annotate writeup/nips2010_submission.tex @ 535:caf7769ca19c

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author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Tue, 01 Jun 2010 22:25:35 -0400
parents 4d6493d171f6
children 84f42fe05594
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1 \documentclass{article} % For LaTeX2e
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2 \usepackage{nips10submit_e,times}
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4 \usepackage{amsthm,amsmath,bbm}
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5 \usepackage[psamsfonts]{amssymb}
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6 \usepackage{algorithm,algorithmic}
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7 \usepackage[utf8]{inputenc}
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8 \usepackage{graphicx,subfigure}
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9 \usepackage[numbers]{natbib}
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11 %\setlength\parindent{0mm}
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12
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13 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
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14 \author{The IFT6266 Gang}
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16 \begin{document}
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18 %\makeanontitle
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19 \maketitle
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20
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21 \vspace*{-2mm}
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22 \begin{abstract}
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23 Recent theoretical and empirical work in statistical machine learning has
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24 demonstrated the importance of learning algorithms for deep
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25 architectures, i.e., function classes obtained by composing multiple
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26 non-linear transformations. Self-taught learning (exploiting unlabeled
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27 examples or examples from other distributions) has already been applied
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28 to deep learners, but mostly to show the advantage of unlabeled
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29 examples. Here we explore the advantage brought by {\em out-of-distribution
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30 examples} and show that {\em deep learners benefit more from them than a
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31 corresponding shallow learner}, in the area
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32 of handwritten character recognition. In fact, we show that they reach
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33 human-level performance on both handwritten digit classification and
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34 62-class handwritten character recognition. For this purpose we
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35 developed a powerful generator of stochastic variations and noise
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36 processes character images, including not only affine transformations but
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37 also slant, local elastic deformations, changes in thickness, background
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38 images, grey level changes, contrast, occlusion, and various types of pixel and
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39 spatially correlated noise. The out-of-distribution examples are
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40 obtained by training with these highly distorted images or
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41 by including object classes different from those in the target test set.
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42 \end{abstract}
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43 \vspace*{-2mm}
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45 \section{Introduction}
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46 \vspace*{-1mm}
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48 Deep Learning has emerged as a promising new area of research in
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49 statistical machine learning (see~\citet{Bengio-2009} for a review).
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50 Learning algorithms for deep architectures are centered on the learning
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51 of useful representations of data, which are better suited to the task at hand.
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52 This is in great part inspired by observations of the mammalian visual cortex,
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53 which consists of a chain of processing elements, each of which is associated with a
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54 different representation of the raw visual input. In fact,
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55 it was found recently that the features learnt in deep architectures resemble
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56 those observed in the first two of these stages (in areas V1 and V2
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57 of visual cortex)~\citep{HonglakL2008}, and that they become more and
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58 more invariant to factors of variation (such as camera movement) in
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59 higher layers~\citep{Goodfellow2009}.
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60 Learning a hierarchy of features increases the
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61 ease and practicality of developing representations that are at once
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62 tailored to specific tasks, yet are able to borrow statistical strength
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63 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
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64 feature representation can lead to higher-level (more abstract, more
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65 general) features that are more robust to unanticipated sources of
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66 variance extant in real data.
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67
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68 Whereas a deep architecture can in principle be more powerful than a
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69 shallow one in terms of representation, depth appears to render the
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70 training problem more difficult in terms of optimization and local minima.
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71 It is also only recently that successful algorithms were proposed to
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72 overcome some of these difficulties. All are based on unsupervised
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73 learning, often in an greedy layer-wise ``unsupervised pre-training''
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74 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
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75 applied here, is the Denoising
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76 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which
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77 performed similarly or better than previously proposed Restricted Boltzmann
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78 Machines in terms of unsupervised extraction of a hierarchy of features
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79 useful for classification. The principle is that each layer starting from
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80 the bottom is trained to encode its input (the output of the previous
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81 layer) and to reconstruct it from a corrupted version. After this
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82 unsupervised initialization, the stack of denoising auto-encoders can be
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83 converted into a deep supervised feedforward neural network and fine-tuned by
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84 stochastic gradient descent.
