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annotate doc/v2_planning/learner.txt @ 1036:89e76e6e074f

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XG added to optimization team
author Xavier Glorot <glorotxa@iro.umontreal.ca>
date Tue, 07 Sep 2010 12:08:37 -0400
parents 38f799f8b6cd
children 88b296cfba50
rev   line source
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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2 Discussion of Function Specification for Learner Types
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3 ======================================================
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5 In its most abstract form, a learner is an object with the
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6 following semantics:
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7
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8 * A learner has named hyper-parameters that control how it learns (these can be viewed
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9 as options of the constructor, or might be set directly by a user)
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11 * A learner also has an internal state that depends on what it has learned.
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12
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13 * A learner reads and produces data, so the definition of learner is
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14 intimately linked to the definition of dataset (and task).
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15
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16 * A learner has one or more 'train' or 'adapt' functions by which
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17 it is given a sample of data (typically either the whole training set, or
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18 a mini-batch, which contains as a special case a single 'example'). Learners
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19 interface with datasets in order to obtain data. These functions cause the
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20 learner to change its internal state and take advantage to some extent
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21 of the data provided. The 'train' function should take charge of
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22 completely exploiting the dataset, as specified per the hyper-parameters,
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23 so that it would typically be called only once. An 'adapt' function
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24 is meant for learners that can operate in an 'online' setting where
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25 data continually arrive and the control loop (when to stop) is to
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26 be managed outside of it. For most intents and purposes, the
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27 'train' function could also handle the 'online' case by providing
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28 the controlled iterations over the dataset (which would then be
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29 seen as a stream of examples).
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30 * learner.train(dataset)
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31 * learner.adapt(data)
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32
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33 * Different types of learners can then exploit their internal state
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34 in order to perform various computations after training is completed,
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35 or in the middle of training, e.g.,
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36
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37 * y=learner.predict(x)
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38 for learners that see (x,y) pairs during training and predict y given x,
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39 or for learners that see only x's and learn a transformation of it (i.e. feature extraction).
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40 Here and below, x and y are tensor-like objects whose first index iterates
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41 over particular examples in a batch or minibatch of examples.
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42
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43 * p=learner.probability(examples)
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44 p=learner.log_probability(examples)
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45 for learners that can estimate probability density or probability functions,
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46 note that example could be a pair (x,y) for learners that expect each example
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47 to represent such a pair. The second form is provided in case the example
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48 is high-dimensional and computations in the log-domain are numerically preferable.
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49 The first dimension of examples or of x and y is an index over a minibatch or a dataset.
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50
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51 * p=learner.free_energy(x)
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52 for learners that can estimate a log unnormalized probability; the output has the same length as the input.
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53
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54 * c=learner.costs(examples)
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55 returns a matrix of costs (one row per example, i.e., again the output has the same length
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56 as the input), the first column of which represents the cost whose expectation
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57 we wish to minimize over new samples from the unknown underlying data distribution.
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60 Some learners may be able to handle x's and y's that contain missing values.
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61
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62 * For convenience, some of these operations could be bundled, e.g.
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63
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64 * [prediction,costs] = learner.predict_and_adapt((x,y))
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65
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66 * Some learners could include in their internal state not only what they
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67 have learned but some information about recently seen examples that conditions
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68 the expected distribution of upcoming examples. In that case, they might
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69 be used, e.g. in an online setting as follows:
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70 for (x,y) in data_stream:
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71 [prediction,costs]=learner.predict((x,y))
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72 accumulate_statistics(prediction,costs)
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73
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74 * In some cases, each example is itself a (possibly variable-size) sequence
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75 or other variable-size object (e.g. an image, or a video)
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86 James's idea for Learner Interface
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87 ===================================
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88
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89 Theory:
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90 -------
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91
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92 Think about the unfolding of a learning algorithm as exploring a path in a vast
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93 directed graph.
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94
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95 There are some source nodes, which are potential initial conditions for the
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96 learning algorithm.
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97
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98 At any node, there are a number of outgoing labeled edges that represent
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99 distinct directions of exploration: like "allocate a model with N hidden units",
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100 or "set the l1 weight decay on such-and-such units to 0.1" or "adapt for T
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101 iterations" or "refresh the GPU dataset memory with the next batch of data".
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102
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103 Not all nodes have the same outgoing edge labels. The dataset, model, and
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104 optimization algorithm implementations may each have their various
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105 hyper-parameters with various restrictions on what values they can take, and
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106 when they can be changed.
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107
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108 Every move in this graph incurs some storage and computational expense, and
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109 explores the graph.
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111 Learners typically engage in goal-directed exploration of this graph - for
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112 example to find the node with the best validation-set performance given a
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113 certain computational budget. We might often be interested in the best node
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114 found.
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116 The predict(), log_probability(), free_energy() etc correspond to costs that we
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117 can measure at any particular node (at some computational expense) to see how we
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118 are doing in our exploration.
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119
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120 Many semantically distinct components come into the definition of this graph:
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121 the model (e.g. DAA) the dataset (e.g. an online one), the inference and
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122 learning strategy. I'm not sure what to call this graph than an 'experiment
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123 graph'... so I'll go with that for now.
