annotate writeup/nips2010_submission.tex @ 557:17d16700e0c8

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author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Thu, 03 Jun 2010 09:17:01 -0400
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1 \documentclass{article} % For LaTeX2e
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2 \usepackage{nips10submit_e,times}
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3 \usepackage{wrapfig}
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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 demonstrated the importance of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple non-linear transformations. Self-taught learning (exploiting unlabeled examples or examples from other distributions) has already been applied to deep learners, but mostly to show the advantage of unlabeled examples. Here we explore the advantage brought by {\em out-of-distribution examples} and show that {\em deep learners benefit more from them than a corresponding shallow learner}, in the area of handwritten character recognition. In fact, we show that they reach human-level performance on both handwritten digit classification and 62-class handwritten character recognition. For this purpose we developed a powerful generator of stochastic variations and noise processes for character images, including not only affine transformations but also slant, local elastic deformations, changes in thickness, background images, grey level changes, contrast, occlusion, and various types of noise. The out-of-distribution examples are obtained from these highly distorted images or by including examples of object classes different from those in the target test set.
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24 \end{abstract}
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25 \vspace*{-3mm}
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27 \section{Introduction}
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28 \vspace*{-1mm}
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30 Deep Learning has emerged as a promising new area of research in
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31 statistical machine learning (see~\citet{Bengio-2009} for a review).
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32 Learning algorithms for deep architectures are centered on the learning
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33 of useful representations of data, which are better suited to the task at hand.
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34 This is in great part inspired by observations of the mammalian visual cortex,
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35 which consists of a chain of processing elements, each of which is associated with a
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36 different representation of the raw visual input. In fact,
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37 it was found recently that the features learnt in deep architectures resemble
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38 those observed in the first two of these stages (in areas V1 and V2
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39 of visual cortex)~\citep{HonglakL2008}, and that they become more and
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40 more invariant to factors of variation (such as camera movement) in
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41 higher layers~\citep{Goodfellow2009}.
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42 Learning a hierarchy of features increases the
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43 ease and practicality of developing representations that are at once
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44 tailored to specific tasks, yet are able to borrow statistical strength
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45 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
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46 feature representation can lead to higher-level (more abstract, more
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47 general) features that are more robust to unanticipated sources of
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48 variance extant in real data.
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49
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50 Whereas a deep architecture can in principle be more powerful than a
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51 shallow one in terms of representation, depth appears to render the
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52 training problem more difficult in terms of optimization and local minima.
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53 It is also only recently that successful algorithms were proposed to
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54 overcome some of these difficulties. All are based on unsupervised
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55 learning, often in an greedy layer-wise ``unsupervised pre-training''
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56 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
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57 applied here, is the Denoising
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58 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}),
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59 which
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60 performed similarly or better than previously proposed Restricted Boltzmann
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61 Machines in terms of unsupervised extraction of a hierarchy of features
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62 useful for classification. The principle is that each layer starting from
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63 the bottom is trained to encode its input (the output of the previous
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64 layer) and to reconstruct it from a corrupted version. After this
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65 unsupervised initialization, the stack of DAs can be
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66 converted into a deep supervised feedforward neural network and fine-tuned by
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67 stochastic gradient descent.
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68
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69 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
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70 of semi-supervised and multi-task learning: the learner can exploit examples
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71 that are unlabeled and/or come from a distribution different from the target
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72 distribution, e.g., from other classes than those of interest.
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73 It has already been shown that deep learners can clearly take advantage of
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74 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
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75 but more needs to be done to explore the impact
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76 of {\em out-of-distribution} examples and of the multi-task setting
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77 (one exception is~\citep{CollobertR2008}, which uses very different kinds
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78 of learning algorithms). In particular the {\em relative
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79 advantage} of deep learning for these settings has not been evaluated.
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80 The hypothesis discussed in the conclusion is that a deep hierarchy of features
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81 may be better able to provide sharing of statistical strength
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82 between different regions in input space or different tasks.
