n_visible: number of visible units
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96
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97 :type n_hidden: int
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98 :param n_hidden: number of hidden units
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99
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100 :type W: theano.tensor.TensorType
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101 :param W: Theano variable pointing to a set of weights that should be
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102 shared belong the dA and another architecture; if dA should
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103 be standalone set this to None
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104
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105 :type bhid: theano.tensor.TensorType
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106 :param bhid: Theano variable pointing to a set of biases values (for
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107 hidden units) that should be shared belong dA and another
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108 architecture; if dA should be standalone set this to None
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109
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110 :type bvis: theano.tensor.TensorType
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111 :param bvis: Theano variable pointing to a set of biases values (for
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112 visible units) that should be shared belong dA and another
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113 architecture; if dA should be standalone set this to None
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114
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115
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116 """
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117 self.n_visible = n_visible
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118 self.n_hidden = n_hidden
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119
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120 # create a Theano random generator that gives symbolic random values
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121 if not theano_rng :
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122 theano_rng = RandomStreams(rng.randint(2**30))
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123
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124 # note : W' was written as `W_prime` and b' as `b_prime`
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125 if not W:
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126 # W is initialized with `initial_W` which is uniformely sampled
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127 # from -6./sqrt(n_visible+n_hidden) and 6./sqrt(n_hidden+n_visible)
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128 # the output of uniform if converted using asarray to dtype
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129 # theano.config.floatX so that the code is runable on GPU
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130 initial_W = numpy.asarray( numpy_rng.uniform(
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131 low = -numpy.sqrt(6./(n_hidden+n_visible)),
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132 high = numpy.sqrt(6./(n_hidden+n_visible)),
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133 size = (n_visible, n_hidden)), dtype = theano.config.floatX)
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134 W = theano.shared(value = initial_W, name ='W')
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135
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136 if not bvis:
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137 bvis = theano.shared(value = numpy.zeros(n_visible,
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138 dtype = theano.config.floatX))
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139
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140 if not bhid:
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141 bhid = theano.shared(value = numpy.zeros(n_hidden,
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142 dtype = theano.config.floatX))
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143
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144
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145 self.W = W
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146 # b corresponds to the bias of the hidden
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147 self.b = bhid
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148 # b_prime corresponds to the bias of the visible
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149 self.b_prime = bvis
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150 # tied weights, therefore W_prime is W transpose
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151 self.W_prime = self.W.T
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152 self.theano_rng = theano_rng
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153 # if no input is given, generate a variable representing the input
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154 if input == None :
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155 # we use a matrix because we expect a minibatch of several examples,
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156 # each example being a row
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157 self.x = T.dmatrix(name = 'input')
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158 else:
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159 self.x = input
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160
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161 self.params = [self.W, self.b, self.b_prime]
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162
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163 def get_corrupted_input(self, input, corruption_level):
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164 """ This function keeps ``1-corruption_level`` entries of the inputs the same
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165 and zero-out randomly selected subset of size ``coruption_level``
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166 Note : first argument of theano.rng.binomial is the shape(size) of
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167 random numbers that it should produce
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168 second argument is the number of trials
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169 third argument is the probability of success of any trial
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170
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171 this will produce an array of 0s and 1s where 1 has a probability of
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172 1 - ``corruption_level`` and 0 with ``corruption_level``
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173 """
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174 return self.theano_rng.binomial( size = input.shape, n = 1, prob = 1 - corruption_level) * input
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175
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176
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177 def get_hidden_values(self, input):
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178 """ Computes the values of the hidden layer """
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179 return T.nnet.sigmoid(T.dot(input, self.W) + self.b)
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180
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181 def get_reconstructed_input(self, hidden ):
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182 """ Computes the reconstructed input given the values of the hidden layer """
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183 return T.nnet.sigmoid(T.dot(hidden, self.W_prime) + self.b_prime)
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184
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185 def get_cost_updates(self, corruption_level, learning_rate):
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186 """ This function computes the cost and the updates for one trainng
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187 step of the dA """
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188
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189 tilde_x = self.get_corrupted_input(self.x, corruption_level)
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190 y = self.get_hidden_values( tilde_x)
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191 z = self.get_reconstructed_input(y)
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192 # note : we sum over the size of a datapoint; if we are using minibatches,
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193 # L will be a vector, with one entry per example in minibatch
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194 L = - T.sum( self.x*T.log(z) + (1-self.x)*T.log(1-z), axis=1 )
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195 # note : L is now a vector, where each element is the cross-entropy cost
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196 # of the reconstruction of the corresponding example of the
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197 # minibatch. We need to compute the average of all these to get
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198 # the cost of the minibatch
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199 cost = T.mean(L)
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200
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201 # compute the gradients of the cost of the `dA` with respect
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202 # to its parameters
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203 gparams = T.grad(cost, self.params)
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204 # generate the list of updates