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85
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86 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
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87 of semi-supervised and multi-task learning: the learner can exploit examples
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88 that are unlabeled and/or come from a distribution different from the target
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89 distribution, e.g., from other classes that those of interest.
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90 It has already been shown that deep learners can clearly take advantage of
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91 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
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92 but more needs to be done to explore the impact
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93 of {\em out-of-distribution} examples and of the multi-task setting
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94 (one exception is~\citep{CollobertR2008}, but using very different kinds
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95 of learning algorithms). In particular the {\em relative
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96 advantage} of deep learning for this settings has not been evaluated.
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97 The hypothesis explored here is that a deep hierarchy of features
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98 may be better able to provide sharing of statistical strength
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99 between different regions in input space or different tasks,
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100 as discussed in the conclusion.
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101
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102 In this paper we ask the following questions:
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103
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104 %\begin{enumerate}
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105 $\bullet$ %\item
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106 Do the good results previously obtained with deep architectures on the
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107 MNIST digit images generalize to the setting of a much larger and richer (but similar)
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108 dataset, the NIST special database 19, with 62 classes and around 800k examples?
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109
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110 $\bullet$ %\item
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111 To what extent does the perturbation of input images (e.g. adding
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112 noise, affine transformations, background images) make the resulting
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113 classifiers better not only on similarly perturbed images but also on
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114 the {\em original clean examples}?
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115
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116 $\bullet$ %\item
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117 Do deep architectures {\em benefit more from such out-of-distribution}
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118 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
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119
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120 $\bullet$ %\item
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121 Similarly, does the feature learning step in deep learning algorithms benefit more
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122 training with similar but different classes (i.e. a multi-task learning scenario) than
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123 a corresponding shallow and purely supervised architecture?
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124 %\end{enumerate}
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125
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126 Our experimental results provide positive evidence towards all of these questions.
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127
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128 \vspace*{-1mm}
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129 \section{Perturbation and Transformation of Character Images}
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130 \label{s:perturbations}
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131 \vspace*{-1mm}
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132
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133 This section describes the different transformations we used to stochastically
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134 transform source images in order to obtain data. More details can
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135 be found in this technical report~\citep{ift6266-tr-anonymous}.
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136 The code for these transformations (mostly python) is available at
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137 {\tt http://anonymous.url.net}. All the modules in the pipeline share
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138 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
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139 amount of deformation or noise introduced.
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140
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141 There are two main parts in the pipeline. The first one,
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142 from slant to pinch below, performs transformations. The second
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143 part, from blur to contrast, adds different kinds of noise.
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144
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145 \begin{figure}[ht]
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146 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/transfo.png}}}
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147 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE
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148 \caption{Illustration of each transformation applied alone to the same image
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149 of an upper-case h (top left). First row (from left to right) : original image, slant,
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150 thickness, affine transformation (translation, rotation, shear),
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151 local elastic deformation; second row (from left to right) :
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152 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to right) :
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153 background image, salt and pepper noise, spatially Gaussian noise, scratches,
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154 grey level and contrast changes.}
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155 \label{fig:transfo}
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156 \end{figure}
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157
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158 {\large\bf Transformations}
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159
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160 \vspace*{2mm}
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161
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162 {\bf Slant.}
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163 We mimic slant by shifting each row of the image
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164 proportionally to its height: $shift = round(slant \times height)$.
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165 The $slant$ coefficient can be negative or positive with equal probability
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166 and its value is randomly sampled according to the complexity level:
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167 $slant \sim U[0,complexity]$, so the
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168 maximum displacement for the lowest or highest pixel line is of
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169 $round(complexity \times 32)$.
