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Experiment to test the performance of shallower networks.
author Salah Rifai <salahmeister@gmail.com>
date Sun, 09 Jan 2011 12:45:44 -0500
parents a0fdc1f134da
children
rev   line source
597
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1 %\documentclass[twoside,11pt]{article} % For LaTeX2e
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2 \documentclass{article} % For LaTeX2e
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3 \usepackage{nips10submit_e}
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4 \usepackage{times}
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11 %\usepackage{algorithm,algorithmic} % not used after all
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12 \usepackage{graphicx,subfigure}
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13 \usepackage[numbers]{natbib}
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21 \begin{document}
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22
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23 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
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24 \author{
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25 Yoshua Bengio \and
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26 Frédéric Bastien \and
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27 Arnaud Bergeron \and
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28 Nicolas Boulanger-Lewandowski \and
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29 Thomas Breuel \and
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30 Youssouf Chherawala \and
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31 Moustapha Cisse \and
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32 Myriam Côté \and
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33 Dumitru Erhan \and
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34 Jeremy Eustache \and
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35 Xavier Glorot \and
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36 Xavier Muller \and
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37 Sylvain Pannetier Lebeuf \and
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38 Razvan Pascanu \and
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39 Salah Rifai \and
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40 Francois Savard \and
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41 Guillaume Sicard
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42 }
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43 \date{{\tt bengioy@iro.umontreal.ca}, Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
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44 %\jmlrheading{}{2010}{}{10/2010}{XX/2011}{Yoshua Bengio et al}
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45 %\editor{}
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46
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47 %\makeanontitle
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48 \maketitle
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49
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50 %{\bf Running title: Deep Self-Taught Learning}
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51
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52 \vspace*{-2mm}
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53 \begin{abstract}
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54 Recent theoretical and empirical work in statistical machine learning has demonstrated the potential of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple levels of representation. Self-taught learning (exploiting unlabeled examples or examples from other distributions) has already been applied to deep learners, but mostly to show the advantage of unlabeled examples. Here we explore the advantage brought by {\em out-of-distribution examples}. For this purpose we developed a powerful generator of stochastic variations and noise processes for character images, including not only affine transformations but also slant, local elastic deformations, changes in thickness, background images, grey level changes, contrast, occlusion, and various types of noise. The out-of-distribution examples are obtained from these highly distorted images or by including examples of object classes different from those in the target test set. We show that {\em deep learners benefit more from out-of-distribution examples than a corresponding shallow learner}, at least in a large-scale handwritten character recognition setting. In fact, we show that they {\em beat previously published results and reach human-level performance}.
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55 \end{abstract}
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56 \vspace*{-3mm}
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57
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58 %\begin{keywords}
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59 %Deep learning, self-taught learning, out-of-distribution examples, handwritten character recognition, multi-task learning
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60 %\end{keywords}
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61 %\keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition}
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64
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65 \section{Introduction}
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66 \vspace*{-1mm}
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67
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68 {\bf Deep Learning} has emerged as a promising new area of research in
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69 statistical machine learning~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,VincentPLarochelleH2008,ranzato-08,TaylorHintonICML2009,Larochelle-jmlr-2009,Salakhutdinov+Hinton-2009,HonglakL2009,HonglakLNIPS2009,Jarrett-ICCV2009,Taylor-cvpr-2010}. See \citet{Bengio-2009} for a review.
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70 Learning algorithms for deep architectures are centered on the learning
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71 of useful representations of data, which are better suited to the task at hand,
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72 and are organized in a hierarchy with multiple levels.
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73 This is in part inspired by observations of the mammalian visual cortex,
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74 which consists of a chain of processing elements, each of which is associated with a
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75 different representation of the raw visual input. In fact,
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76 it was found recently that the features learnt in deep architectures resemble
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77 those observed in the first two of these stages (in areas V1 and V2
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78 of visual cortex) \citep{HonglakL2008}, and that they become more and
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79 more invariant to factors of variation (such as camera movement) in
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80 higher layers~\citep{Goodfellow2009}.
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81 Learning a hierarchy of features increases the
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82 ease and practicality of developing representations that are at once
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83 tailored to specific tasks, yet are able to borrow statistical strength
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84 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
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85 feature representation can lead to higher-level (more abstract, more
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86 general) features that are more robust to unanticipated sources of
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87 variance extant in real data.
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88
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89 {\bf Self-taught learning}~\citep{RainaR2007} is a paradigm that combines principles
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90 of semi-supervised and multi-task learning: the learner can exploit examples
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91 that are unlabeled and possibly come from a distribution different from the target
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92 distribution, e.g., from other classes than those of interest.
