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annotate baseline/log_reg/log_reg.py @ 207:43af74a348ac

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author Arnaud Bergeron <abergeron@gmail.com>
date Thu, 04 Mar 2010 20:43:21 -0500
parents 777f48ba30df
children 7be1f086a89e
rev   line source
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1 """
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2 This tutorial introduces logistic regression using Theano and stochastic
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3 gradient descent.
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4
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5 Logistic regression is a probabilistic, linear classifier. It is parametrized
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6 by a weight matrix :math:`W` and a bias vector :math:`b`. Classification is
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7 done by projecting data points onto a set of hyperplanes, the distance to
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8 which is used to determine a class membership probability.
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9
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10 Mathematically, this can be written as:
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11
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12 .. math::
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13 P(Y=i|x, W,b) &= softmax_i(W x + b) \\
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14 &= \frac {e^{W_i x + b_i}} {\sum_j e^{W_j x + b_j}}
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15
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16
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17 The output of the model or prediction is then done by taking the argmax of
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18 the vector whose i'th element is P(Y=i|x).
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19
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20 .. math::
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21
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22 y_{pred} = argmax_i P(Y=i|x,W,b)
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23
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24
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25 This tutorial presents a stochastic gradient descent optimization method
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26 suitable for large datasets, and a conjugate gradient optimization method
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27 that is suitable for smaller datasets.
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28
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29
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30 References:
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31
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32 - textbooks: "Pattern Recognition and Machine Learning" -
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33 Christopher M. Bishop, section 4.3.2
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34
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35 """
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36 __docformat__ = 'restructedtext en'
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37
198
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38 import numpy, time
158
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39
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40 import theano
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41 import theano.tensor as T
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42 from ift6266 import datasets
158
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43
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44 class LogisticRegression(object):
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45 """Multi-class Logistic Regression Class
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46
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47 The logistic regression is fully described by a weight matrix :math:`W`
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48 and bias vector :math:`b`. Classification is done by projecting data
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49 points onto a set of hyperplanes, the distance to which is used to
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50 determine a class membership probability.
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51 """
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52
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53
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54 def __init__( self, input, n_in, n_out ):
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55 """ Initialize the parameters of the logistic regression
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56
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57 :type input: theano.tensor.TensorType
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58 :param input: symbolic variable that describes the input of the
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59 architecture (one minibatch)
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60
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61 :type n_in: int
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62 :param n_in: number of input units, the dimension of the space in
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63 which the datapoints lie
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64
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65 :type n_out: int
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66 :param n_out: number of output units, the dimension of the space in
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67 which the labels lie
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68
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69 """
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70
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71 # initialize with 0 the weights W as a matrix of shape (n_in, n_out)
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72 self.W = theano.shared( value = numpy.zeros(( n_in, n_out ), dtype = theano.config.floatX ),
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73 name =' W')
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74 # initialize the baises b as a vector of n_out 0s
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75 self.b = theano.shared( value = numpy.zeros(( n_out, ), dtype = theano.config.floatX ),
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76 name = 'b')
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77
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78
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79 # compute vector of class-membership probabilities in symbolic form
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80 self.p_y_given_x = T.nnet.softmax( T.dot( input, self.W ) + self.b )
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81
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82 # compute prediction as class whose probability is maximal in
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83 # symbolic form
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84 self.y_pred=T.argmax( self.p_y_given_x, axis =1 )
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85
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86 # parameters of the model
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87 self.params = [ self.W, self.b ]
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88
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89
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90 def negative_log_likelihood( self, y ):
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91 """Return the mean of the negative log-likelihood of the prediction
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92 of this model under a given target distribution.
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93
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94 .. math::
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95
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96 \frac{1}{|\mathcal{D}|} \mathcal{L} (\theta=\{W,b\}, \mathcal{D}) =
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97 \frac{1}{|\mathcal{D}|} \sum_{i=0}^{|\mathcal{D}|} \log(P(Y=y^{(i)}|x^{(i)}, W,b)) \\
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98 \ell (\theta=\{W,b\}, \mathcal{D})
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99
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100 :type y: theano.tensor.TensorType
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101 :param y: corresponds to a vector that gives for each example the
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102 correct label
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103
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104 Note: we use the mean instead of the sum so that
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105 the learning rate is less dependent on the batch size
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106 """
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107 # y.shape[0] is (symbolically) the number of rows in y, i.e., number of examples (call it n) in the minibatch
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108 # T.arange(y.shape[0]) is a symbolic vector which will contain [0,1,2,... n-1]
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109 # T.log(self.p_y_given_x) is a matrix of Log-Probabilities (call it LP) with one row per example and one column per class
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110 # LP[T.arange(y.shape[0]),y] is a vector v containing [LP[0,y[0]], LP[1,y[1]], LP[2,y[2]], ..., LP[n-1,y[n-1]]]
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111 # and T.mean(LP[T.arange(y.shape[0]),y]) is the mean (across minibatch examples) of the elements in v,
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112 # i.e., the mean log-likelihood across the minibatch.