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170 \vspace*{0mm}
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171
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172 {\bf Thickness.}
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173 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
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174 are applied. The neighborhood of each pixel is multiplied
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175 element-wise with a {\em structuring element} matrix.
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176 The pixel value is replaced by the maximum or the minimum of the resulting
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177 matrix, respectively for dilation or erosion. Ten different structural elements with
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178 increasing dimensions (largest is $5\times5$) were used. For each image,
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179 randomly sample the operator type (dilation or erosion) with equal probability and one structural
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180 element from a subset of the $n$ smallest structuring elements where $n$ is
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181 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
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182 for erosion. A neutral element is always present in the set, and if it is
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183 chosen no transformation is applied. Erosion allows only the six
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184 smallest structural elements because when the character is too thin it may
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185 be completely erased.
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186 \vspace*{0mm}
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187
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188 {\bf Affine Transformations.}
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189 A $2 \times 3$ affine transform matrix (with
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190 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
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191 Each pixel $(x,y)$ of the output image takes the value of the pixel
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192 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This
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193 produces scaling, translation, rotation and shearing.
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194 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
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195 forbid important rotations (not to confuse classes) but to give good
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196 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
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197 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
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198 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
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199 complexity]$.
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200 \vspace*{0mm}
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201
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202 {\bf Local Elastic Deformations.}
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203 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
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204 which provides more details.
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205 Two ``displacements'' fields are generated and applied, for horizontal
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206 and vertical displacements of pixels.
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207 To generate a pixel in either field, first a value between -1 and 1 is
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208 chosen from a uniform distribution. Then all the pixels, in both fields, are
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209 multiplied by a constant $\alpha$ which controls the intensity of the
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210 displacements (larger $\alpha$ translates into larger wiggles).
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211 Each field is convoluted with a Gaussian 2D kernel of
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212 standard deviation $\sigma$. Visually, this results in a blur.
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213 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
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214 \sqrt[3]{complexity}$.
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215 \vspace*{0mm}
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216
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217 {\bf Pinch.}
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218 This is a GIMP filter called ``Whirl and
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219 pinch'', but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
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220 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
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221 For a square input image, this is akin to drawing a circle of
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222 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
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223 that disk (region inside circle) will have its value recalculated by taking
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224 the value of another ``source'' pixel in the original image. The position of
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225 that source pixel is found on the line that goes through $C$ and $P$, but
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226 at some other distance $d_2$. Define $d_1$ to be the distance between $P$
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227 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
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228 d_1$, where $pinch$ is a parameter to the filter.
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229 The actual value is given by bilinear interpolation considering the pixels
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230 around the (non-integer) source position thus found.
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231 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
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232
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233 \vspace*{1mm}
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234
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235 {\large\bf Injecting Noise}
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236
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237 \vspace*{1mm}
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238
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239 {\bf Motion Blur.}
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240 This is a ``linear motion blur'' in GIMP
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241 terminology, with two parameters, $length$ and $angle$. The value of
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242 a pixel in the final image is approximately the mean value of the $length$ first pixels
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243 found by moving in the $angle$ direction.
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244 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
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245 \vspace*{0mm}
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246
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247 {\bf Occlusion.}
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248 Selects a random rectangle from an {\em occluder} character
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249 images and places it over the original {\em occluded} character
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250 image. Pixels are combined by taking the max(occluder,occluded),
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251 closer to black. The rectangle corners
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252 are sampled so that larger complexity gives larger rectangles.
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253 The destination position in the occluded image are also sampled
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254 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
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255 This filter has a probability of 60\% of not being applied.
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256 \vspace*{0mm}
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257
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258 {\bf Pixel Permutation.}
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259 This filter permutes neighbouring pixels. It selects first
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260 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
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261 sequentially exchanged with one other pixel in its $V4$ neighbourhood. The number
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262 of exchanges to the left, right, top, bottom is equal or does not differ
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263 from more than 1 if the number of selected pixels is not a multiple of 4.