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93 It has already been shown that deep learners can clearly take advantage of
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94 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
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95 but more needs to be done to explore the impact
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96 of {\em out-of-distribution} examples and of the {\em multi-task} setting
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97 (one exception is~\citep{CollobertR2008}, which uses a different kind
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98 of learning algorithm). In particular the {\em relative
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99 advantage of deep learning} for these settings has not been evaluated.
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100 The hypothesis discussed in the conclusion is that in the context of
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101 multi-task learning and the availability of out-of-distribution training examples,
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102 a deep hierarchy of features
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103 may be better able to provide {\em sharing of statistical strength}
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104 between different regions in input space or different tasks, compared to
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105 a shallow learner.
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106
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107 \iffalse
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108 Whereas a deep architecture can in principle be more powerful than a
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109 shallow one in terms of representation, depth appears to render the
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110 training problem more difficult in terms of optimization and local minima.
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111 It is also only recently that successful algorithms were proposed to
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112 overcome some of these difficulties. All are based on unsupervised
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113 learning, often in an greedy layer-wise ``unsupervised pre-training''
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114 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
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115 applied here, is the Denoising
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116 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}),
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117 which
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118 performed similarly or better than previously proposed Restricted Boltzmann
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119 Machines in terms of unsupervised extraction of a hierarchy of features
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120 useful for classification. Each layer is trained to denoise its
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121 input, creating a layer of features that can be used as input for the next layer.
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122 \fi
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123
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124 %The principle is that each layer starting from
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125 %the bottom is trained to encode its input (the output of the previous
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126 %layer) and to reconstruct it from a corrupted version. After this
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127 %unsupervised initialization, the stack of DAs can be
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128 %converted into a deep supervised feedforward neural network and fine-tuned by
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129 %stochastic gradient descent.
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130
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131 %
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132 The {\bf main claim} of this paper is that deep learners (with several levels of representation) can
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133 {\bf benefit more from self-taught learning than shallow learners} (with a single
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134 level), both in the context of the multi-task setting and from {\em
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135 out-of-distribution examples} in general. Because we are able to improve on state-of-the-art
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136 performance and reach human-level performance
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137 on a large-scale task, we consider that this paper is also a contribution
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138 to advance the application of machine learning to handwritten character recognition.
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139 More precisely, we ask and answer the following questions:
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140
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141 %\begin{enumerate}
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142 $\bullet$ %\item
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143 Do the good results previously obtained with deep architectures on the
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144 MNIST digit images generalize to the setting of a similar but much larger and richer
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145 dataset, the NIST special database 19, with 62 classes and around 800k examples?
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146
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147 $\bullet$ %\item
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148 To what extent does the perturbation of input images (e.g. adding
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149 noise, affine transformations, background images) make the resulting
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150 classifiers better not only on similarly perturbed images but also on
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151 the {\em original clean examples}? We study this question in the
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152 context of the 62-class and 10-class tasks of the NIST special database 19.
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153
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154 $\bullet$ %\item
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155 Do deep architectures {\em benefit {\bf more} from such out-of-distribution}
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156 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
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157 We use highly perturbed examples to generate out-of-distribution examples.
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158
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159 $\bullet$ %\item
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160 Similarly, does the feature learning step in deep learning algorithms benefit {\bf more}
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161 from training with moderately {\em different classes} (i.e. a multi-task learning scenario) than
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162 a corresponding shallow and purely supervised architecture?
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163 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case)
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164 to answer this question.
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165 %\end{enumerate}
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166
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167 Our experimental results provide positive evidence towards all of these questions,
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168 as well as {\em classifiers that reach human-level performance on 62-class isolated character
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169 recognition and beat previously published results on the NIST dataset (special database 19)}.
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170 To achieve these results, we introduce in the next section a sophisticated system
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171 for stochastically transforming character images and then explain the methodology,
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172 which is based on training with or without these transformed images and testing on
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173 clean ones. We measure the relative advantage of out-of-distribution examples
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174 (perturbed or out-of-class)
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175 for a deep learner vs a supervised shallow one.
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176 Code for generating these transformations as well as for the deep learning
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177 algorithms are made available at {\tt http://anonymous.url.net}.%{\tt http://hg.assembla.com/ift6266}.
597
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178 We also estimate the relative advantage for deep learners of training with
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179 other classes than those of interest, by comparing learners trained with
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180 62 classes with learners trained with only a subset (on which they
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181 are then tested).
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182 The conclusion discusses
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183 the more general question of why deep learners may benefit so much from
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184 the self-taught learning framework. Since out-of-distribution data
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185 (perturbed or from other related classes) is very common, this conclusion
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186 is of practical importance.