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83 %
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84 In this paper we ask the following questions:
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86 %\begin{enumerate}
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87 $\bullet$ %\item
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88 Do the good results previously obtained with deep architectures on the
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89 MNIST digit images generalize to the setting of a much larger and richer (but similar)
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90 dataset, the NIST special database 19, with 62 classes and around 800k examples?
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91
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92 $\bullet$ %\item
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93 To what extent does the perturbation of input images (e.g. adding
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94 noise, affine transformations, background images) make the resulting
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95 classifiers better not only on similarly perturbed images but also on
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96 the {\em original clean examples}?
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98 $\bullet$ %\item
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99 Do deep architectures {\em benefit more from such out-of-distribution}
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100 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
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101
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102 $\bullet$ %\item
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103 Similarly, does the feature learning step in deep learning algorithms benefit more
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104 from training with moderately different classes (i.e. a multi-task learning scenario) than
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105 a corresponding shallow and purely supervised architecture?
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106 %\end{enumerate}
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107
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108 Our experimental results provide positive evidence towards all of these questions.
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109 To achieve these results, we introduce in the next section a sophisticated system
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110 for stochastically transforming character images and then explain the methodology.
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111 The conclusion discusses
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112 the more general question of why deep learners may benefit so much from
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113 the self-taught learning framework.
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114
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115 \vspace*{-1mm}
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116 \section{Perturbation and Transformation of Character Images}
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117 \label{s:perturbations}
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118 \vspace*{-1mm}
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119
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120 \begin{wrapfigure}[8]{l}{0.15\textwidth}
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121 %\begin{minipage}[b]{0.14\linewidth}
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122 \vspace*{-5mm}
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123 \begin{center}
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124 \includegraphics[scale=.4]{images/Original.PNG}\\
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125 {\bf Original}
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126 \end{center}
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127 \end{wrapfigure}
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128 %\vspace{0.7cm}
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129 %\end{minipage}%
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130 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
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131 This section describes the different transformations we used to stochastically
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132 transform source images such as the one on the left
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133 in order to obtain data from a larger distribution which
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134 covers a domain substantially larger than the clean characters distribution from
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135 which we start.
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136 Although character transformations have been used before to
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137 improve character recognizers, this effort is on a large scale both
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138 in number of classes and in the complexity of the transformations, hence
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139 in the complexity of the learning task.
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140 More details can
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141 be found in this technical report~\citep{ift6266-tr-anonymous}.
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142 The code for these transformations (mostly python) is available at
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143 {\tt http://anonymous.url.net}. All the modules in the pipeline share
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144 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
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145 amount of deformation or noise introduced.
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146 There are two main parts in the pipeline. The first one,
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147 from slant to pinch below, performs transformations. The second
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148 part, from blur to contrast, adds different kinds of noise.
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149 %\end{minipage}
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150
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151 \vspace*{1mm}
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152 %\subsection{Transformations}
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153 {\large\bf 2.1 Transformations}
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154 \vspace*{1mm}
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155
501
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156
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157 \begin{wrapfigure}[7]{l}{0.15\textwidth}
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158 %\begin{minipage}[b]{0.14\linewidth}
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159 %\centering
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160 \begin{center}
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161 \vspace*{-5mm}
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162 \includegraphics[scale=.4]{images/Thick_only.PNG}\\
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163 {\bf Thickness}
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164 \end{center}
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165 %\vspace{.6cm}
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166 %\end{minipage}%
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167 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
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168 \end{wrapfigure}
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169 To change character {\bf thickness}, morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
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170 are applied. The neighborhood of each pixel is multiplied
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171 element-wise with a {\em structuring element} matrix.
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172 The pixel value is replaced by the maximum or the minimum of the resulting
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173 matrix, respectively for dilation or erosion. Ten different structural elements with
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174 increasing dimensions (largest is $5\times5$) were used. For each image,
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175 randomly sample the operator type (dilation or erosion) with equal probability and one structural
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176 element from a subset of the $n=round(m \times complexity)$ smallest structuring elements
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177 where $m=10$ for dilation and $m=6$ for erosion (to avoid completely erasing thin characters).