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264 % TODO: The previous sentence is hard to parse
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265 This filter has a probability of 80\% of not being applied.
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266 \vspace*{0mm}
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267
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268 {\bf Gaussian Noise.}
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269 This filter simply adds, to each pixel of the image independently, a
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270 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
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271 It has a probability of 70\% of not being applied.
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272 \vspace*{0mm}
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273
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274 {\bf Background Images.}
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parents: 467
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275 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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276 background behind the letter. The background is chosen by first selecting,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
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277 at random, an image from a set of images. Then a 32$\times$32 sub-region
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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278 of that image is chosen as the background image (by sampling position
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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279 uniformly while making sure not to cross image borders).
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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280 To combine the original letter image and the background image, contrast
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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281 adjustments are made. We first get the maximal values (i.e. maximal
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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282 intensity) for both the original image and the background image, $maximage$
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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283 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
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284 Each background pixel value is multiplied by $\frac{max(maximage -
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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285 contrast, 0)}{maxbg}$ (higher contrast yield darker
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286 background). The output image pixels are max(background,original).
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287 \vspace*{0mm}
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288
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289 {\bf Salt and Pepper Noise.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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290 This filter adds noise $\sim U[0,1]$ to random subsets of pixels.
Yoshua Bengio <bengioy@iro.umontreal.ca>
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291 The number of selected pixels is $0.2 \times complexity$.
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292 This filter has a probability of not being applied at all of 75\%.
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293 \vspace*{0mm}
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294
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295 {\bf Spatially Gaussian Noise.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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296 Different regions of the image are spatially smoothed.
Yoshua Bengio <bengioy@iro.umontreal.ca>
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297 The image is convolved with a symmetric Gaussian kernel of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
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298 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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299 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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300 between $0$ and $1$. We also create a symmetric averaging window, of the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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301 kernel size, with maximum value at the center. For each image we sample
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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302 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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303 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
304 initialize to zero a mask matrix of the image size. For each selected pixel
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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305 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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306 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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307 image \times mask}{mask+1}$.
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308 This filter has a probability of not being applied at all of 75\%.
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309 \vspace*{0mm}
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310
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311 {\bf Scratches.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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312 The scratches module places line-like white patches on the image. The
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
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313 lines are heavily transformed images of the digit ``1'' (one), chosen
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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314 at random among five thousands such 1 images. The 1 image is
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
315 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
316 complexity)^2$, using bi-cubic interpolation,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
317 Two passes of a grey-scale morphological erosion filter
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
318 are applied, reducing the width of the line
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
319 by an amount controlled by $complexity$.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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320 This filter is only applied only 15\% of the time. When it is applied, 50\%
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
321 of the time, only one patch image is generated and applied. In 30\% of
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
322 cases, two patches are generated, and otherwise three patches are
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
323 generated. The patch is applied by taking the maximal value on any given
523
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
324 patch or the original image, for each of the 32x32 pixel locations.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
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325 \vspace*{0mm}
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parents: 522
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326
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
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327 {\bf Grey Level and Contrast Changes.}
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
328 This filter changes the contrast and may invert the image polarity (white
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
329 on black to black on white). The contrast $C$ is defined here as the
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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330 difference between the maximum and the minimum pixel value of the image.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
331 Contrast $\sim U[1-0.85 \times complexity,1]$ (so contrast $\geq 0.15$).
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
332 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
333 polarity is inverted with $0.5$ probability.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
334
499
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
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335 \iffalse
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
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336 \begin{figure}[ht]
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
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337 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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338 \caption{Illustration of the pipeline of stochastic
519
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
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339 transformations applied to the image of a lower-case \emph{t}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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340 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
341 left to right, first top line, then bottom line) shows the result
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
342 of applying one of the modules in the pipeline. The last image
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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343 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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344 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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345 \end{figure}
499
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
346 \fi
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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347
479
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Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
348
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
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349 \vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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350 \section{Experimental Setup}
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
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351 \vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
352
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
353 Whereas much previous work on deep learning algorithms had been performed on
516
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Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
354 the MNIST digits classification task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
355 with 60~000 examples, and variants involving 10~000
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
356 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
357 to focus here on the case of much larger training sets, from 10 times to
530
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
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358 to 1000 times larger.