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187
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188 \vspace*{-3mm}
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189 %\newpage
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190 \section{Perturbed and Transformed Character Images}
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191 \label{s:perturbations}
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192 \vspace*{-2mm}
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193
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194 Figure~\ref{fig:transform} shows the different transformations we used to stochastically
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195 transform $32 \times 32$ source images (such as the one in Fig.\ref{fig:torig})
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196 in order to obtain data from a larger distribution which
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197 covers a domain substantially larger than the clean characters distribution from
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198 which we start.
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199 Although character transformations have been used before to
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200 improve character recognizers, this effort is on a large scale both
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201 in number of classes and in the complexity of the transformations, hence
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202 in the complexity of the learning task.
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203 The code for these transformations (mostly python) is available at
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204 {\tt http://anonymous.url.net}. All the modules in the pipeline share
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205 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
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206 amount of deformation or noise introduced.
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207 There are two main parts in the pipeline. The first one,
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208 from slant to pinch below, performs transformations. The second
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209 part, from blur to contrast, adds different kinds of noise.
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210 More details can be found in~\citep{ift6266-tr-anonymous}.
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211
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212 \begin{figure}[ht]
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213 \centering
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214 \subfigure[Original]{\includegraphics[scale=0.6]{images/Original.png}\label{fig:torig}}
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215 \subfigure[Thickness]{\includegraphics[scale=0.6]{images/Thick_only.png}}
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216 \subfigure[Slant]{\includegraphics[scale=0.6]{images/Slant_only.png}}
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217 \subfigure[Affine Transformation]{\includegraphics[scale=0.6]{images/Affine_only.png}}
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218 \subfigure[Local Elastic Deformation]{\includegraphics[scale=0.6]{images/Localelasticdistorsions_only.png}}
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219 \subfigure[Pinch]{\includegraphics[scale=0.6]{images/Pinch_only.png}}
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220 %Noise
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221 \subfigure[Motion Blur]{\includegraphics[scale=0.6]{images/Motionblur_only.png}}
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222 \subfigure[Occlusion]{\includegraphics[scale=0.6]{images/occlusion_only.png}}
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223 \subfigure[Gaussian Smoothing]{\includegraphics[scale=0.6]{images/Bruitgauss_only.png}}
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224 \subfigure[Pixels Permutation]{\includegraphics[scale=0.6]{images/Permutpixel_only.png}}
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225 \subfigure[Gaussian Noise]{\includegraphics[scale=0.6]{images/Distorsiongauss_only.png}}
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226 \subfigure[Background Image Addition]{\includegraphics[scale=0.6]{images/background_other_only.png}}
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227 \subfigure[Salt \& Pepper]{\includegraphics[scale=0.6]{images/Poivresel_only.png}}
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228 \subfigure[Scratches]{\includegraphics[scale=0.6]{images/Rature_only.png}}
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229 \subfigure[Grey Level \& Contrast]{\includegraphics[scale=0.6]{images/Contrast_only.png}}
598
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230 \caption{Top left (a): example original image. Others (b-o): examples of the effect
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231 of each transformation module taken separately. Actual perturbed examples are obtained by
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232 a pipeline of these, with random choices about which module to apply and how much perturbation
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233 to apply.}
597
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234 \label{fig:transform}
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235 \vspace*{-2mm}
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236 \end{figure}
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237
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238 \vspace*{-3mm}
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239 \section{Experimental Setup}
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240 \vspace*{-1mm}
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241
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242 Much previous work on deep learning had been performed on
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243 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
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244 with 60~000 examples, and variants involving 10~000
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245 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}.
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246 The focus here is on much larger training sets, from 10 times to
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247 to 1000 times larger, and 62 classes.
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248
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249 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
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250 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
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251 and {\bf OCR data} (scanned machine printed characters). Once a character
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252 is sampled from one of these sources (chosen randomly), the second step is to
598
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253 apply a pipeline of transformations and/or noise processes outlined in section \ref{s:perturbations}.
597
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254
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255 To provide a baseline of error rate comparison we also estimate human performance
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256 on both the 62-class task and the 10-class digits task.
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257 We compare the best Multi-Layer Perceptrons (MLP) against
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258 the best Stacked Denoising Auto-encoders (SDA), when
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259 both models' hyper-parameters are selected to minimize the validation set error.
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260 We also provide a comparison against a precise estimate
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261 of human performance obtained via Amazon's Mechanical Turk (AMT)
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262 service ({\tt http://mturk.com}).
597
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263 AMT users are paid small amounts
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264 of money to perform tasks for which human intelligence is required.
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265 Mechanical Turk has been used extensively in natural language processing and vision.
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266 %processing \citep{SnowEtAl2008} and vision
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267 %\citep{SorokinAndForsyth2008,whitehill09}.