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178 A neutral element (no transformation)
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179 is always present in the set. is applied.
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180 %\vspace{.4cm}
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181 %\end{minipage}
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182 %\vspace{-.7cm}
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183
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184 \begin{minipage}[b]{0.14\linewidth}
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185 \centering
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186 \includegraphics[scale=.4]{images/Slant_only.PNG}\\
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187 {\bf Slant}
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188 \end{minipage}%
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189 \hspace{0.3cm}\begin{minipage}[b]{0.83\linewidth}
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190 %\centering
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191 %\vspace*{-15mm}
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192 To produce {\bf slant}, each row of the image is shifted
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193 proportionally to its height: $shift = round(slant \times height)$.
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194 $slant \sim U[-complexity,complexity]$.
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195 \vspace{1.5cm}
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196 \end{minipage}
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197 %\vspace*{-4mm}
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198
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199 %\begin{minipage}[b]{0.14\linewidth}
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200 %\centering
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201 \begin{wrapfigure}[8]{l}{0.15\textwidth}
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202 \vspace*{-6mm}
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203 \begin{center}
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204 \includegraphics[scale=.4]{images/Affine_only.PNG}\\
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205 {\bf Affine Transformation}
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206 \end{center}
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207 \end{wrapfigure}
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208 %\end{minipage}%
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209 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
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210 A $2 \times 3$ {\bf affine transform} matrix (with
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211 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$.
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212 Output pixel $(x,y)$ takes the value of input pixel
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213 nearest to $(ax+by+c,dx+ey+f)$,
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214 producing scaling, translation, rotation and shearing.
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215 Marginal distributions of $(a,b,c,d,e,f)$ have been tuned to
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216 forbid large rotations (not to confuse classes) but to give good
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217 variability of the transformation: $a$ and $d$ $\sim U[1-3
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218 complexity,1+3\,complexity]$, $b$ and $e$ $\sim[-3 \,complexity,3\,
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219 complexity]$ and $c$ and $f$ $\sim U[-4 \,complexity, 4 \,
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220 complexity]$.\\
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221 %\end{minipage}
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222
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223 \vspace*{-4.5mm}
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224
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225 \begin{minipage}[t]{\linewidth}
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226 \begin{wrapfigure}[7]{l}{0.15\textwidth}
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227 %\hspace*{-8mm}\begin{minipage}[b]{0.25\linewidth}
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228 %\centering
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229 \begin{center}
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230 \vspace*{-4mm}
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231 \includegraphics[scale=.4]{images/Localelasticdistorsions_only.PNG}\\
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232 {\bf Local Elastic}
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233 \end{center}
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234 \end{wrapfigure}
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235 %\end{minipage}%
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236 %\hspace{-3mm}\begin{minipage}[b]{0.85\linewidth}
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237 %\vspace*{-20mm}
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238 The {\bf local elastic} deformation
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239 module induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
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240 which provides more details.
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241 The intensity of the displacement fields is given by
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242 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are
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243 convolved with a Gaussian 2D kernel (resulting in a blur) of
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244 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$.
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245 %\vspace{.9cm}
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246 \end{minipage}
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247
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248 \vspace*{5mm}
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249
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250 %\begin{minipage}[b]{0.14\linewidth}
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251 %\centering
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252 \begin{wrapfigure}[7]{l}{0.15\textwidth}
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253 \vspace*{-5mm}
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254 \begin{center}
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255 \includegraphics[scale=.4]{images/Pinch_only.PNG}\\
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256 {\bf Pinch}
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257 \end{center}
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258 \end{wrapfigure}
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259 %\vspace{.6cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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260 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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261 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
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262 The {\bf pinch} module applies the ``Whirl and pinch'' GIMP filter with whirl was set to 0.