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
359
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
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360 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
499
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
361 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
362 and {\bf OCR data} (scanned machine printed characters). Once a character
530
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
363 is sampled from one of these sources (chosen randomly), the pipeline of
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
364 the transformations and/or noise processes described in section \ref{s:perturbations}
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
365 is applied to the image.
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
366
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
367 We compare the best MLPs against
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
368 the best SDAs (both models' hyper-parameters are selected to minimize the validation set error),
530
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
369 along with a comparison against a precise estimate
502
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
370 of human performance obtained via Amazon's Mechanical Turk (AMT)
530
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
371 service (http://mturk.com).
502
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
372 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
373 of money to perform tasks for which human intelligence is required.
522
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
374 Mechanical Turk has been used extensively in natural language processing and vision.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
375 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
376 %\citep{SorokinAndForsyth2008,whitehill09}.
530
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
377 AMT users were presented
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
378 with 10 character images and asked to choose 10 corresponding ASCII
502
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
379 characters. They were forced to make a hard choice among the
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
380 62 or 10 character classes (all classes or digits only).
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
381 Three users classified each image, allowing
530
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
382 to estimate inter-human variability. A total 2500 images/dataset were classified.
502
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
383
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
384 \vspace*{-1mm}
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
385 \subsection{Data Sources}
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
386 \vspace*{-1mm}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
387
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
388 %\begin{itemize}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
389 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
390 {\bf NIST.}
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
391 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
392 widely used for training and testing character
516
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Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
393 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
519
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
394 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
395 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
519
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
396 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
534
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
397 The fourth partition (called $hsf_4$, 82587 examples),
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
398 experimentally recognized to be the most difficult one, is the one recommended
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
399 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}
534
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
400 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
401 model selection.
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
402 The performances reported by previous work on that dataset mostly use only the digits.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
403 Here we use all the classes both in the training and testing phase. This is especially
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
404 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
405 Note that the distribution of the classes in the NIST training and test sets differs
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
406 substantially, with relatively many more digits in the test set, and more uniform distribution
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
407 of letters in the test set, compared to the training set (in the latter, the letters are distributed
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
408 more like the natural distribution of letters in text).
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
409
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
410 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
411 {\bf Fonts.}
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
412 In order to have a good variety of sources we downloaded an important number of free fonts from:
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
413 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
414 % TODO: pointless to anonymize, it's not pointing to our work
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
415 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
416 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
479
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
417 directly as input to our models.
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
418
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
419 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
420 {\bf Captchas.}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
421 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
422 generating characters of the same format as the NIST dataset. This software is based on
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
423 a random character class generator and various kinds of transformations similar to those described in the previous sections.
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
424 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
425 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
426 depending on the value of the complexity parameter provided by the user of the data source.
