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annotate linear_regression.py @ 90:a289b8bed64c

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corrected comment
author Frederic Bastien <bastienf@iro.umontreal.ca>
date Mon, 05 May 2008 17:13:07 -0400
parents 3499918faa9d
children c4726e19b8ec
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(Learner):
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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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13
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14 The predictor is obtained analytically.
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15
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16 The L2 regularization coefficient is obtained analytically.
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17 For each (input[t],output[t]) pair in a minibatch,::
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18
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19 output_t = b + W * input_t
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20
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21 where b and W are obtained by minimizing::
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22
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23 lambda sum_{ij} W_{ij}^2 + sum_t ||output_t - target_t||^2
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24
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25 Let X be the whole training set inputs matrix (one input example per row),
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26 with the first column full of 1's, and Let Y the whole training set
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27 targets matrix (one example's target vector per row).
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28 Let theta = the matrix with b in its first column and W in the others,
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29 then each theta[:,i] is the solution of the linear system::
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30
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31 XtX * theta[:,i] = XtY[:,i]
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32
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33 where XtX is a (n_inputs+1)x(n_inputs+1) matrix containing X'*X
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34 plus lambda on the diagonal except at (0,0),
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35 and XtY is a (n_inputs+1)*n_outputs matrix containing X'*Y.
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36
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37 The fields and attributes expected and produced by use and update are the following:
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38
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39 - Input and output fields (example-wise quantities):
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40
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41 - 'input' (always expected by use and update as an input_dataset field)
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42 - 'target' (optionally expected by use and update as an input_dataset field)
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43 - 'output' (optionally produced by use as an output dataset field)
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44 - 'squared_error' (optionally produced by use as an output dataset field, needs 'target') = example-wise squared error
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45
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46 - optional input attributes (optionally expected as input_dataset attributes)
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47
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48 - 'lambda' (only used by update)
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49 - 'b' (only used by use)
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50 - 'W' (only used by use)
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51
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52 - optional output attributes (available in self and optionally in output dataset)
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53
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54 - 'b' (only set by update)
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55 - 'W' (only set by update)
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56 - 'regularization_term' (only set by update)
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57 - 'XtX' (only set by update)
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58 - 'XtY' (only set by update)
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59
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60 """
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61
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62 # definitions specifiques a la regression lineaire:
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63
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64 def global_inputs(self):
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65 self.lambda = as_scalar(0.,'lambda')
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66 self.theta = t.matrix('theta')
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67 self.W = self.theta[:,1:]
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68 self.b = self.theta[:,0]
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69 self.XtX = t.matrix('XtX')
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70 self.XtY = t.matrix('XtY')
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71
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72 def global_outputs(self):
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73 self.regularizer = self.lambda * t.dot(self.W,self.W)
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74 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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75 self.loss_function = Function([self.W,self.lambda,self.squared_error],[self.loss])
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76
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77 def initialize(self):
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78 self.XtX.resize((1+self.n_inputs,1+self.n_inputs))
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79 self.XtY.resize((1+self.n_inputs,self.n_outputs))
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80 self.XtX.data[:,:]=0
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81 self.XtY.data[:,:]=0
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82 numpy.diag(self.XtX.data)[1:]=self.lambda.data
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83
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84 def updated_variables(self):
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85 self.new_XtX = self.XtX + t.dot(self.extended_input.T,self.extended_input)
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86 self.new_XtY = self.XtY + t.dot(self.extended_input.T,self.target)
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87 self.new_theta = t.solve(self.XtX,self.XtY)
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88
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89 def minibatch_wise_inputs(self):
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90 self.input = t.matrix('input') # n_examples x n_inputs
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91 self.target = t.matrix('target') # n_examples x n_outputs
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92
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93 def minibatch_wise_outputs(self):
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94 # self.input is a (n_examples, n_inputs) minibatch matrix
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95 self.extended_input = t.prepend_one_to_each_row(self.input)
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96 self.output = t.dot(self.input,self.W.T) + self.b # (n_examples , n_outputs) matrix
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97 self.squared_error = t.sum_within_rows(t.sqr(self.output-self.target)) # (n_examples ) vector
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98
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99 def attributeNames(self):
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100 return ["lambda","b","W","regularization_term","XtX","XtY"]
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101
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102 def defaultOutputFields(self, input_fields):
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103 output_fields = ["output"]
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104 if "target" in input_fields:
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105 output_fields.append("squared_error")
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106 return output_fields
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107
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108 # poutine generale basee sur ces fonctions
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109
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110 def minibatchwise_use_functions(self, input_fields, output_fields, stats_collector):
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111 if not output_fields:
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112 output_fields = self.defaultOutputFields(input_fields)
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113 if stats_collector:
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114 stats_collector_inputs = stats_collector.inputUpdateAttributes()