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124
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125
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126
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127
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128
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129 Use Cases
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130 ----------
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131
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132 Early stopping
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133 ~~~~~~~~~~~~~~
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134
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135 Early stopping can be implemented as a learner that progresses along a
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136 particular kind of edge (e.g. "train more") until a stopping criterion (in terms
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137 of a cost computed from nodes along the path) is met.
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138
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139
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140 Grid Search
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141 ~~~~~~~~~~~
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142
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143 Grid search is a learner policy that can be implemented in an experiment graph
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144 where all paths have the form:
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145
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146 ( "set param 0 to X",
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147 "set param 1 to Y",
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148 ... ,
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149 "set param N to Z",
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150 adapt,
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151 [early stop...],
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152 test)
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153
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154 It would explore all paths of this form and then return the best node.
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155
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156
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157 Stagewise learning of DBNs combined with early stopping and grid search
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158 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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159
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160 This would be a learner that is effective for experiment graphs that reflect the
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161 greedy-stagewise optimization of DBNs.
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162
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163
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164 Boosting
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165 ~~~~~~~~
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166
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167 Given an ExperimentGraph that permits re-weighting of examples, it is
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168 straightforward to write a meta-ExperimentGraph around it that implements AdaBoost.
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169 A meta-meta-ExperimentGraph around that that does early-stopping would complete
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170 the picture and make a useful boosting implementation.
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171
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172
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173
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174 Implementation Details / API
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175 ----------------------------
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176
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177 ExperimentGraph
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178 ~~~~~~~~~~~~~~~
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179
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180 One API that needs to be defined for this perspective to be practical is the
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181 ExperimentGraph. I'll present it in terms of global functions, but an
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182 object-oriented things probably makes more sense in the code itself.
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183
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184
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185 def explored_nodes(graph):
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186 """Return iterator over explored nodes (ints? objects?)"""
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187
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188 def forget_nodes(graph, nodes):
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189 """Clear the nodes from memory (save space)"""
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190
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191 def all_edges_from(graph, node):
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192 """Return iterator over all possible edges
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193
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194 Edges might be parametric - like "set learn_rate to (float)"
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195
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196 Edges might contain a reference to their 'from' end... not sure.
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197
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198 """
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199 def explored_edges_from(graph, node):
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200 """Return the edges that have been explored
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201 """
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202
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203 def add_node(graph, new_node):
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204 """add a node. It may be serialized."""
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205
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206 def add_edge(graph, edge):
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207 """add edge, it may be serialize"""
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208
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209 def connect(graph, from_node, to_node, edge):
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210 """
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211 to_node = None for un-explored edge
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212 """
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213
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214 It makes sense to have one ExperimentGraph implementation for each storage
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215 mechanism - Memory, JobMan, sqlite, couchdb, mongodb, etc.
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216
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217 The nodes should be serializable objects (like the 'learner' objects in Yoshua's
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218 text above, so that you can do node.learner.predict() if the edge leading to
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219 `node` trained something new).
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220
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221 The nodes could also contain the various costs (train, valid, test), and other
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222 experiment statistics that are node-specific.
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223
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224
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225 Some implementations might also include functions for asynchronous updating of
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226 the ExperimentGraph:
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227
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228
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229 ExperimentGraphEdge
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230 ~~~~~~~~~~~~~~~~~~~
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231
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232 The ExperimentGraph is primarily a dictionary container for nodes and edges.
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233 An ExperimentGraphEdge implementation is the model-dependent component that
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234 actually interprets the edges as computations.
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235
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236 def estimate_compute_time(graph, node, edge):
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237 """Return an estimated walltime expense for the computation"""
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238
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239 def compute_edge(graph, node, edge, async=False, priority=1):
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240 """Run the computations assocated with this graph edge, and store the
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241 resulting 'to_node' to the graph when complete.
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242
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243 If async is True, the function doesn't return until the graph is updated
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244 with `to_node`.
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245
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246 The priority is used by implementations that use cluster software or
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247 something to manage a worker pool that computes highest-priority edges
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248 first.
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249
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250 """
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251
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252 def list_compute_queue(graph):
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253 """Return edges scheduled for exploration (and maybe a handle for
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254 where/when they started running and other backend details)
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255 """
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256
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257 Different implementations of ExperimentGraphExplorer will correspond to
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258 different experiments. There can also be ExperimentGraphExplorer
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259 implementations that are proxies, and perform the computations in different
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260 threads, or across ssh, or cluster software.
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261
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262
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263 Learner
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parents: 1002
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264 ~~~~~~~
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James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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265
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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266 A learner is a program that implements a policy for graph exploration by
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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267 exploiting the ExperimentGraph and ExperimentGraphEdge interfaces.
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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268
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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269 The convenience of the API hinges on the extent to which we can implement
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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270 policies that work on different experiment-graphs (where the labels on the edges
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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271 and semantics are different). The use-cases above make me optimistic that it
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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272 will work sufficiently well to be worth doing in the absence of better ideas.
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parents: 1002
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273
38f799f8b6cd v2_planning - thoughts on learner
James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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274
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James Bergstra <bergstrj@iro.umontreal.ca>
parents: 1002
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275
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parents: 1002
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276