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v2planning optimization - added API
author James Bergstra <bergstrj@iro.umontreal.ca>
date Thu, 09 Sep 2010 11:32:42 -0400
parents bc3f7834db83
children 19033ef1636d e342de3ae485
rev   line source
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1
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2 Comittee: AB, PL, GM, IG, RP, NB, PV
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3 Leader: ?
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5 Discussion of Function Specification for Learner Types
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6 ======================================================
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7
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8 In its most abstract form, a learner is an object with the
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9 following semantics:
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11 * A learner has named hyper-parameters that control how it learns (these can be viewed
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12 as options of the constructor, or might be set directly by a user)
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13
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14 * A learner also has an internal state that depends on what it has learned.
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16 * A learner reads and produces data, so the definition of learner is
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17 intimately linked to the definition of dataset (and task).
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18
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19 * A learner has one or more 'train' or 'adapt' functions by which
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20 it is given a sample of data (typically either the whole training set, or
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21 a mini-batch, which contains as a special case a single 'example'). Learners
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22 interface with datasets in order to obtain data. These functions cause the
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23 learner to change its internal state and take advantage to some extent
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24 of the data provided. The 'train' function should take charge of
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25 completely exploiting the dataset, as specified per the hyper-parameters,
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26 so that it would typically be called only once. An 'adapt' function
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27 is meant for learners that can operate in an 'online' setting where
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28 data continually arrive and the control loop (when to stop) is to
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29 be managed outside of it. For most intents and purposes, the
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30 'train' function could also handle the 'online' case by providing
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31 the controlled iterations over the dataset (which would then be
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32 seen as a stream of examples).
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33 * learner.train(dataset)
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34 * learner.adapt(data)
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35
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36 * Different types of learners can then exploit their internal state
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37 in order to perform various computations after training is completed,
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38 or in the middle of training, e.g.,
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39
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40 * y=learner.predict(x)
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41 for learners that see (x,y) pairs during training and predict y given x,
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42 or for learners that see only x's and learn a transformation of it (i.e. feature extraction).
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43 Here and below, x and y are tensor-like objects whose first index iterates
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44 over particular examples in a batch or minibatch of examples.
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45
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46 * p=learner.probability(examples)
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47 p=learner.log_probability(examples)
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48 for learners that can estimate probability density or probability functions,
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49 note that example could be a pair (x,y) for learners that expect each example
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50 to represent such a pair. The second form is provided in case the example
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51 is high-dimensional and computations in the log-domain are numerically preferable.
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52 The first dimension of examples or of x and y is an index over a minibatch or a dataset.
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53
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54 * p=learner.free_energy(x)
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55 for learners that can estimate a log unnormalized probability; the output has the same length as the input.
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56
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57 * c=learner.costs(examples)
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58 returns a matrix of costs (one row per example, i.e., again the output has the same length
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59 as the input), the first column of which represents the cost whose expectation
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60 we wish to minimize over new samples from the unknown underlying data distribution.
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61
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63 Some learners may be able to handle x's and y's that contain missing values.
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64
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65 * For convenience, some of these operations could be bundled, e.g.
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66
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67 * [prediction,costs] = learner.predict_and_adapt((x,y))
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68
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69 * Some learners could include in their internal state not only what they
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70 have learned but some information about recently seen examples that conditions
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71 the expected distribution of upcoming examples. In that case, they might
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72 be used, e.g. in an online setting as follows:
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73 for (x,y) in data_stream:
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74 [prediction,costs]=learner.predict((x,y))
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75 accumulate_statistics(prediction,costs)
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76
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77 * In some cases, each example is itself a (possibly variable-size) sequence
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78 or other variable-size object (e.g. an image, or a video)
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89 James's idea for Learner Interface
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90 ===================================
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91
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92 Theory:
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93 -------
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94
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95 Think about the unfolding of a learning algorithm as exploring a path in a vast
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96 directed graph.
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97
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98 There are some source nodes, which are potential initial conditions for the
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99 learning algorithm.
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100
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101 At any node, there are a number of outgoing labeled edges that represent
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102 distinct directions of exploration: like "allocate a model with N hidden units",
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103 or "set the l1 weight decay on such-and-such units to 0.1" or "adapt for T
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104 iterations" or "refresh the GPU dataset memory with the next batch of data".
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105
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106 Not all nodes have the same outgoing edge labels. The dataset, model, and
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107 optimization algorithm implementations may each have their various
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108 hyper-parameters with various restrictions on what values they can take, and
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109 when they can be changed.
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110
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111 Every move in this graph incurs some storage and computational expense, and
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112 explores the graph.
