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fixed indentation.
author Frederic Bastien <nouiz@nouiz.org>
date Fri, 25 Feb 2011 16:38:33 -0500
parents 0e12ea6ba661
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2 Use Cases (Functional Requirements)
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3 ===================================
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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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9 Evaluate a classifier on MNIST
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10 -------------------------------
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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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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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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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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 .. code-block:: python
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61 vm.call(
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62 halflife_stopper(
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63 # OD: is n_hidden supposed to be n_classes instead?
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64 initial_model=random_linear_classifier(MNIST.n_inputs, MNIST.n_hidden, r_seed=234432),
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65 burnin=100,
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66 score_fn = vm_lambda(('learner_obj',),
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67 classification_accuracy(
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68 examples=MNIST.validation_dataset,
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69 function=as_classifier('learner_obj'))),
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70
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71 step_fn = vm_lambda(('learner_obj',),
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72 sgd_step_fn(
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73 parameters = vm_getattr('learner_obj', 'params'),
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74 cost_and_updates=classif_nll('learner_obj',
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75 example_stream=minibatches(
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76 source=MNIST.training_dataset,
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77 batchsize=100,
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78 loop=True)),
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79 momentum=0.9,
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80 anneal_at_iter=50,
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81 n_iter=100))) #step_fn goes through lots of examples (e.g. an epoch)
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82
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83 Although I expect this specific code might have to change quite a bit in a final
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84 version, I want to draw attention to a few aspects of it:
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85
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86 - we build a symbolic expression graph that contains the whole program, not just
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87 the learning algorithm
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88
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89 - the configuration language allows for callable objects (e.g. functions,
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90 curried functions) to be arguments
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91
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92 - there is a lambda function-constructor (vm_lambda) we can use in this language
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93
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94 - APIs and protocols are at work in establishing conventions for
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95 parameter-passing so that sub-expressions (e.g. datasets, optimization
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96 algorithms, etc.) can be swapped.
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97
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98 - there are no APIs for things which are not passed as arguments (i.e. the logic
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99 of the whole program is not exposed via some uber-API).
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100
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101 OD comments: I didn't have time to look closely at the details, but overall I
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102 like the general feel of it. At least I'd expect us to need something like
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103 that to be able to handle the multiple use cases we want to support. I must
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104 say I'm a bit worried though that it could become scary pretty fast to the
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105 newcomer, with 'lambda functions' and 'virtual machines'.
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106 Anyway, one point I would like to comment on is the line that creates the
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107 linear classifier. I hope that, as much as possible, we can avoid the need to
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108 specify dataset dimensions / number of classes in algorithm constructors. I
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109 regularly had issues in PLearn with the fact we had for instance to give the
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110 number of inputs when creating a neural network. I much prefer when this kind
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111 of thing can be figured out at runtime:
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112
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113 - Any parameter you can get rid of is a significant gain in
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114 user-friendliness.
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115 - It's not always easy to know in advance e.g. the dimension of your input
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116 dataset. Imagine for instance this dataset is obtained in a first step
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117 by going through a PCA whose number of output dimensions is set so as to
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118 keep 90% of the variance.
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119 - It seems to me it fits better the idea of a symbolic graph: my intuition
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120 (that may be very different from what you actually have in mind) is to
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121 see an experiment as a symbolic graph, which you instantiate when you
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122 provide the input data. One advantage of this point of view is it makes
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123 it natural to re-use the same block components on various datasets /
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124 splits, something we often want to do.
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125
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126 K-fold cross validation of a classifier
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127 ---------------------------------------
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128
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129 .. code-block:: python
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130
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131 splits = kfold_cross_validate(
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132 # OD: What would these parameters mean?
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133 indexlist = range(1000)
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134 train = 8,
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135 valid = 1,
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136 test = 1,
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137 )
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138
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139 trained_models = [
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140 halflife_early_stopper(
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141 initial_model=alloc_model('param1', 'param2'),
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142 burnin=100,
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143 score_fn = vm_lambda(('learner_obj',),
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144 classification_error(
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145 function=as_classifier('learner_obj'),
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146 dataset=MNIST.subset(validation_set))),
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147 step_fn = vm_lambda(('learner_obj',),
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148 sgd_step_fn(
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149 parameters = vm_getattr('learner_obj', 'params'),
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150 cost_and_updates=classif_nll('learner_obj',
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151 example_stream=minibatches(
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152 source=MNIST.subset(train_set),
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153 batchsize=100,
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154 loop=True)),
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155 n_iter=100)))
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156 for (train_set, validation_set, test_set) in splits]
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157
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158 vm.call(trained_models, param1=1, param2=2)
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159 vm.call(trained_models, param1=3, param2=4)
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160
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161 I want to draw attention to the fact that the call method treats the expression
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162 tree as one big lambda expression, with potentially free variables that must be
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163 assigned - here the 'param1' and 'param2' arguments to `alloc_model`. There is
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164 no need to have separate compile and run steps like in Theano because these
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165 functions are expected to be long-running, and called once.
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166
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167
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168 Analyze the results of the K-fold cross validation
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169 --------------------------------------------------
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170
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171 It often happens that a user doesn't know what statistics to compute *before*
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172 running a bunch of learning jobs, but only afterward. This can be done by
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173 extending the symbolic program, and calling the extended function.
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174
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175 vm.call(
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176 [pylearn.min(pylearn_getattr(model, 'weights')) for model in trained_models],
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177 param1=1, param2=2)
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178
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179 If this is run after the previous calls:
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180
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181 vm.call(trained_models, param1=1, param2=2)
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182 vm.call(trained_models, param1=3, param2=4)
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183
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184 Then it should run very quickly, because the `vm` can cache the return values of
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185 the trained_models when param1=1 and param2=2.
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186
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187