annotate linear_regression.py @ 110:8fa1ef2411a0

Worked on OneShotTLearner and implementation of LinearRegression
author bengioy@bengiomac.local
date Tue, 06 May 2008 22:24:55 -0400
parents c4916445e025
children 88257dfedf8c
rev   line source
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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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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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24 output_t = b + W * input_t
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26 where b and W are obtained by minimizing::
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28 lambda sum_{ij} W_{ij}^2 + sum_t ||output_t - target_t||^2
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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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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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42 The fields and attributes expected and produced by use and update are the following:
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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 - 'parameters' = (b, W) tuple
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60 - 'regularization_term'
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61 - 'XtX'
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62 - 'XtY'
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64 """
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66 def attributeNames(self):
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67 return ["lambda","parameters","b","W","regularization_term","XtX","XtY"]
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69 def useInputAttributes(self):
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70 return ["b","W"]
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72 def useOutputAttributes(self):
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73 return []
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75 def updateInputAttributes(self):
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76 return ["lambda","XtX","XtY"]
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78 def updateOutputAttributes(self):
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79 return ["parameters"] + self.updateMinibatchOutputAttributes() + self.updateEndOutputAttributes()
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81 def updateMinibatchInputFields(self):
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82 return ["input","target"]
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83
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84 def updateMinibatchInputAttributes(self):
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85 return ["XtX","XtY"]
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87 def updateMinibatchOutputAttributes(self):
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88 return ["new_XtX","new_XtY"]
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89
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90 def updateEndInputAttributes(self):
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91 return ["theta","XtX","XtY"]
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93 def updateEndOutputAttributes(self):
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94 return ["new_theta","b","W","regularization_term"] # CHECK: WILL b AND W CONTAIN OLD OR NEW THETA? @todo i.e. order of computation = ?
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96 def defaultOutputFields(self, input_fields):
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97 output_fields = ["output"]
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98 if "target" in input_fields:
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99 output_fields.append("squared_error")
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100 return output_fields
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101
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102 def __init__(self):
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103 self._input = t.matrix('input') # n_examples x n_inputs
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104 self._target = t.matrix('target') # n_examples x n_outputs
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105 self._lambda = as_scalar(0.,'lambda')
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106 self._theta = t.matrix('theta')
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107 self._W = self._theta[:,1:]
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108 self._b = self._theta[:,0]
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109 self._XtX = t.matrix('XtX')
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110 self._XtY = t.matrix('XtY')
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111 self._extended_input = t.prepend_one_to_each_row(self._input)
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112 self._output = t.dot(self._input,self._W.T) + self._b # (n_examples , n_outputs) matrix
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113 self._squared_error = t.sum_within_rows(t.sqr(self._output-self._target)) # (n_examples ) vector
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114 self._regularizer = self._lambda * t.dot(self._W,self._W)
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115 self._new_XtX = add_inplace(self._XtX,t.dot(self._extended_input.T,self._extended_input))
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116 self._new_XtY = add_inplace(self._XtY,t.dot(self._extended_input.T,self._target))
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117 self._new_theta = t.solve_inplace(self._theta,self._XtX,self._XtY)
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118
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119 OneShotTLearner.__init__(self)
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120 self.allocate()
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121
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122 def allocate(self,minibatch):
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123 minibatch_n_inputs = minibatch["input"].shape[1]
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124 minibatch_n_outputs = minibatch["target"].shape[1]
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125 if not self._n_inputs:
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126 self._n_inputs = minibatch_n_inputs
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127 self._n_outputs = minibatch_n_outputs
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128 self.XtX = numpy.zeros((1+self._n_inputs,1+self._n_inputs))
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129 self.XtY = numpy.zeros((1+self._n_inputs,self._n_outputs))
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130 self.theta = numpy.zeros((self._n_outputs,1+self._n_inputs))
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131 self.forget()
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132 elif self._n_inputs!=minibatch_n_inputs or self._n_outputs!=minibatch_n_outputs:
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133 # if the input or target changes dimension on the fly, we forget everything
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134 self.forget()
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135
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136 def forget(self):
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137 if self._n_inputs and self._n_outputs:
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138 self.XtX.resize((1+self.n_inputs,1+self.n_inputs))
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139 self.XtY.resize((1+self.n_inputs,self.n_outputs))
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140 self.XtX.data[:,:]=0
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141 self.XtY.data[:,:]=0
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142 numpy.diag(self.XtX.data)[1:]=self.lambda
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143
110
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144 def updateEnd(self):
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145 TLearner.updateEnd(self)
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146 self.parameters = (self.W,self.b)
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147