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114 Learners typically engage in goal-directed exploration of this graph - for
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115 example to find the node with the best validation-set performance given a
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116 certain computational budget. We might often be interested in the best node
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117 found.
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118
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119 The predict(), log_probability(), free_energy() etc correspond to costs that we
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120 can measure at any particular node (at some computational expense) to see how we
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121 are doing in our exploration.
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122
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123 Many semantically distinct components come into the definition of this graph:
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124 the model (e.g. DAA) the dataset (e.g. an online one), the inference and
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125 learning strategy. I'm not sure what to call this graph than an 'experiment
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126 graph'... so I'll go with that for now.
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127
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128
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129
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130
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131
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132 Use Cases
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133 ----------
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134
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135 Early stopping
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136 ~~~~~~~~~~~~~~
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137
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138 Early stopping can be implemented as a learner that progresses along a
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139 particular kind of edge (e.g. "train more") until a stopping criterion (in terms
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140 of a cost computed from nodes along the path) is met.
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141
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142
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143 Grid Search
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144 ~~~~~~~~~~~
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145
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146 Grid search is a learner policy that can be implemented in an experiment graph
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147 where all paths have the form:
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148
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149 ( "set param 0 to X",
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150 "set param 1 to Y",
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151 ... ,
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152 "set param N to Z",
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153 adapt,
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154 [early stop...],
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155 test)
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156
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157 It would explore all paths of this form and then return the best node.
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158
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159
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160 Stagewise learning of DBNs combined with early stopping and grid search
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161 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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162
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163 This would be a learner that is effective for experiment graphs that reflect the
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164 greedy-stagewise optimization of DBNs.
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165
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166
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167 Boosting
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168 ~~~~~~~~
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169
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170 Given an ExperimentGraph that permits re-weighting of examples, it is
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171 straightforward to write a meta-ExperimentGraph around it that implements AdaBoost.
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172 A meta-meta-ExperimentGraph around that that does early-stopping would complete
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173 the picture and make a useful boosting implementation.
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174
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175
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176 Using External Hyper-Parameter Optimization Software
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177 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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178 TODO: use-case - show how we could use the optimizer from
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179 http://www.cs.ubc.ca/labs/beta/Projects/ParamILS/
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180
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181
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182 Implementation Details / API
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183 ----------------------------
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184
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185 Learner
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186 ~~~~~~~
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187 An object that allows us to explore the graph discussed above. Specifically, it represents
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188 an explored node in that graph.
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189
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190 def active_instructions()
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191 """ Return a list/set of Instruction instances (see below) that the Learner is prepared
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192 to handle.
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193 """
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194
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195 def copy(), deepcopy()
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196 """ Learners should be serializable """
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197
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198
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199 To make the implementation easier, I found it was helpful to introduce a string-valued
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200 `fsa_state` member attribute and associate methods to these states. That made it
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201 syntactically easy to build relatively complex finite-state transition graphs to describe
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202 which instructions were active at which times in the life-cycle of a learner.
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203
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204
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205 Instruction
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206 ~~~~~~~~~~~
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207 An object that represents a potential edge in the graph discussed above. It is an
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208 operation that a learner can perform.
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209
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210 arg_types
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211 """a list of Type object (see below) indicating what args are required by execute"""
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212
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213 def execute(learner, args, kwargs):
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214 """ Perform some operation on the learner (follow an edge in the graph discussed above)
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215 and modify the learner in-place. Calling execute 'moves' the learner from one node in
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216 the graph along an edge. To have the old learner as well, it must be copied prior to
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217 calling execute().
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218 """
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219
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220 def expense(learner, args, kwargs, resource_type='CPUtime'):
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221 """ Return an estimated cost of performing this instruction (calling execute), in time,
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222 space, number of computers, disk requierement, etc.
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223 """
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224
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225 Type
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226 ~~~~
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227 An object that describes a parameter domain for a call to Instruction.execute.
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228 It is not necessary that a Type specifies exactly which arguments are legal, but it should
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229 `include` all legal arguments, and exclude as many illegal ones as possible.
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230
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231 def includes(value):
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232 """return True if value is a legal argument"""
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233
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234
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235 To make things a bit more practical, there are some Type subclasses like Int, Float, Str,
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236 ImageDataset, SgdOptimizer, that include additional attributes (e.g. min, max, default) so
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237 that automatic graph exploration algorithms can generate legal arguments with reasonable
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238 efficiency.
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239
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240
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241
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242 The proxy pattern is a powerful way to combine learners. Especially when proxy Learner
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243 instances also introduce Proxy Instruction classes.