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268 AMT users were presented
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269 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII
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270 characters. They were forced to choose a single character class (either among the
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271 62 or 10 character classes) for each image.
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272 80 subjects classified 2500 images per (dataset,task) pair.
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273 Different humans labelers sometimes provided a different label for the same
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274 example, and we were able to estimate the error variance due to this effect
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275 because each image was classified by 3 different persons.
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276 The average error of humans on the 62-class task NIST test set
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277 is 18.2\%, with a standard error of 0.1\%.
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278
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279 \vspace*{-3mm}
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280 \subsection{Data Sources}
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281 \vspace*{-2mm}
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282
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283 %\begin{itemize}
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284 %\item
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285 {\bf NIST.}
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286 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
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287 widely used for training and testing character
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288 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
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289 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
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290 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
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291 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
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292 The fourth partition (called $hsf_4$, 82587 examples),
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293 experimentally recognized to be the most difficult one, is the one recommended
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294 by NIST as a testing set and is used in our work as well as some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
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295 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for
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296 model selection.
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297 The performances reported by previous work on that dataset mostly use only the digits.
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298 Here we use all the classes both in the training and testing phase. This is especially
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299 useful to estimate the effect of a multi-task setting.
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300 The distribution of the classes in the NIST training and test sets differs
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301 substantially, with relatively many more digits in the test set, and a more uniform distribution
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302 of letters in the test set (whereas in the training set they are distributed
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303 more like in natural text).
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304 %\vspace*{-1mm}
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305
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306 %\item
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307 {\bf Fonts.}
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308 In order to have a good variety of sources we downloaded an important number of free fonts from:
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309 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
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310 % TODO: pointless to anonymize, it's not pointing to our work
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311 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
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312 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
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313 directly as input to our models.
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314 \vspace*{-1mm}
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315
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316 %\item
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317 {\bf Captchas.}
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318 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
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319 generating characters of the same format as the NIST dataset. This software is based on
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320 a random character class generator and various kinds of transformations similar to those described in the previous sections.
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321 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
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322 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
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323 depending on the value of the complexity parameter provided by the user of the data source.
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324 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
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325 \vspace*{-1mm}
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326
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327 %\item
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328 {\bf OCR data.}
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329 A large set (2 million) of scanned, OCRed and manually verified machine-printed
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330 characters where included as an
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331 additional source. This set is part of a larger corpus being collected by the Image Understanding
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332 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
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333 ({\tt http://www.iupr.com}), and which will be publicly released.
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334 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
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335 %\end{itemize}
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336
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337 \vspace*{-3mm}
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338 \subsection{Data Sets}
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339 \vspace*{-2mm}
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340
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341 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
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342 from one of the 62 character classes.
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343 %\begin{itemize}
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344 \vspace*{-1mm}
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345
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346 %\item
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347 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
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348 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
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349 \vspace*{-1mm}
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350
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351 %\item
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352 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
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353 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
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354 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
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355 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
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356 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
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357 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
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358 \vspace*{-1mm}
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359
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360 %\item
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361 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
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362 except that we only apply
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363 transformations from slant to pinch. Therefore, the character is
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364 transformed but no additional noise is added to the image, giving images
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365 closer to the NIST dataset.
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366 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
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367 %\end{itemize}
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368
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369 \vspace*{-3mm}
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370 \subsection{Models and their Hyperparameters}
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371 \vspace*{-2mm}
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372
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373 The experiments are performed using MLPs (with a single
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374 hidden layer) and SDAs.
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375 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
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376
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377 {\bf Multi-Layer Perceptrons (MLP).}
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378 Whereas previous work had compared deep architectures to both shallow MLPs and
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379 SVMs, we only compared to MLPs here because of the very large datasets used
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380 (making the use of SVMs computationally challenging because of their quadratic
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381 scaling behavior). Preliminary experiments on training SVMs (libSVM) with subsets of the training
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382 set allowing the program to fit in memory yielded substantially worse results
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383 than those obtained with MLPs. For training on nearly a billion examples
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384 (with the perturbed data), the MLPs and SDA are much more convenient than
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385 classifiers based on kernel methods.
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386 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
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387 exponentials) on the output layer for estimating $P(class | image)$.
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388 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
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389 Training examples are presented in minibatches of size 20. A constant learning
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390 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$.
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391 %through preliminary experiments (measuring performance on a validation set),
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392 %and $0.1$ (which was found to work best) was then selected for optimizing on
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393 %the whole training sets.