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113 return -T.mean( T.log( self.p_y_given_x )[ T.arange( y.shape[0] ), y ] )
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114
199
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115 def MSE(self, y):
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116 return -T.mean(abs((self.p_t_given_x)[T.arange(y.shape[0]), y]-y)**2)
158
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117
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118 def errors( self, y ):
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119 """Return a float representing the number of errors in the minibatch
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120 over the total number of examples of the minibatch ; zero one
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121 loss over the size of the minibatch
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122
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123 :type y: theano.tensor.TensorType
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124 :param y: corresponds to a vector that gives for each example the
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125 correct label
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126 """
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127
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128 # check if y has same dimension of y_pred
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129 if y.ndim != self.y_pred.ndim:
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130 raise TypeError( 'y should have the same shape as self.y_pred',
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131 ( 'y', target.type, 'y_pred', self.y_pred.type ) )
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132 # check if y is of the correct datatype
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133 if y.dtype.startswith('int'):
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134 # the T.neq operator returns a vector of 0s and 1s, where 1
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135 # represents a mistake in prediction
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136 return T.mean( T.neq( self.y_pred, y ) )
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137 else:
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138 raise NotImplementedError()
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139
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140 #--------------------------------------------------------------------------------------------------------------------
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141 # MAIN
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142 #--------------------------------------------------------------------------------------------------------------------
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143
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144 def log_reg( learning_rate = 0.13, nb_max_examples =1000000, batch_size = 50, \
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145 dataset=datasets.nist_digits, image_size = 32 * 32, nb_class = 10, \
158
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146 patience = 5000, patience_increase = 2, improvement_threshold = 0.995):
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147
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148 """
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149 Demonstrate stochastic gradient descent optimization of a log-linear
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150 model
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151
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152 This is demonstrated on MNIST.
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153
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154 :type learning_rate: float
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155 :param learning_rate: learning rate used (factor for the stochastic
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156 gradient)
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157
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158 :type nb_max_examples: int
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159 :param nb_max_examples: maximal number of epochs to run the optimizer
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160
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161 :type batch_size: int
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162 :param batch_size: size of the minibatch
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163
198
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164 :type dataset: dataset
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165 :param dataset: a dataset instance from ift6266.datasets
158
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166
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167 :type image_size: int
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168 :param image_size: size of the input image in pixels (width * height)
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169
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170 :type nb_class: int
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171 :param nb_class: number of classes
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172
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173 :type patience: int
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174 :param patience: look as this many examples regardless
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175
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176 :type patience_increase: int
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177 :param patience_increase: wait this much longer when a new best is found
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178
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179 :type improvement_threshold: float
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180 :param improvement_threshold: a relative improvement of this much is considered significant
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181
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182
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183 """
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184 #--------------------------------------------------------------------------------------------------------------------
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185 # Build actual model
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186 #--------------------------------------------------------------------------------------------------------------------
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187
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188 print '... building the model'
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189
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190 # allocate symbolic variables for the data
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191 index = T.lscalar( ) # index to a [mini]batch
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192 x = T.matrix('x') # the data is presented as rasterized images
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193 y = T.ivector('y') # the labels are presented as 1D vector of
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194 # [int] labels
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195
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196 # construct the logistic regression class
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197
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198 classifier = LogisticRegression( input = x, n_in = image_size, n_out = nb_class )
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199
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200 # the cost we minimize during training is the negative log likelihood of
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201 # the model in symbolic format
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202 cost = classifier.negative_log_likelihood( y )
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203
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204 # compiling a Theano function that computes the mistakes that are made by
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205 # the model on a minibatch
198
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206 test_model = theano.function( inputs = [ x, y ],
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207 outputs = classifier.errors( y ))
158
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208
198
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209 validate_model = theano.function( inputs = [ x, y ],
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210 outputs = classifier.errors( y ))
158
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211
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212 # compute the gradient of cost with respect to theta = ( W, b )
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213 g_W = T.grad( cost = cost, wrt = classifier.W )
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214 g_b = T.grad( cost = cost, wrt = classifier.b )
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215
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216 # specify how to update the parameters of the model as a dictionary