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244
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245 For example, it is straightforward to implement a hyper-learner by implementing a Learner with
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246 another learner (sub-learner) as a member attribute. The hyper-learner makes some
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247 modifications to the instruction_set() return value of the sub-learner, typically to introduce
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248 more powerful instructions and hide simpler ones.
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249
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250 It is less straightforward, but consistent with the design to implement a Learner that
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251 encompasses job management. Such a learner would retain the semantics of the
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252 instruction_set of the sub-learner, but would replace the Instruction objects themselves with
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253 Instructions that arranged for remote procedure calls (e.g. jobman, multiprocessing, bqtools,
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254 etc.) Such a learner would replace synchronous instructions (return on completion) with
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255 asynchronous ones (return after scheduling) and the active instruction set would also change
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256 asynchronously, but neither of these things is inconsistent with the Learner API.
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257
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258
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259 TODO
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260 ~~~~
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261
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262 I feel like something is missing from the API - and that is an interface to the graph structure
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263 discussed above. The nodes in this graph are natural places to store meta-information for
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264 visualization, statistics-gathering etc. But none of the APIs above corresponds to the graph
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265 itself. In other words, there is no API through which to attach information to nodes. It is
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266 not good to say that the Learner instance *is* the node because (a) learner instances change
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267 during graph exploration and (b) learner instances are big, and we don't want to have to keep a
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268 whole saved model just to attach meta-info e.g. validation score. Choosing this API spills
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269 over into other committees, so we should get their feedback about how to resolve it.
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270
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271 Comments
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272 ~~~~~~~~
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273
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274 YB asks: it seems to me that what we really need from "Type" is not just
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275 testing that a value is legal, but more practically a function that specifies the
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276 prior distribution for the hyper-parameter, i.e., how to sample from it,
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277 and possibly some representation of it that could be used to infer
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278 a posterior (such as an unnormalized log-density or log-probability).
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279 Having the min and max and default limits us to the uniform distribution,
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280 which may not always be appropriate. For example sometimes we'd like
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281 Gaussian (-infty to infty) or Exponential (0 to infty) or Poisson (non-negative integers).
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282 For that reason, I think that "Type" is not a very good name.
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283 How about "Prior" or "Density" or something like that?
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284
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285 OD asks: (I hope it's ok to leave comments even though I'm not in committee... I'm
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286 interested to see how the learner interface is shaping up so I'll be keeping
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287 an eye on this file)
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288 I'm wondering what's the benefit of such an API compared to simply defining a
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289 new method for each instruction. It seems to me that typically, the 'execute'
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290 method would end up being something like
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291 if instruction == 'do_x':
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292 self.do_x(..)
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293 elif instruction == 'do_y':
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294 self.do_y(..)
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295 ...
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296 so why not directly call do_x / do_y instead?
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297
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298
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299 JB replies: I agree with you, and in the implementation of a Learner I suggest
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300 using Python decorators to get the best of both worlds:
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301
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302 class NNet(Learner):
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303
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304 ...
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305
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306 @Instruction.new(arg_types=(Float(min=-8, max=-1, default=-4),))
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307 def set_log_lr(self, log_lr):
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308 self.lr.value = numpy.exp(log_lr)
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309
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310 ...
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311
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312 The Learner base class can implement a instruction_set() that walks through the
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313 methods of 'self' and pick out the ones that have corresponding instructions.
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314 But anyone can call the method normally. The NNet class can also have methods
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315 that are not instructions.
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316
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317 OD replies: Ok thanks. I'm still unsure what is the end goal, but I'll keep
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318 watching while you guys work on it, and hopefully it'll become clearer for me ;)
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319
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320 RP asks: James correct me if I'm wrong, but I think each instruction has a execute
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321 command. The job of the learner is to traverse the graph and for each edge
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322 that it decides to cross to call the execute of that edge. Maybe James has
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323 something else in mind, but this was my understanding.
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324
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325 JB replies: close, but let me make a bit of a clarification. The job of a
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326 Learner is simply to implement the API of a Learner - to list what edges are
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327 available and to be able to cross them if asked. The code *using* the Learner
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328 (client) decides which edges to cross. The client may also be a Learner, but
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329 maybe not.
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330
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331
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332
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333 Just another view/spin on the same idea (Razvan)
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334 ================================================
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335
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336
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337 My idea is probably just a spin off from what James wrote. It is an extension
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338 of what I send on the mailing list some time ago.
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339
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340 Big Picture
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341 -----------
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342
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343 What do we care about ?