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394 \vspace*{-1mm}
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395
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396
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397 {\bf Stacked Denoising Auto-Encoders (SDA).}
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398 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
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399 can be used to initialize the weights of each layer of a deep MLP (with many hidden
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400 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
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401 apparently setting parameters in the
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402 basin of attraction of supervised gradient descent yielding better
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403 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised
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404 pre-training phase} uses all of the training images but not the training labels.
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405 Each layer is trained in turn to produce a new representation of its input
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406 (starting from the raw pixels).
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407 It is hypothesized that the
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408 advantage brought by this procedure stems from a better prior,
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409 on the one hand taking advantage of the link between the input
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410 distribution $P(x)$ and the conditional distribution of interest
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411 $P(y|x)$ (like in semi-supervised learning), and on the other hand
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412 taking advantage of the expressive power and bias implicit in the
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413 deep architecture (whereby complex concepts are expressed as
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414 compositions of simpler ones through a deep hierarchy).
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415
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416 \begin{figure}[ht]
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417 \vspace*{-2mm}
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418 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
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419 \vspace*{-2mm}
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420 \caption{Illustration of the computations and training criterion for the denoising
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421 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
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422 the layer (i.e. raw input or output of previous layer)
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423 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
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424 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
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425 is compared to the uncorrupted input $x$ through the loss function
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426 $L_H(x,z)$, whose expected value is approximately minimized during training
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427 by tuning $\theta$ and $\theta'$.}
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428 \label{fig:da}
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boulanni <nicolas_boulanger@hotmail.com>
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429 \vspace*{-2mm}
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boulanni <nicolas_boulanger@hotmail.com>
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430 \end{figure}
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boulanni <nicolas_boulanger@hotmail.com>
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431
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432 Here we chose to use the Denoising
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boulanni <nicolas_boulanger@hotmail.com>
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433 Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for
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boulanni <nicolas_boulanger@hotmail.com>
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434 these deep hierarchies of features, as it is simple to train and
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435 explain (see Figure~\ref{fig:da}, as well as
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436 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
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437 provides efficient inference, and yielded results
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boulanni <nicolas_boulanger@hotmail.com>
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438 comparable or better than RBMs in series of experiments
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439 \citep{VincentPLarochelleH2008}. During training, a Denoising
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440 Auto-encoder is presented with a stochastically corrupted version
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441 of the input and trained to reconstruct the uncorrupted input,
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442 forcing the hidden units to represent the leading regularities in
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443 the data. Here we use the random binary masking corruption
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444 (which sets to 0 a random subset of the inputs).
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445 Once it is trained, in a purely unsupervised way,
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446 its hidden units' activations can
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447 be used as inputs for training a second one, etc.
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448 After this unsupervised pre-training stage, the parameters
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449 are used to initialize a deep MLP, which is fine-tuned by
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450 the same standard procedure used to train them (see previous section).
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451 The SDA hyper-parameters are the same as for the MLP, with the addition of the
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452 amount of corruption noise (we used the masking noise process, whereby a
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453 fixed proportion of the input values, randomly selected, are zeroed), and a
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454 separate learning rate for the unsupervised pre-training stage (selected
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455 from the same above set). The fraction of inputs corrupted was selected
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456 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
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457 of hidden layers but it was fixed to 3 based on previous work with
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458 SDAs on MNIST~\citep{VincentPLarochelleH2008}. The size of the hidden
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459 layers was kept constant across hidden layers, and the best results
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460 were obtained with the largest values that we could experiment
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461 with given our patience, with 1000 hidden units.
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462
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boulanni <nicolas_boulanger@hotmail.com>
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463 \vspace*{-1mm}
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boulanni <nicolas_boulanger@hotmail.com>
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464
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465 \begin{figure}[ht]
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boulanni <nicolas_boulanger@hotmail.com>
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466 %\vspace*{-2mm}
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467 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
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468 %\vspace*{-3mm}
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469 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
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470 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
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471 of all models, on NIST and NISTP test sets.
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472 Right: error rates on NIST test digits only, along with the previous results from
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473 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
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474 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
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475 \label{fig:error-rates-charts}
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476 \vspace*{-2mm}
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boulanni <nicolas_boulanger@hotmail.com>
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477 \end{figure}
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478
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479
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480 \begin{figure}[ht]
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481 \vspace*{-3mm}
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482 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
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483 \vspace*{-3mm}
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484 \caption{Relative improvement in error rate due to self-taught learning.
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485 Left: Improvement (or loss, when negative)
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486 induced by out-of-distribution examples (perturbed data).