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205 updates = {}
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206 for param, gparam in zip(self.params, gparams):
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207 updates[param] = param - learning_rate*gparam
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208
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209 return (cost, updates)
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210
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211
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212
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213
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214 def test_dA( learning_rate = 0.1, training_epochs = 15, dataset ='mnist.pkl.gz' ):
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215
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216 """
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217 This demo is tested on MNIST
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218
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219 :type learning_rate: float
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220 :param learning_rate: learning rate used for training the DeNosing AutoEncoder
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221
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222 :type training_epochs: int
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223 :param training_epochs: number of epochs used for training
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224
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225 :type dataset: string
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226 :param dataset: path to the picked dataset
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227
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228 """
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229 datasets = load_data(dataset)
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230 train_set_x, train_set_y = datasets[0]
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231
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232 batch_size = 20 # size of the minibatch
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233
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234 # compute number of minibatches for training, validation and testing
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235 n_train_batches = train_set_x.value.shape[0] / batch_size
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236
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237 # allocate symbolic variables for the data
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238 index = T.lscalar() # index to a [mini]batch
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239 x = T.matrix('x') # the data is presented as rasterized images
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240
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241 ####################################
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242 # BUILDING THE MODEL NO CORRUPTION #
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243 ####################################
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244
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245 rng = numpy.random.RandomState(123)
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246 theano_rng = RandomStreams( rng.randint(2**30))
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247
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248 da = dA(numpy_rng = rng, theano_rng = theano_rng, input = x,
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249 n_visible = 28*28, n_hidden = 500)
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250
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251 cost, updates = da.get_cost_updates(corruption_level = 0.,
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252 learning_rate = learning_rate)
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253
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254
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255 train_da = theano.function([index], cost, updates = updates,
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256 givens = {x:train_set_x[index*batch_size:(index+1)*batch_size]})
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257
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258 start_time = time.clock()
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259
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260 ############
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261 # TRAINING #
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262 ############
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263
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264 # go through training epochs
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265 for epoch in xrange(training_epochs):
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266 # go through trainng set
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267 c = []
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268 for batch_index in xrange(n_train_batches):
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269 c.append(train_da(batch_index))
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270
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271 print 'Training epoch %d, cost '%epoch, numpy.mean(c)
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272
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273 end_time = time.clock()
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274
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275 training_time = (end_time - start_time)
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276
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277 print ('Training took %f minutes' %(training_time/60.))
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278
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279 image = PIL.Image.fromarray(tile_raster_images( X = da.W.value.T,
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280 img_shape = (28,28),tile_shape = (10,10),
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281 tile_spacing=(1,1)))
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282 image.save('filters_corruption_0.png')
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283
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284 #####################################
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285 # BUILDING THE MODEL CORRUPTION 30% #
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286 #####################################
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287
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288 rng = numpy.random.RandomState(123)
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289 theano_rng = RandomStreams( rng.randint(2**30))
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290
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291 da = dA(numpy_rng = rng, theano_rng = theano_rng, input = x,
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292 n_visible = 28*28, n_hidden = 500)
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293
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294 cost, updates = da.get_cost_updates(corruption_level = 0.3,
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295 learning_rate = learning_rate)
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296
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297
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298 train_da = theano.function([index], cost, updates = updates,
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299 givens = {x:train_set_x[index*batch_size:(index+1)*batch_size]})
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300
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301 start_time = time.clock()
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302
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303 ############
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304 # TRAINING #
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305 ############
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306
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307 # go through training epochs
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308 for epoch in xrange(training_epochs):
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309 # go through trainng set
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310 c = []
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311 for batch_index in xrange(n_train_batches):
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312 c.append(train_da(batch_index))
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313
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314 print 'Training epoch %d, cost '%epoch, numpy.mean(c)
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315
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316 end_time = time.clock()
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317
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318 training_time = (end_time - start_time)
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319
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320 print ('Training took %f minutes' %(training_time/60.))
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321
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322 image = PIL.Image.fromarray(tile_raster_images( X = da.W.value.T,
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323 img_shape = (28,28),tile_shape = (10,10),
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324 tile_spacing=(1,1)))
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325 image.save('filters_corruption_30.png')
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326
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327
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328
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329 if __name__ == '__main__':
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330 test_dA()