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217 updates = { classifier.W: classifier.W - learning_rate * g_W,\
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218 classifier.b: classifier.b - learning_rate * g_b}
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219
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220 # compiling a Theano function `train_model` that returns the cost, but in
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221 # the same time updates the parameter of the model based on the rules
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222 # defined in `updates`
198
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223 train_model = theano.function( inputs = [ x, y ],
158
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224 outputs = cost,
198
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diff changeset
225 updates = updates)
158
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226
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227 #--------------------------------------------------------------------------------------------------------------------
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228 # Train model
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229 #--------------------------------------------------------------------------------------------------------------------
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230
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231 print '... training the model'
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232 # early-stopping parameters
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233 patience = 5000 # look as this many examples regardless
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234 patience_increase = 2 # wait this much longer when a new best is
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235 # found
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236 improvement_threshold = 0.995 # a relative improvement of this much is
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237 # considered significant
198
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238 validation_frequency = patience * 0.5
158
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239 # go through this many
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240 # minibatche before checking the network
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241 # on the validation set; in this case we
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242 # check every epoch
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243
198
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diff changeset
244 best_params = None
158
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245 best_validation_loss = float('inf')
198
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diff changeset
246 test_score = 0.
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247 start_time = time.clock()
158
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248
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249 done_looping = False
198
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250 n_iters = nb_max_examples / batch_size
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diff changeset
251 epoch = 0
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252 iter = 0
158
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253
198
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diff changeset
254 while ( iter < n_iters ) and ( not done_looping ):
158
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255
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256 epoch = epoch + 1
198
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257 for x, y in dataset.train(batch_size):
158
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258
198
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259 minibatch_avg_cost = train_model( x, y )
158
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260 # iteration number
198
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261 iter += 1
158
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262
198
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263 if iter % validation_frequency == 0:
158
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264 # compute zero-one loss on validation set
198
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265 validation_losses = [ validate_model( xv, yv ) for xv, yv in dataset.valid(batch_size) ]
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266 this_validation_loss = numpy.mean( validation_losses )
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267
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268 print('epoch %i, iter %i, validation error %f %%' % \
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269 ( epoch, iter, this_validation_loss*100. ) )
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270
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271
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272 # if we got the best validation score until now
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273 if this_validation_loss < best_validation_loss:
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274 #improve patience if loss improvement is good enough
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275 if this_validation_loss < best_validation_loss * \
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276 improvement_threshold :
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277 patience = max( patience, iter * patience_increase )
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278
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279 best_validation_loss = this_validation_loss
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280 # test it on the test set
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281
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282 test_losses = [test_model(xt, yt) for xt, yt in dataset.test(batch_size)]
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283 test_score = numpy.mean(test_losses)
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284
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285 print((' epoch %i, iter %i, test error of best '
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286 'model %f %%') % \
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287 (epoch, iter, test_score*100.))
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288
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289 if patience <= iter :
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290 done_looping = True
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291 break
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292
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293 end_time = time.clock()
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294 print(('Optimization complete with best validation score of %f %%,'
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295 'with test performance %f %%') %
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296 ( best_validation_loss * 100., test_score * 100.))
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297 print ('The code ran for %f minutes' % ((end_time-start_time) / 60.))
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298
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299 ###### return validation_error, test_error, nb_exemples, time
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300
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301 if __name__ == '__main__':
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302 log_reg()
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303
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304
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305 def jobman_log_reg(state, channel):
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306 (validation_error, test_error, nb_exemples, time) = log_reg( learning_rate = state.learning_rate,\
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307 nb_max_examples = state.nb_max_examples,\
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308 batch_size = state.batch_size,\
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309 dataset_name = state.dataset_name, \
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310 image_size = state.image_size, \
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311 nb_class = state.nb_class )
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312
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313 state.validation_error = validation_error
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314 state.test_error = test_error
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315 state.nb_exemples = nb_exemples
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316 state.time = time
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317 return channel.COMPLETE
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318
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319
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320
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321
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322
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323