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487 Right: Improvement (or loss, when negative) induced by multi-task
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488 learning (training on all classes and testing only on either digits,
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489 upper case, or lower-case). The deep learner (SDA) benefits more from
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490 both self-taught learning scenarios, compared to the shallow MLP.}
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491 \label{fig:improvements-charts}
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492 \vspace*{-2mm}
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diff changeset
493 \end{figure}
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494
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495 \section{Experimental Results}
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diff changeset
496 \vspace*{-2mm}
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497
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498 %%\vspace*{-1mm}
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499 %\subsection{SDA vs MLP vs Humans}
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500 %%\vspace*{-1mm}
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diff changeset
501 The models are either trained on NIST (MLP0 and SDA0),
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
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502 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
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503 on either NIST, NISTP or P07, either on the 62-class task
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504 or on the 10-digits task. Training (including about half
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505 for unsupervised pre-training, for DAs) on the larger
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506 datasets takes around one day on a GPU-285.
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507 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
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508 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
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509 SDA2), along with the previous results on the digits NIST special database
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510 19 test set from the literature, respectively based on ARTMAP neural
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511 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
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512 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
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513 ~\citep{Milgram+al-2005}.% More detailed and complete numerical results
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514 %(figures and tables, including standard errors on the error rates) can be
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515 %found in Appendix.
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diff changeset
516 The deep learner not only outperformed the shallow ones and
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diff changeset
517 previously published performance (in a statistically and qualitatively
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diff changeset
518 significant way) but when trained with perturbed data
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519 reaches human performance on both the 62-class task
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520 and the 10-class (digits) task.
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diff changeset
521 17\% error (SDA1) or 18\% error (humans) may seem large but a large
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diff changeset
522 majority of the errors from humans and from SDA1 are from out-of-context
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523 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
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524 ``c'' and a ``C'' are often indistinguishible).
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diff changeset
525
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diff changeset
526 In addition, as shown in the left of
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
527 Figure~\ref{fig:improvements-charts}, the relative improvement in error
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
528 rate brought by self-taught learning is greater for the SDA, and these
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
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diff changeset
529 differences with the MLP are statistically and qualitatively
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diff changeset
530 significant.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
531 The left side of the figure shows the improvement to the clean
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
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diff changeset
532 NIST test set error brought by the use of out-of-distribution examples
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
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parents:
diff changeset
533 (i.e. the perturbed examples examples from NISTP or P07).
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
534 Relative percent change is measured by taking
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
535 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
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parents:
diff changeset
536 The right side of
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boulanni <nicolas_boulanger@hotmail.com>
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diff changeset
537 Figure~\ref{fig:improvements-charts} shows the relative improvement
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
538 brought by the use of a multi-task setting, in which the same model is
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
539 trained for more classes than the target classes of interest (i.e. training
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
540 with all 62 classes when the target classes are respectively the digits,
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
541 lower-case, or upper-case characters). Again, whereas the gain from the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
542 multi-task setting is marginal or negative for the MLP, it is substantial
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
543 for the SDA. Note that to simplify these multi-task experiments, only the original
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
544 NIST dataset is used. For example, the MLP-digits bar shows the relative
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
545 percent improvement in MLP error rate on the NIST digits test set
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
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parents:
diff changeset
546 is $100\% \times$ (single-task
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
547 model's error / multi-task model's error - 1). The single-task model is
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
548 trained with only 10 outputs (one per digit), seeing only digit examples,
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
549 whereas the multi-task model is trained with 62 outputs, with all 62
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
550 character classes as examples. Hence the hidden units are shared across
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
551 all tasks. For the multi-task model, the digit error rate is measured by
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
552 comparing the correct digit class with the output class associated with the
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
553 maximum conditional probability among only the digit classes outputs. The
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
554 setting is similar for the other two target classes (lower case characters
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
555 and upper case characters).
