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annotate linear_regression.py @ 107:c4916445e025

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Comments from Pascal V.
author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Tue, 06 May 2008 19:54:43 -0400
parents c4726e19b8ec
children 8fa1ef2411a0
rev   line source
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1
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2 from learner import *
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3 from theano import tensor as t
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4 from compile import Function
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5 from theano.scalar import as_scalar
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6
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7 # this is one of the simplest example of learner, and illustrates
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8 # the use of theano
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9 class LinearRegression(OneShotTLearner):
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10 """
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11 Implement linear regression, with or without L2 regularization
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12 (the former is called Ridge Regression and the latter Ordinary Least Squares).
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14 The predictor parameters are obtained analytically from the training set.
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15 Training can proceed sequentially (with multiple calls to update with
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16 different disjoint subsets of the training sets). After each call to
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17 update the predictor is ready to be used (and optimized for the union
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18 of all the training sets passed to update since construction or since
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19 the last call to forget).
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21 The L2 regularization coefficient is obtained analytically.
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22 For each (input[t],output[t]) pair in a minibatch,::
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23
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24 output_t = b + W * input_t
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25
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26 where b and W are obtained by minimizing::
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27
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28 lambda sum_{ij} W_{ij}^2 + sum_t ||output_t - target_t||^2
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29
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30 Let X be the whole training set inputs matrix (one input example per row),
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31 with the first column full of 1's, and Let Y the whole training set
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32 targets matrix (one example's target vector per row).
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33 Let theta = the matrix with b in its first column and W in the others,
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34 then each theta[:,i] is the solution of the linear system::
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36 XtX * theta[:,i] = XtY[:,i]
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37
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38 where XtX is a (n_inputs+1)x(n_inputs+1) matrix containing X'*X
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39 plus lambda on the diagonal except at (0,0),
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40 and XtY is a (n_inputs+1)*n_outputs matrix containing X'*Y.
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41
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42 The fields and attributes expected and produced by use and update are the following:
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43
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44 - Input and output fields (example-wise quantities):
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46 - 'input' (always expected by use and update as an input_dataset field)
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47 - 'target' (optionally expected by use and update as an input_dataset field)
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48 - 'output' (optionally produced by use as an output dataset field)
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49 - 'squared_error' (optionally produced by use as an output dataset field, needs 'target') = example-wise squared error
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51 - optional attributes (optionally expected as input_dataset attributes)
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52 (warning, this may be dangerous, the 'use' method will use those provided in the
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53 input_dataset rather than those learned during 'update'; currently no support
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54 for providing these to update):
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56 - 'lambda'
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57 - 'b'
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58 - 'W'
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59 - 'regularization_term'
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61 """
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62
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63 def attributeNames(self):
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64 return ["lambda","b","W","regularization_term"]
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67 def __init__(self):
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68 self.input = t.matrix('input') # n_examples x n_inputs
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69 self.target = t.matrix('target') # n_examples x n_outputs
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70 self.lambda = as_scalar(0.,'lambda')
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71 self.theta = t.matrix('theta')
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72 self.W = self.theta[:,1:]
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73 self.b = self.theta[:,0]
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74 self.XtX = t.matrix('XtX')
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75 self.XtY = t.matrix('XtY')
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76 self.regularizer = self.lambda * t.dot(self.W,self.W)
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77 self.squared_error =
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78 self.loss = self.regularizer + t.sum(self.squared_error) # this only makes sense if the whole training set fits in memory in a minibatch
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79 self.loss_function = Function([self.W,self.lambda,self.squared_error],[self.loss])
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80 self.new_XtX = self.XtX + t.dot(self.extended_input.T,self.extended_input)
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81 self.new_XtY = self.XtY + t.dot(self.extended_input.T,self.target)
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82 self.new_theta = t.solve(self.XtX,self.XtY)
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83
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84 def initialize(self):
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85 self.XtX.resize((1+self.n_inputs,1+self.n_inputs))
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86 self.XtY.resize((1+self.n_inputs,self.n_outputs))
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87 self.XtX.data[:,:]=0
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88 self.XtY.data[:,:]=0
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89 numpy.diag(self.XtX.data)[1:]=self.lambda.data
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90
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91 def updated_variables(self):
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92
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93 def minibatch_wise_inputs(self):
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94 def minibatch_wise_outputs(self):
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95 # self.input is a (n_examples, n_inputs) minibatch matrix
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96 self.extended_input = t.prepend_one_to_each_row(self.input)
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97 self.output = t.dot(self.input,self.W.T) + self.b # (n_examples , n_outputs) matrix
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98 self.squared_error = t.sum_within_rows(t.sqr(self.output-self.target)) # (n_examples ) vector
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99
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100 def attributeNames(self):
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101 return ["lambda","b","W","regularization_term","XtX","XtY"]
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102
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103 def defaultOutputFields(self, input_fields):
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104 output_fields = ["output"]
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105 if "target" in input_fields:
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106 output_fields.append("squared_error")
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107 return output_fields
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108
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109 # poutine generale basee sur ces fonctions
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110
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111
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112 def __init__(self,lambda=0.,max_memory_use=500):
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113 """
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114 @type lambda: float
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115 @param lambda: regularization coefficient
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116 """
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117
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118 W=t.matrix('W')
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119 # b is a broadcastable row vector (can be replicated into
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120 # as many rows as there are examples in the minibach)
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121 b=t.row('b')
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122 minibatch_input = t.matrix('input') # n_examples x n_inputs
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123 minibatch_target = t.matrix('target') # n_examples x n_outputs
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124 minibatch_output = t.dot(minibatch_input,W.T) + b # n_examples x n_outputs
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125 lambda = as_scalar(lambda)
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126 regularizer = self.lambda * t.dot(W,W)
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127 example_squared_error = t.sum_within_rows(t.sqr(minibatch_output-minibatch_target))
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128 self.output_function = Function([W,b,minibatch_input],[minibatch_output])
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129 self.squared_error_function = Function([minibatch_output,minibatch_target],[self.example_squared_error])
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130 self.loss_function = Function([W,squared_error],[self.regularizer + t.sum(self.example_squared_error)])
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131 self.W=None
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132 self.b=None
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133 self.XtX=None
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134 self.XtY=None
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135
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136 def forget(self):
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137 if self.W:
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138 self.XtX *= 0
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139 self.XtY *= 0
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140
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141 def use(self,input_dataset,output_fieldnames=None,copy_inputs=True):
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142 input_fieldnames = input_dataset.fieldNames()
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143 assert "input" in input_fieldnames
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144 if not output_fields:
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145 output_fields = ["output"]
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146 if "target" in input_fieldnames:
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147 output_fields += ["squared_error"]
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148 else:
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149 if "squared_error" in output_fields or "total_loss" in output_fields:
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150 assert "target" in input_fieldnames
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151
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152 use_functions = []
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153 for output_fieldname in output_fieldnames:
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154 if output_fieldname=="output":
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155 use_functions.append(self.output_function)
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156 elif output_fieldname=="squared_error":
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157 use_functions.append(lambda self.output_function)
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158
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159 n_examples = len(input_dataset)
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160
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161 for minibatch in input_dataset.minibatches(minibatch_size=minibatch_size, allow_odd_last_minibatch=True):
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162 use_function(
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163