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author Frederic Bastien <nouiz@nouiz.org>
date Fri, 17 Sep 2010 16:19:17 -0400
parents 21d25bed2ce9
children 0e12ea6ba661
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1
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2 Use Cases (Functional Requirements)
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3 ===================================
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4
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5 These use cases exhibit pseudo-code for some of the sorts of tasks listed in the
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6 requirements (requirements.txt)
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8
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9 Evaluate a classifier on MNIST
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10 -------------------------------
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11
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12 The evaluation of a classifier on MNIST requires iterating over examples in some
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13 set (e.g. validation, test) and comparing the model's prediction with the
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14 correct answer. The score of the classifier is the number of correct
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15 predictions divided by the total number of predictions.
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16
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17 To perform this calculation, the user should specify:
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18 - the classifier (e.g. a function operating on weights loaded from disk)
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19 - the dataset (e.g. MNIST)
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20 - the subset of examples on which to evaluate (e.g. test set)
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21
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22 For example:
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23
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24 vm.call(classification_accuracy(
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25 function = classifier,
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26 examples = MNIST.validation_iterator))
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29 The user types very few things beyond the description of the fields necessary
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30 for the computation, no boilerplate. The `MNIST.validation_iterator` must
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31 respect a protocol that remains to be worked out.
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32
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33 The `vm.call` is a compilation & execution step, as opposed to the
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34 symbolic-graph building performed by the `classification_accuracy` call.
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37
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38 Train a linear classifier on MNIST
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39 ----------------------------------
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40
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41 The training of a linear classifier requires specification of
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42
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43 - problem dimensions (e.g. n. of inputs, n. of classes)
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44 - parameter initialization method
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45 - regularization
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46 - dataset
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47 - schedule for obtaining training examples (e.g. batch, online, minibatch,
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48 weighted examples)
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49 - algorithm for adapting parameters (e.g. SGD, Conj. Grad)
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50 - a stopping criterion (may be in terms of validation examples)
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51
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52 Often the dataset determines the problem dimensions.
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53
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54 Often the training examples and validation examples come from the same set (e.g.
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55 a large matrix of all examples) but this is not necessarily the case.
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56
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57 There are many ways that the training could be configured, but here is one:
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58
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59
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60 vm.call(
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61 halflife_stopper(
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62 # OD: is n_hidden supposed to be n_classes instead?
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63 initial_model=random_linear_classifier(MNIST.n_inputs, MNIST.n_hidden, r_seed=234432),
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64 burnin=100,
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65 score_fn = vm_lambda(('learner_obj',),
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66 classification_accuracy(
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67 examples=MNIST.validation_dataset,
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68 function=as_classifier('learner_obj'))),
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69
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70 step_fn = vm_lambda(('learner_obj',),
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71 sgd_step_fn(
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72 parameters = vm_getattr('learner_obj', 'params'),
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73 cost_and_updates=classif_nll('learner_obj',
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74 example_stream=minibatches(
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75 source=MNIST.training_dataset,
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76 batchsize=100,
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77 loop=True)),
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78 momentum=0.9,
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79 anneal_at_iter=50,
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80 n_iter=100))) #step_fn goes through lots of examples (e.g. an epoch)
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81
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82 Although I expect this specific code might have to change quite a bit in a final
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83 version, I want to draw attention to a few aspects of it:
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84
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85 - we build a symbolic expression graph that contains the whole program, not just
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86 the learning algorithm
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87
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88 - the configuration language allows for callable objects (e.g. functions,
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89 curried functions) to be arguments
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90
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91 - there is a lambda function-constructor (vm_lambda) we can use in this language
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92
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93 - APIs and protocols are at work in establishing conventions for
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94 parameter-passing so that sub-expressions (e.g. datasets, optimization
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95 algorithms, etc.) can be swapped.
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96
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97 - there are no APIs for things which are not passed as arguments (i.e. the logic
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98 of the whole program is not exposed via some uber-API).
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99
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100 OD comments: I didn't have time to look closely at the details, but overall I
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101 like the general feel of it. At least I'd expect us to need something like
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102 that to be able to handle the multiple use cases we want to support. I must
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103 say I'm a bit worried though that it could become scary pretty fast to the
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104 newcomer, with 'lambda functions' and 'virtual machines'.
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105 Anyway, one point I would like to comment on is the line that creates the
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106 linear classifier. I hope that, as much as possible, we can avoid the need to
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107 specify dataset dimensions / number of classes in algorithm constructors. I
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108 regularly had issues in PLearn with the fact we had for instance to give the
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109 number of inputs when creating a neural network. I much prefer when this kind
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110 of thing can be figured out at runtime:
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111 - Any parameter you can get rid of is a significant gain in
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112 user-friendliness.
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113 - It's not always easy to know in advance e.g. the dimension of your input
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114 dataset. Imagine for instance this dataset is obtained in a first step
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115 by going through a PCA whose number of output dimensions is set so as to
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116 keep 90% of the variance.
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117 - It seems to me it fits better the idea of a symbolic graph: my intuition
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118 (that may be very different from what you actually have in mind) is to
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119 see an experiment as a symbolic graph, which you instantiate when you
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120 provide the input data. One advantage of this point of view is it makes
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121 it natural to re-use the same block components on various datasets /
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122 splits, something we often want to do.
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123
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124 K-fold cross validation of a classifier
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125 ---------------------------------------
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126
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127 splits = kfold_cross_validate(
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128 # OD: What would these parameters mean?
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129 indexlist = range(1000)
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130 train = 8,
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131 valid = 1,
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132 test = 1,
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133 )
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134
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135 trained_models = [
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136 halflife_early_stopper(
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137 initial_model=alloc_model('param1', 'param2'),
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138 burnin=100,
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139 score_fn = vm_lambda(('learner_obj',),
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140 classification_error(
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141 function=as_classifier('learner_obj'),
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142 dataset=MNIST.subset(validation_set))),
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143 step_fn = vm_lambda(('learner_obj',),
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144 sgd_step_fn(
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145 parameters = vm_getattr('learner_obj', 'params'),
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146 cost_and_updates=classif_nll('learner_obj',
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147 example_stream=minibatches(
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148 source=MNIST.subset(train_set),
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149 batchsize=100,
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150 loop=True)),
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151 n_iter=100)))
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152 for (train_set, validation_set, test_set) in splits]
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153
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154 vm.call(trained_models, param1=1, param2=2)
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155 vm.call(trained_models, param1=3, param2=4)
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156
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157 I want to draw attention to the fact that the call method treats the expression
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158 tree as one big lambda expression, with potentially free variables that must be
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159 assigned - here the 'param1' and 'param2' arguments to `alloc_model`. There is
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160 no need to have separate compile and run steps like in Theano because these
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161 functions are expected to be long-running, and called once.
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162
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163
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164 Analyze the results of the K-fold cross validation
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165 --------------------------------------------------
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166
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167 It often happens that a user doesn't know what statistics to compute *before*
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168 running a bunch of learning jobs, but only afterward. This can be done by
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169 extending the symbolic program, and calling the extended function.
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170
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171 vm.call(
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172 [pylearn.min(pylearn_getattr(model, 'weights')) for model in trained_models],
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173 param1=1, param2=2)
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174
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175 If this is run after the previous calls:
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176
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177 vm.call(trained_models, param1=1, param2=2)
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178 vm.call(trained_models, param1=3, param2=4)
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179
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180 Then it should run very quickly, because the `vm` can cache the return values of
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181 the trained_models when param1=1 and param2=2.
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182
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183