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parents: 539
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263 A pinch is ``similar to projecting the image onto an elastic
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13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
264 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
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265 For a square input image, draw a radius-$r$ disk
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
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266 around $C$. Any pixel $P$ belonging to
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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267 that disk has its value replaced by
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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268 the value of a ``source'' pixel in the original image,
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parents: 554
diff changeset
269 on the line that goes through $C$ and $P$, but
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parents: 554
diff changeset
270 at some other distance $d_2$. Define $d_1=distance(P,C) = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
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diff changeset
271 d_1$, where $pinch$ is a parameter of the filter.
464
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272 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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273 around the (non-integer) source position thus found.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
274 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
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275 %\vspace{1.5cm}
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276 %\end{minipage}
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277
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278 \vspace{2mm}
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279
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280 {\large\bf 2.2 Injecting Noise}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
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281 %\subsection{Injecting Noise}
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282 \vspace{2mm}
484
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283
555
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diff changeset
284 %\vspace*{-.2cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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diff changeset
285 \begin{minipage}[t]{0.14\linewidth}
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diff changeset
286 \centering
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diff changeset
287 \vspace*{-2mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
288 \includegraphics[scale=.4]{images/Motionblur_only.PNG}\\
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diff changeset
289 {\bf Motion Blur}
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290 \end{minipage}%
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291 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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292 %\vspace*{.5mm}
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293 The {\bf motion blur} module is GIMP's ``linear motion blur'', which
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parents: 555
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294 has parameters $length$ and $angle$. The value of
555
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parents: 554
diff changeset
295 a pixel in the final image is approximately the mean of the first $length$ pixels
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
296 found by moving in the $angle$ direction,
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
297 $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
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parents: 554
diff changeset
298 \vspace{5mm}
551
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299 \end{minipage}
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300
555
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301 \vspace*{1mm}
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302
555
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303 \begin{minipage}[t]{0.14\linewidth}
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304 \centering
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305 \includegraphics[scale=.4]{images/occlusion_only.PNG}\\
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diff changeset
306 {\bf Occlusion}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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diff changeset
307 %\vspace{.5cm}
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diff changeset
308 \end{minipage}%
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309 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
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diff changeset
310 \vspace*{-18mm}
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diff changeset
311 The {\bf occlusion} module selects a random rectangle from an {\em occluder} character
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
312 image and places it over the original {\em occluded}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
313 image. Pixels are combined by taking the max(occluder,occluded),
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
314 closer to black. The rectangle corners
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
315 are sampled so that larger complexity gives larger rectangles.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
316 The destination position in the occluded image are also sampled
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
317 according to a normal distribution (more details in~\citet{ift6266-tr-anonymous}).
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diff changeset
318 This module is skipped with probability 60\%.
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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parents: 554
diff changeset
319 %\vspace{7mm}
551
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diff changeset
320 \end{minipage}
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diff changeset
321
555
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322 \vspace*{1mm}
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diff changeset
323
555
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diff changeset
324 \begin{wrapfigure}[8]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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diff changeset
325 \vspace*{-6mm}
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diff changeset
326 \begin{center}
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327 %\begin{minipage}[t]{0.14\linewidth}
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diff changeset
328 %\centering
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329 \includegraphics[scale=.4]{images/Bruitgauss_only.PNG}\\
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parents: 554
diff changeset
330 {\bf Gaussian Smoothing}
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parents: 554
diff changeset
331 \end{center}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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diff changeset
332 \end{wrapfigure}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
333 %\vspace{.5cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
334 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
335 %\hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
557
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parents: 555
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336 With the {\bf Gaussian smoothing} module,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
337 different regions of the image are spatially smoothed by convolving
554
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 553
diff changeset
338 the image with a symmetric Gaussian kernel of
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
339 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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340 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
554
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 553
diff changeset
341 between $0$ and $1$. We also create a symmetric weighted averaging window, of the
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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342 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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343 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
344 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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345 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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346 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex
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parents:
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347 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex
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parents:
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348 image \times mask}{mask+1}$.