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
427 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
428
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
429 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
430 {\bf OCR data.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
431 A large set (2 million) of scanned, OCRed and manually verified machine-printed
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
432 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
433 additional source. This set is part of a larger corpus being collected by the Image Understanding
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
434 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
435 ({\tt http://www.iupr.com}), and which will be publicly released.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
436 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
437 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
438
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
439 \vspace*{-1mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
440 \subsection{Data Sets}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
441 \vspace*{-1mm}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
442
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
443 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
444 from one of the 62 character classes.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
445 %\begin{itemize}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
446
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
447 %\item
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
448 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
449 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
450
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
451 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
452 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
453 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
454 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
455 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
456 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
457 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
458
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
459 %\item
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
460 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
461 except that we only apply
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
462 transformations from slant to pinch. Therefore, the character is
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
463 transformed but no additional noise is added to the image, giving images
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
464 closer to the NIST dataset.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
465 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
466 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
467
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
468 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
469 \subsection{Models and their Hyperparameters}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
470 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
471
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
472 The experiments are performed with Multi-Layer Perceptrons (MLP) with a single
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
473 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
474 \emph{Note that all hyper-parameters are selected based on performance on the {\bf NISTP} validation set.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
475
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
476 {\bf Multi-Layer Perceptrons (MLP).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
477 Whereas previous work had compared deep architectures to both shallow MLPs and
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
478 SVMs, we only compared to MLPs here because of the very large datasets used
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
479 (making the use of SVMs computationally challenging because of their quadratic
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
480 scaling behavior).
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
481 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
482 exponentials) on the output layer for estimating $P(class | image)$.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
483 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
484 Training examples are presented in minibatches of size 20. A constant learning
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
485 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
486 through preliminary experiments (measuring performance on a validation set),
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
487 and $0.1$ was then selected for optimizing on the whole training sets.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
488
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
489 \begin{figure}[ht]
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
490 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
491 \caption{Illustration of the computations and training criterion for the denoising
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
492 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
493 the layer (i.e. raw input or output of previous layer)
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
494 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
495 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
496 is compared to the uncorrupted input $x$ through the loss function
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
497 $L_H(x,z)$, whose expected value is approximately minimized during training
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
498 by tuning $\theta$ and $\theta'$.}
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
499 \label{fig:da}
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
500 \end{figure}
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
501
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
502 {\bf Stacked Denoising Auto-Encoders (SDA).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
503 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
504 can be used to initialize the weights of each layer of a deep MLP (with many hidden
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
505 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
506 apparently setting parameters in the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
507 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
508 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
509 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
510 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
511 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
512 $P(y|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
513 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
514 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
515 compositions of simpler ones through a deep hierarchy).
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
516
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
517 Here we chose to use the Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
518 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
519 these deep hierarchies of features, as it is very simple to train and
532
2e33885730cf changements aux charts.ods
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 529
diff changeset
520 explain (see Figure~\ref{fig:da}, as well as
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
521 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
522 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
523 comparable or better than RBMs in series of experiments
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
524 \citep{VincentPLarochelleH2008}. During training, a Denoising
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
525 Auto-Encoder is presented with a stochastically corrupted version
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
526 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
527 forcing the hidden units to represent the leading regularities in
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
528 the data. Once it is trained, in a purely unsupervised way,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
529 its hidden units activations can
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
530 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
531 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
532 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
533 the same standard procedure used to train them (see previous section).
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
534 The SDA hyper-parameters are the same as for the MLP, with the addition of the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
535 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
536 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
537 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
538 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
539 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
540 of hidden layers but it was fixed to 3 based on previous work with
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
541 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
542
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
543 \vspace*{-1mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
544
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
545 \begin{figure}[ht]
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
546 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
547 \caption{Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
548 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
549 of all models, on 3 different test sets (NIST, NISTP, P07).
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
550 Right: error rates on NIST test digits only, along with the previous results from
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
551 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
552 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
553
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
554 \label{fig:error-rates-charts}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
555 \vspace*{-1mm}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
556 \end{figure}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
557
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
558
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
559 \section{Experimental Results}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
560
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
561 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
562 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
563 %\vspace*{-1mm}
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
564 The models are either trained on NIST (MLP0 and SDA0),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
565 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
566 on either NIST, NISTP or P07, either on all 62 classes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
567 or only on the digits (considering only the outputs
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
568 associated with digit classes).
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
569 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
570 comparing Humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
571 SDA2), along with the previous results on the digits NIST special database
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
572 19 test set from the literature respectively based on ARTMAP neural
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
573 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
516
092dae9a5040 make the reference more compact.
Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
574 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
575 ~\citep{Milgram+al-2005}. More detailed and complete numerical results
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
576 (figures and tables, including standard errors on the error rates) can be
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
577 found in Appendix I of the supplementary material.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
578 The deep learner not only outperformed the shallow ones and
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
579 previously published performance (in a statistically and qualitatively
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
580 significant way) but when trained with perturbed data
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
581 reaches human performance on both the 62-class task
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
582 and the 10-class (digits) task.
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
583
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
584 \begin{figure}[ht]
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
585 \vspace*{-2mm}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
586 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
587 \caption{Relative improvement in error rate due to self-taught learning.
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
588 Left: Improvement (or loss, when negative)
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
589 induced by out-of-distribution examples (perturbed data).
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
590 Right: Improvement (or loss, when negative) induced by multi-task
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
591 learning (training on all classes and testing only on either digits,
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
592 upper case, or lower-case). The deep learner (SDA) benefits more from
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
593 both self-taught learning scenarios, compared to the shallow MLP.}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
594 \label{fig:improvements-charts}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
595 \vspace*{-2mm}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
596 \end{figure}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
597
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
598 In addition, as shown in the left of
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
599 Figure~\ref{fig:improvements-charts}, the relative improvement in error
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
600 rate brought by self-taught learning is greater for the SDA, and these
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
601 differences with the MLP are statistically and qualitatively
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
602 significant.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
603 The left side of the figure shows the improvement to the clean
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
604 NIST test set error brought by the use of out-of-distribution examples
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
605 (i.e. the perturbed examples examples from NISTP or P07).
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
606 Relative change is measured by taking
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
607 (original model's error / perturbed-data model's error - 1).
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
608 The right side of
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
609 Figure~\ref{fig:improvements-charts} shows the relative improvement
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
610 brought by the use of a multi-task setting, in which the same model is
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
611 trained for more classes than the target classes of interest (i.e. training
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
612 with all 62 classes when the target classes are respectively the digits,
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
613 lower-case, or upper-case characters). Again, whereas the gain from the
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
614 multi-task setting is marginal or negative for the MLP, it is substantial
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
615 for the SDA. Note that for these multi-task experiment, only the original
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
616 NIST dataset is used. For example, the MLP-digits bar shows the relative
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
617 improvement in MLP error rate on the NIST digits test set (1 - single-task
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
618 model's error / multi-task model's error). The single-task model is
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
619 trained with only 10 outputs (one per digit), seeing only digit examples,
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
620 whereas the multi-task model is trained with 62 outputs, with all 62
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
621 character classes as examples. Hence the hidden units are shared across
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
622 all tasks. For the multi-task model, the digit error rate is measured by
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
623 comparing the correct digit class with the output class associated with the
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
624 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
625 setting is similar for the other two target classes (lower case characters
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
626 and upper case characters).
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
627
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
628 %\vspace*{-1mm}
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
629 %\subsection{Perturbed Training Data More Helpful for SDA}
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
630 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
631
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
632 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
633 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
634 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
635
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
636 \iffalse
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
637 As previously seen, the SDA is better able to benefit from the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
638 transformations applied to the data than the MLP. In this experiment we
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
639 define three tasks: recognizing digits (knowing that the input is a digit),
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
640 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
641 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
642 consider the digit classification task as the target task and we want to
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
643 evaluate whether training with the other tasks can help or hurt, and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
644 whether the effect is different for MLPs versus SDAs. The goal is to find
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
645 out if deep learning can benefit more (or less) from multiple related tasks
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
646 (i.e. the multi-task setting) compared to a corresponding purely supervised
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
647 shallow learner.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
648
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
649 We use a single hidden layer MLP with 1000 hidden units, and a SDA
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
650 with 3 hidden layers (1000 hidden units per layer), pre-trained and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
651 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
652
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
653 Our results show that the MLP benefits marginally from the multi-task setting
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
654 in the case of digits (5\% relative improvement) but is actually hurt in the case
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
655 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
656 On the other hand the SDA benefited from the multi-task setting, with relative
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
657 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
658 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
659 \fi
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
660
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
661
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
662 \vspace*{-1mm}
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
663 \section{Conclusions and Discussion}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
664 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
665
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
666 We have found that the self-taught learning framework is more beneficial
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
667 to a deep learner than to a traditional shallow and purely
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
668 supervised learner. More precisely,
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
669 the answers are positive for all the questions asked in the introduction.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
670 %\begin{itemize}
487
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 486
diff changeset
671
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
672 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
673 Do the good results previously obtained with deep architectures on the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
674 MNIST digits generalize to the setting of a much larger and richer (but similar)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
675 dataset, the NIST special database 19, with 62 classes and around 800k examples?