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
556 %%\vspace*{-1mm}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
557 %\subsection{Perturbed Training Data More Helpful for SDA}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
558 %%\vspace*{-1mm}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
559
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
560 %%\vspace*{-1mm}
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parents:
diff changeset
561 %\subsection{Multi-Task Learning Effects}
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parents:
diff changeset
562 %%\vspace*{-1mm}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
563
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
564 \iffalse
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
565 As previously seen, the SDA is better able to benefit from the
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
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parents:
diff changeset
566 transformations applied to the data than the MLP. In this experiment we
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
567 define three tasks: recognizing digits (knowing that the input is a digit),
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
568 recognizing upper case characters (knowing that the input is one), and
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
569 recognizing lower case characters (knowing that the input is one). We
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parents:
diff changeset
570 consider the digit classification task as the target task and we want to
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
571 evaluate whether training with the other tasks can help or hurt, and
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
572 whether the effect is different for MLPs versus SDAs. The goal is to find
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
573 out if deep learning can benefit more (or less) from multiple related tasks
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parents:
diff changeset
574 (i.e. the multi-task setting) compared to a corresponding purely supervised
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
575 shallow learner.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
576
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
577 We use a single hidden layer MLP with 1000 hidden units, and a SDA
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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578 with 3 hidden layers (1000 hidden units per layer), pre-trained and
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
579 fine-tuned on NIST.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
580
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
581 Our results show that the MLP benefits marginally from the multi-task setting
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
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582 in the case of digits (5\% relative improvement) but is actually hurt in the case
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boulanni <nicolas_boulanger@hotmail.com>
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583 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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584 On the other hand the SDA benefited from the multi-task setting, with relative
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
585 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
586 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
587 \fi
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
588
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
589
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
590 \vspace*{-2mm}
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parents:
diff changeset
591 \section{Conclusions and Discussion}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
592 \vspace*{-2mm}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
593
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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594 We have found that the self-taught learning framework is more beneficial
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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595 to a deep learner than to a traditional shallow and purely
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boulanni <nicolas_boulanger@hotmail.com>
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diff changeset
596 supervised learner. More precisely,
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parents:
diff changeset
597 the answers are positive for all the questions asked in the introduction.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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598 %\begin{itemize}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
599
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
600 $\bullet$ %\item
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
601 {\bf Do the good results previously obtained with deep architectures on the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
602 MNIST digits generalize to a much larger and richer (but similar)
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
603 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
604 Yes, the SDA {\em systematically outperformed the MLP and all the previously
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
605 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
606 performance} at around 17\% error on the 62-class task and 1.4\% on the digits,
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
607 and beating previously published results on the same data.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
608
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
609 $\bullet$ %\item
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
610 {\bf To what extent do self-taught learning scenarios help deep learners,
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
611 and do they help them more than shallow supervised ones}?
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
612 We found that distorted training examples not only made the resulting
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
613 classifier better on similarly perturbed images but also on
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
614 the {\em original clean examples}, and more importantly and more novel,
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
615 that deep architectures benefit more from such {\em out-of-distribution}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
616 examples. MLPs were helped by perturbed training examples when tested on perturbed input
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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617 images (65\% relative improvement on NISTP)
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
618 but only marginally helped (5\% relative improvement on all classes)
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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619 or even hurt (10\% relative loss on digits)
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
620 with respect to clean examples . On the other hand, the deep SDAs
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
621 were significantly boosted by these out-of-distribution examples.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
622 Similarly, whereas the improvement due to the multi-task setting was marginal or
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
623 negative for the MLP (from +5.6\% to -3.6\% relative change),
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
624 it was quite significant for the SDA (from +13\% to +27\% relative change),
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
625 which may be explained by the arguments below.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
626 %\end{itemize}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
627
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
628 In the original self-taught learning framework~\citep{RainaR2007}, the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
629 out-of-sample examples were used as a source of unsupervised data, and
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
630 experiments showed its positive effects in a \emph{limited labeled data}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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631 scenario. However, many of the results by \citet{RainaR2007} (who used a
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
632 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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633 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
634 We note instead that, for deep
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
635 architectures, our experiments show that such a positive effect is accomplished
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
636 even in a scenario with a \emph{large number of labeled examples},
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
637 i.e., here, the relative gain of self-taught learning is probably preserved
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
638 in the asymptotic regime.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
639
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
640 {\bf Why would deep learners benefit more from the self-taught learning framework}?
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
641 The key idea is that the lower layers of the predictor compute a hierarchy
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
642 of features that can be shared across tasks or across variants of the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
643 input distribution. A theoretical analysis of generalization improvements
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
644 due to sharing of intermediate features across tasks already points
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
645 towards that explanation~\cite{baxter95a}.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
646 Intermediate features that can be used in different
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
647 contexts can be estimated in a way that allows to share statistical
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
648 strength. Features extracted through many levels are more likely to
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
649 be more abstract and more invariant to some of the factors of variation
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
650 in the underlying distribution (as the experiments in~\citet{Goodfellow2009} suggest),
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
651 increasing the likelihood that they would be useful for a larger array
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
652 of tasks and input conditions.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
653 Therefore, we hypothesize that both depth and unsupervised
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
654 pre-training play a part in explaining the advantages observed here, and future
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
655 experiments could attempt at teasing apart these factors.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
656 And why would deep learners benefit from the self-taught learning
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
657 scenarios even when the number of labeled examples is very large?