557
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349 This module is skipped with probability 75\%.
555
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350 %\end{minipage}
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diff changeset
351
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352 \newpage
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353
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354 \vspace*{-9mm}
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parents: 554
diff changeset
355
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parents: 554
diff changeset
356 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth}
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diff changeset
357 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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diff changeset
358 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
359 \begin{wrapfigure}[7]{l}{0.15\textwidth}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
360 \vspace*{-5mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
361 \begin{center}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
362 \includegraphics[scale=.4]{images/Permutpixel_only.PNG}\\
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
363 {\small\bf Permute Pixels}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
364 \end{center}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
365 \end{wrapfigure}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
366 %\end{minipage}%
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
367 %\hspace{-0cm}\begin{minipage}[t]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
368 %\vspace*{-20mm}
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
369 This module {\bf permutes neighbouring pixels}. It first selects
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
370 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each of them are then
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
371 sequentially exchanged with one other in as $V4$ neighbourhood.
557
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
372 This module is skipped with probability 80\%.\\
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
373 \vspace*{1mm}
551
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Frederic Bastien <nouiz@nouiz.org>
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diff changeset
374 \end{minipage}
555
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diff changeset
375
557
17d16700e0c8 encore du visuel de Myriam
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diff changeset
376 \vspace{-3mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
377
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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diff changeset
378 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
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parents: 554
diff changeset
379 \begin{wrapfigure}[7]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
380 %\vspace*{-3mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
381 \begin{center}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
382 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
383 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
384 \vspace*{-5mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
385 \includegraphics[scale=.4]{images/Distorsiongauss_only.PNG}\\
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
386 {\small \bf Gauss. Noise}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
387 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
388 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
389 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
390 %\hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
391 \vspace*{12mm}
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
392 The {\bf Gaussian noise} module simply adds, to each pixel of the image independently, a
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
393 noise $\sim Normal(0,(\frac{complexity}{10})^2)$.
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
394 This module is skipped with probability 70\%.
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
395 %\vspace{1.1cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
396 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
397
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
398 \vspace*{1.2cm}
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
399
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
400 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
401 \begin{minipage}[t]{0.14\linewidth}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
402 \centering
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
403 \includegraphics[scale=.4]{images/background_other_only.png}\\
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
404 {\small \bf Bg Image}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
405 \end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
406 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
407 \vspace*{-18mm}
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
408 Following~\citet{Larochelle-jmlr-2009}, the {\bf background image} module adds a random
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
409 background image behind the letter, from a randomly chosen natural image,
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
410 with contrast adjustments depending on $complexity$, to preserve
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
411 more or less of the original character image.
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
412 %\vspace{.8cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
413 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
414 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
415 %\vspace{-.7cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
416
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
417 \begin{minipage}[t]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
418 \centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
419 \includegraphics[scale=.4]{images/Poivresel_only.PNG}\\
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
420 {\small \bf Salt \& Pepper}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
421 \end{minipage}%
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
422 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
423 \vspace*{-18mm}
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
424 The {\bf salt and pepper noise} module adds noise $\sim U[0,1]$ to random subsets of pixels.
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
425 The number of selected pixels is $0.2 \times complexity$.
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
426 This module is skipped with probability 75\%.
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
427 %\vspace{.9cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
428 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
429 %\vspace{-.7cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
430
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
431 \vspace{1mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
432
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
433 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
434 \begin{wrapfigure}[7]{l}{0.14\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
435 %\begin{minipage}[t]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
436 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
437 \begin{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
438 \vspace*{-4mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
439 \hspace*{-1mm}\includegraphics[scale=.4]{images/Rature_only.PNG}\\
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
440 {\bf Scratches}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
441 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
442 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
443 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
444 %\hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
445 %\vspace{.4cm}
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
446 The {\bf scratches} module places line-like white patches on the image. The
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
447 lines are heavily transformed images of the digit ``1'' (one), chosen
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
448 at random among 500 such 1 images,
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
449 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
554
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 553
diff changeset
450 complexity)^2$ (in degrees), using bi-cubic interpolation.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
451 Two passes of a grey-scale morphological erosion filter
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
452 are applied, reducing the width of the line
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
453 by an amount controlled by $complexity$.