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
676 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
677 published results on this dataset} (the ones that we are aware of), {\bf in fact reaching human-level
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
678 performance} at around 17\% error on the 62-class task and 1.4\% on the digits.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
679
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
680 $\bullet$ %\item
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
681 To what extent do self-taught learning scenarios help deep learners,
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
682 and do they help them more than shallow supervised ones?
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
683 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
684 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
685 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
686 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
687 examples. MLPs were helped by perturbed training examples when tested on perturbed input
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
688 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
689 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
690 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
691 with respect to clean examples . On the other hand, the deep SDAs
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
692 were very significantly boosted by these out-of-distribution examples.
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
693 Similarly, whereas the improvement due to the multi-task setting was marginal or
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
694 negative for the MLP (from +5.6\% to -3.6\% relative change),
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
695 it was very significant for the SDA (from +13\% to +27\% relative change).
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
696 %\end{itemize}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
697
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
698 In the original self-taught learning framework~\citep{RainaR2007}, the
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
699 out-of-sample examples were used as a source of unsupervised data, and
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
700 experiments showed its positive effects in a \emph{limited labeled data}
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
701 scenario. However, many of the results by \citet{RainaR2007} (who used a
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
702 shallow, sparse coding approach) suggest that the relative gain of self-taught
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
703 learning diminishes as the number of labeled examples increases, (essentially,
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
704 a ``diminishing returns'' scenario occurs). We note instead that, for deep
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
705 architectures, our experiments show that such a positive effect is accomplished
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
706 even in a scenario with a \emph{very large number of labeled examples}.
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
707
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
708 Why would deep learners benefit more from the self-taught learning framework?
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
709 The key idea is that the lower layers of the predictor compute a hierarchy
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
710 of features that can be shared across tasks or across variants of the
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
711 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
712 contexts can be estimated in a way that allows to share statistical
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
713 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
714 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
715 increasing the likelihood that they would be useful for a larger array
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
716 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
717 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
718 pre-training play a part in explaining the advantages observed here, and future
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
719 experiments could attempt at teasing apart these factors.
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
720 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
721 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
722 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
723 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
724 it was found that online learning on a huge dataset did not make the
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
725 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
726 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
727 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
728 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
729 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
730 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
731 (with or without self-taught settings), and more labeled examples
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
732 does not allow to go from the poorer basins of attraction discovered
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
733 by the purely supervised shallow models to the kind of better basins associated
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
734 with deep learning and self-taught learning.
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
735
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
736 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
737 can be executed on-line at {\tt http://deep.host22.com}.
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
738
498
7ff00c27c976 add missing file for bibtex and make it smaller.
Frederic Bastien <nouiz@nouiz.org>
parents: 496
diff changeset
739 \newpage
496
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
740 {
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
741 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,aigaion-shorter,specials}
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
742 %\bibliographystyle{plainnat}
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
743 \bibliographystyle{unsrtnat}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
744 %\bibliographystyle{apalike}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
745 }
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
746
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
747
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
748 \end{document}