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344 ~~~~~~~~~~~~~~~~~~~~~~~
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345
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346 This is the list of the main points that I have in mind :
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347
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348 * Re-usability
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349 * Extensibility
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350 * Simplicity or easily readable code ( connected to re-usability )
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351 * Modularity ( connected to extensibility )
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352 * Fast to write code ( - sort of comes out of simplicity)
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353 * Efficient code
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354
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355
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356 Composition
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357 ~~~~~~~~~~~
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358
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359 To me this reads as code generated by composing pieces. Imagine this :
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360 you start of with something primitive that I will call a "variable", which
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361 probably is a very unsuitable name. And then you compose those intial
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362 "variables" or transform them through several "functions". Each such
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363 "function" hides some logic, that you as the user don't care about.
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364 You can have low-level or micro "functions" and high-level or macro
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365 "functions", where a high-level function is just a certain compositional
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366 pattern of low-level "functions". There are several classes of "functions"
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367 and "variables" that can be inter-changable. This is how modularity is
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368 obtained, by chainging between functions from a certain class.
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369
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370 Now when you want to research something, what you do is first select
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371 the step you want to look into. If you are lucky you can re-write this
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372 step as certain decomposition of low-level transformations ( there can be
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373 multiple such decompositions). If not you have to implement such a
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374 decompositions acording to your needs. Pick the low-level transformations you want
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375 to change and write new versions that implement your logic.
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376
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377 I think the code will be easy to read, because it is just applying a fixed
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378 set of transformations, one after the other. The one who writes the code can
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379 decide how explicit he wants to write things by switching between high-level
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380 and low-level functions.
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381
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382 I think the code this way is re-usable, because you can just take this chain
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383 of transformation and replace the one you care about, without looking into
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384 the rest.
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385
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386 You get this fractal property of the code. Zooming in, you always get just
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387 a set of functions applied to a set of variables. In the begining those might
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388 not be there, and you would have to create new "low level" decompositions,
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389 maybe even new "variables" that get data between those decompositions.
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390
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391 The thing with variables here, is that I don't want this "functions" to have
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392 a state. All the information is passed along through these variables. This
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393 way understanding the graph is easy, debugging it is also easier ( then having
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394 all these hidden states ..)
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395
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396 Note that while doing so we might ( and I strongly think we should) create
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397 a (symbolic) DAG of operations. ( this is where it becomes what James was saying).
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398 In such a DAG the "variables" will the nodes and the functions will be edges.
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399 I think having a DAG is useful in many ways (all this are things that one
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400 might think about implementing in a far future, I'm not proposing to implement
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401 them unless we want to use them - like the reconstruction ):
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402 * there exist the posibility of writing optimizations ( theano style )
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403 * there exist the posibility to add global view utility functions ( like
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404 a reconstruction function for SdA - extremely low level here), or global
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405 view diagnostic tools
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406 * the posibility of creating a GUI ( where you just create the Graph by
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407 picking transforms and variables from a list ) or working interactively
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408 and then generating code that will reproduce the graph
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409 * you can view the graph and different granularity levels to understand
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410 things ( global diagnostics)
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411
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412 We should have a taxonomy of possible classes of functions and possible
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413 classes of variables, but those should not be exclusive. We can work at a high
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414 level for now, and decompose those high level functions to lower level when
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415 we need to. We can introduce new classes of functions or intermediate
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416 variables between those low level functions.
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417
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418
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419 Similarities with James' idea
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420 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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421
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422 As I said before, this is I think just another view on what James proposed.
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423 The learner in his case is the module that traverses the graph of this
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424 operations, which makes sense here as well.
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425
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426 The 'execute' command in his api is just applying a function to some variables in
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427 my case.
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428
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429 The learner keeps track of the graph that is formed I think in both cases.
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430
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431 His view is a bit more general. I see the graph as fully created by the user,
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432 and the learner just has to go from the start to the end. In his case the
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433 traversal is conditioned on some policies. I think these ideas can be mixed /
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434 united. What I would see in my case to have this functionality is something
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435 similar to the lazy linker for Theano.
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436
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437
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438
1052
84f62533e7a8 v2planning learner - reply to comments
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439 JB asks: There is definitely a strong theme of graphs in both suggestions,
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440 furthermore graphs that have heavy-duty nodes and light-weight edges. But I
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441 don't necessarily think that we're proposing the same thing. One difference is
84f62533e7a8 v2planning learner - reply to comments
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442 that the graph I talked about would be infinite in most cases of interest, so
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443 it's not going to be representable by Theano's data structures (even with lazy
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444 if). Another difference is that the graph I had in mind doesn't feel fractal -
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445 it would be very common for a graph edge to be atomic. A proxy pattern, such as
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446 in a hyper-learner would create a notion of being able to zoom in, but other
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447 than that, i'm not sure what you mean.
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448