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115 for attribute in stats_collector_inputs:
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116 if attribute not in input_fields:
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117 output_fields.append(attribute)
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118 key = (input_fields,output_fields)
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119 if key not in self.use_functions_dictionary:
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120 self.use_functions_dictionary[key]=Function(self.names2attributes(input_fields),
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121 self.names2attributes(output_fields))
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122 return self.use_functions_dictionary[key]
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123
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124 def attributes(self,return_copy=False):
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125 return self.names2attributes(self.attributeNames())
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126
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127 def names2attributes(self,names,return_Result=False, return_copy=False):
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128 if return_Result:
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129 if return_copy:
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130 return [copy.deepcopy(self.__getattr__(name)) for name in names]
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131 else:
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132 return [self.__getattr__(name) for name in names]
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133 else:
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134 if return_copy:
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135 return [copy.deepcopy(self.__getattr__(name).data) for name in names]
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136 else:
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137 return [self.__getattr__(name).data for name in names]
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138
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139 def use(self,input_dataset,output_fieldnames=None,test_stats_collector=None,copy_inputs=True):
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140 minibatchwise_use_function = minibatchwise_use_functions(input_dataset.fieldNames(),output_fieldnames,test_stats_collector)
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141 virtual_output_dataset = ApplyFunctionDataSet(input_dataset,
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142 minibatchwise_use_function,
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143 True,DataSet.numpy_vstack,
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144 DataSet.numpy_hstack)
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145 # actually force the computation
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146 output_dataset = CachedDataSet(virtual_output_dataset,True)
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147 if copy_inputs:
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148 output_dataset = input_dataset | output_dataset
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149 # compute the attributes that should be copied in the dataset
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150 output_dataset.setAttributes(self.attributeNames(),self.attributes(return_copy=True))
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151 if test_stats_collector:
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152 test_stats_collector.update(output_dataset)
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153 for attribute in test_stats_collector.attributeNames():
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154 output_dataset[attribute] = copy.deepcopy(test_stats_collector[attribute])
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155 return output_dataset
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156
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157 def update(self,training_set,train_stats_collector=None):
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158 self.update_start()
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159 for minibatch in training_set.minibatches(self.training_set_input_fields, minibatch_size=self.minibatch_size):
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160 self.update_minibatch(minibatch)
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161 if train_stats_collector:
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162 minibatch_set = minibatch.examples()
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163 minibatch_set.setAttributes(self.attributeNames(),self.attributes())
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164 train_stats_collector.update(minibatch_set)
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165 self.update_end()
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166 return self.use
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167
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168 def __init__(self,lambda=0.,max_memory_use=500):
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169 """
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170 @type lambda: float
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171 @param lambda: regularization coefficient
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172 """
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173
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174 W=t.matrix('W')
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175 # b is a broadcastable row vector (can be replicated into
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176 # as many rows as there are examples in the minibach)
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177 b=t.row('b')
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178 minibatch_input = t.matrix('input') # n_examples x n_inputs
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179 minibatch_target = t.matrix('target') # n_examples x n_outputs
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180 minibatch_output = t.dot(minibatch_input,W.T) + b # n_examples x n_outputs
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181 lambda = as_scalar(lambda)
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182 regularizer = self.lambda * t.dot(W,W)
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183 example_squared_error = t.sum_within_rows(t.sqr(minibatch_output-minibatch_target))
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184 self.output_function = Function([W,b,minibatch_input],[minibatch_output])
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185 self.squared_error_function = Function([minibatch_output,minibatch_target],[self.example_squared_error])
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186 self.loss_function = Function([W,squared_error],[self.regularizer + t.sum(self.example_squared_error)])
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187 self.W=None
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188 self.b=None
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189 self.XtX=None
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190 self.XtY=None
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191
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192 def forget(self):
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193 if self.W:
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194 self.XtX *= 0
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195 self.XtY *= 0
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196
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197 def use(self,input_dataset,output_fieldnames=None,copy_inputs=True):
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198 input_fieldnames = input_dataset.fieldNames()
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199 assert "input" in input_fieldnames
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200 if not output_fields:
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201 output_fields = ["output"]
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202 if "target" in input_fieldnames:
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203 output_fields += ["squared_error"]
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204 else:
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205 if "squared_error" in output_fields or "total_loss" in output_fields:
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206 assert "target" in input_fieldnames
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207
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208 use_functions = []
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209 for output_fieldname in output_fieldnames:
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210 if output_fieldname=="output":
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211 use_functions.append(self.output_function)
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212 elif output_fieldname=="squared_error":
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213 use_functions.append(lambda self.output_function)
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214
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215 n_examples = len(input_dataset)
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216
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217 for minibatch in input_dataset.minibatches(minibatch_size=minibatch_size, allow_odd_last_minibatch=True):
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218 use_function(
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219