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
658 We hypothesize that this is related to the hypotheses studied
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
659 in~\citet{Erhan+al-2010}. In~\citet{Erhan+al-2010}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
660 it was found that online learning on a huge dataset did not make the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
661 advantage of the deep learning bias vanish, and a similar phenomenon
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
662 may be happening here. We hypothesize that unsupervised pre-training
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
663 of a deep hierarchy with self-taught learning initializes the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
664 model in the basin of attraction of supervised gradient descent
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
665 that corresponds to better generalization. Furthermore, such good
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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666 basins of attraction are not discovered by pure supervised learning
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
667 (with or without self-taught settings) from random initialization, and more labeled examples
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
668 does not allow the shallow or purely supervised models to discover
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
669 the kind of better basins associated
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
670 with deep learning and self-taught learning.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
671
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
672 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
673 can be executed on-line at {\tt http://deep.host22.com}.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
674
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
675 \iffalse
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
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676 \section*{Appendix I: Detailed Numerical Results}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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677
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
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678 These tables correspond to Figures 2 and 3 and contain the raw error rates for each model and dataset considered.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
679 They also contain additional data such as test errors on P07 and standard errors.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
680
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
681 \begin{table}[ht]
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
682 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
683 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
684 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
685 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
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686 and using a validation set to select hyper-parameters and other training choices.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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687 \{SDA,MLP\}0 are trained on NIST,
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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688 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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689 The human error rate on digits is a lower bound because it does not count digits that were
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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690 recognized as letters. For comparison, the results found in the literature
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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691 on NIST digits classification using the same test set are included.}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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692 \label{tab:sda-vs-mlp-vs-humans}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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693 \begin{center}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
694 \begin{tabular}{|l|r|r|r|r|} \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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695 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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696 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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697 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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698 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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699 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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700 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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701 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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702 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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703 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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704 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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705 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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706 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
707 \end{tabular}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
708 \end{center}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
709 \end{table}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
710
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
711 \begin{table}[ht]
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
712 \caption{Relative change in error rates due to the use of perturbed training data,
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
713 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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714 A positive value indicates that training on the perturbed data helped for the
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
715 given test set (the first 3 columns on the 62-class tasks and the last one is
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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716 on the clean 10-class digits). Clearly, the deep learning models did benefit more
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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717 from perturbed training data, even when testing on clean data, whereas the MLP
5ab605c9a7d9 NIPS deep learning workshop submission new .tex file compressed to 8 pages
boulanni <nicolas_boulanger@hotmail.com>
parents:
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718 trained on perturbed data performed worse on the clean digits and about the same
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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719 on the clean characters. }
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boulanni <nicolas_boulanger@hotmail.com>
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720 \label{tab:perturbation-effect}
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parents:
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721 \begin{center}
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722 \begin{tabular}{|l|r|r|r|r|} \hline
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723 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
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724 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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725 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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726 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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727 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
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728 \end{tabular}
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boulanni <nicolas_boulanger@hotmail.com>
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729 \end{center}
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boulanni <nicolas_boulanger@hotmail.com>
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730 \end{table}
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boulanni <nicolas_boulanger@hotmail.com>
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diff changeset
731
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boulanni <nicolas_boulanger@hotmail.com>
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diff changeset
732 \begin{table}[ht]
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733 \caption{Test error rates and relative change in error rates due to the use of
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
734 a multi-task setting, i.e., training on each task in isolation vs training
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boulanni <nicolas_boulanger@hotmail.com>
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735 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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736 more from the multi-task setting. All experiments on only on the
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boulanni <nicolas_boulanger@hotmail.com>
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737 unperturbed NIST data, using validation error for model selection.
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boulanni <nicolas_boulanger@hotmail.com>
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738 Relative improvement is 1 - single-task error / multi-task error.}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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739 \label{tab:multi-task}
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740 \begin{center}
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741 \begin{tabular}{|l|r|r|r|} \hline
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boulanni <nicolas_boulanger@hotmail.com>
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742 & single-task & multi-task & relative \\
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boulanni <nicolas_boulanger@hotmail.com>
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743 & setting & setting & improvement \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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744 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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745 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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746 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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747 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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748 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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749 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
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boulanni <nicolas_boulanger@hotmail.com>
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750 \end{tabular}
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751 \end{center}
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752 \end{table}
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boulanni <nicolas_boulanger@hotmail.com>
parents:
diff changeset
753
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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754 \fi
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diff changeset
755
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boulanni <nicolas_boulanger@hotmail.com>
parents:
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756 %\afterpage{\clearpage}
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757 %\clearpage
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758 {
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boulanni <nicolas_boulanger@hotmail.com>
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759 %\bibliographystyle{spbasic} % basic style, author-year citations
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760 \bibliographystyle{plainnat}
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761 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,specials,aigaion-shorter}
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762 %\bibliographystyle{unsrtnat}
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763 %\bibliographystyle{apalike}
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diff changeset
764 }
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diff changeset
765
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parents:
diff changeset
766
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767 \end{document}