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
454 This module is skipped with probability 85\%. The probabilities
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
455 of applying 1, 2, or 3 patches are (50\%,30\%,20\%).
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
456 \end{minipage}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
457
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
458 \vspace*{2mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
459
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
460 \begin{minipage}[t]{0.25\linewidth}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
461 \centering
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
462 \hspace*{-16mm}\includegraphics[scale=.4]{images/Contrast_only.PNG}\\
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
463 {\bf Grey Level \& Contrast}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
464 \end{minipage}%
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
465 \hspace{-12mm}\begin{minipage}[t]{0.82\linewidth}
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
466 \vspace*{-18mm}
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
467 The {\bf grey level and contrast} module changes the contrast by changing grey levels, and may invert the image polarity (white
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
468 to black and black to white). The contrast is $C \sim U[1-0.85 \times complexity,1]$
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
469 so the image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
470 polarity is inverted with probability 50\%.
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
471 %\vspace{.7cm}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
472 \end{minipage}
555
b6dfba0a110c ameliorer l'aspect visuel, Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 554
diff changeset
473 \vspace{2mm}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
474
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
475
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
476 \iffalse
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
477 \begin{figure}[ht]
538
f0ee2212ea7c typos and stuff
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 537 534
diff changeset
478 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
479 \caption{Illustration of the pipeline of stochastic
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
480 transformations applied to the image of a lower-case \emph{t}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
481 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
482 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
483 of applying one of the modules in the pipeline. The last image
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
484 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
485 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
486 \end{figure}
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
487 \fi
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
488
479
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
489
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
490 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
491 \section{Experimental Setup}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
492 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
493
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
494 Much previous work on deep learning had been performed on
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
495 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
496 with 60~000 examples, and variants involving 10~000
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
497 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}.
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
498 The focus here is on much larger training sets, from 10 times to
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
499 to 1000 times larger, and 62 classes.
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
500
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
501 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
502 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
503 and {\bf OCR data} (scanned machine printed characters). Once a character
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
504 is sampled from one of these sources (chosen randomly), the second step is to
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
505 apply a pipeline of transformations and/or noise processes described in section \ref{s:perturbations}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
506
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
507 To provide a baseline of error rate comparison we also estimate human performance
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
508 on both the 62-class task and the 10-class digits task.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
509 We compare the best MLPs against
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
510 the best SDAs (both models' hyper-parameters are selected to minimize the validation set error),
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
511 along with a comparison against a precise estimate
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
512 of human performance obtained via Amazon's Mechanical Turk (AMT)
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
513 service (http://mturk.com).
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
514 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
515 of money to perform tasks for which human intelligence is required.
522
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
516 Mechanical Turk has been used extensively in natural language processing and vision.
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
517 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
518 %\citep{SorokinAndForsyth2008,whitehill09}.
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
519 AMT users were presented
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
520 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
521 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
522 62 or 10 character classes (all classes or digits only).
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
523 80 subjects classified 2500 images per (dataset,task) pair,
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
524 with the guarantee that 3 different subjects classified each image, allowing
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
525 us to estimate inter-human variability (e.g a standard error of 0.1\%
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
526 on the average 18.2\% error done by humans on the 62-class task NIST test set).
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
527
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
528 \vspace*{-3mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
529 \subsection{Data Sources}
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
530 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
531
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
532 %\begin{itemize}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
533 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
534 {\bf NIST.}
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
535 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
536 widely used for training and testing character
516
092dae9a5040 make the reference more compact.
Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
537 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
538 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
539 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
540 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
541 The fourth partition (called $hsf_4$, 82587 examples),
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
542 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
543 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
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
544 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
545 model selection.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
546 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
547 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
548 useful to estimate the effect of a multi-task setting.
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
549 The distribution of the classes in the NIST training and test sets differs
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
550 substantially, with relatively many more digits in the test set, and a more uniform distribution
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
551 of letters in the test set (where the letters are distributed
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
552 more like in natural text).
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
553 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
554
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
555 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
556 {\bf Fonts.}
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
557 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
558 {\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
559 % 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
560 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
561 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
562 directly as input to our models.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
563 \vspace*{-1mm}
479
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
564
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
565 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
566 {\bf Captchas.}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
567 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
568 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
569 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
570 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
571 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
572 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
573 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
574 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
575
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
576 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
577 {\bf OCR data.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
578 A large set (2 million) of scanned, OCRed and manually verified machine-printed
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
579 characters where included as an
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
580 additional source. This set is part of a larger corpus being collected by the Image Understanding
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
581 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
582 ({\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
583 %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
584 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
585
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
586 \vspace*{-3mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
587 \subsection{Data Sets}
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
588 \vspace*{-2mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
589
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
590 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
591 from one of the 62 character classes.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
592 %\begin{itemize}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
593 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
594
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
595 %\item
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
596 {\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
597 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
598 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
599
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
600 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
601 {\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
602 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
603 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
604 $25\%$ 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
605 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
606 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
607 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
608
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
609 %\item
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
610 {\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
611 except that we only apply
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
612 transformations from slant to pinch. Therefore, the character is
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
613 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
614 closer to the NIST dataset.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
615 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
616 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
617
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
618 \vspace*{-3mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
619 \subsection{Models and their Hyperparameters}
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
620 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
621
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
622 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
623 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
553
8f6c09d1140f ca fitte de nouveau
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 552
diff changeset
624 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
625
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
626 {\bf Multi-Layer Perceptrons (MLP).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
627 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
628 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
629 (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
630 scaling behavior).
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
631 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
632 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
633 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
634 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
635 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
636 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
637 and $0.1$ was then selected for optimizing on the whole training sets.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
638 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
639
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
640
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
641 {\bf Stacked Denoising Auto-Encoders (SDA).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
642 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
643 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
644 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
645 apparently setting parameters in the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
646 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
647 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
648 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
649 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
650 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
651 $P(y|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
652 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
653 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
654 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
655
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
656 \begin{figure}[ht]
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
657 \vspace*{-2mm}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
658 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
659 \vspace*{-2mm}
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
660 \caption{Illustration of the computations and training criterion for the denoising
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
661 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
662 the layer (i.e. raw input or output of previous layer)
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
663 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
664 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
665 is compared to the uncorrupted input $x$ through the loss function
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
666 $L_H(x,z)$, whose expected value is approximately minimized during training
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
667 by tuning $\theta$ and $\theta'$.}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
668 \label{fig:da}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
669 \vspace*{-2mm}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
670 \end{figure}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
671
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
672 Here we chose to use the Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
673 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
674 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
675 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
676 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
677 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
678 comparable or better than RBMs in series of experiments
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
679 \citep{VincentPLarochelleH2008}. During training, a Denoising
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
680 Auto-Encoder is presented with a stochastically corrupted version
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
681 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
682 forcing the hidden units to represent the leading regularities in
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
683 the data. Once it is trained, in a purely unsupervised way,
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
684 its hidden units' activations can
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
685 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
686 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
687 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
688 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
689 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
690 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
691 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
692 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
693 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
694 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
695 of hidden layers but it was fixed to 3 based on previous work with
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
696 SDAs on MNIST~\citep{VincentPLarochelleH2008}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
697
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
698 \vspace*{-1mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
699
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
700 \begin{figure}[ht]
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
701 \vspace*{-2mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
702 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
703 \vspace*{-3mm}
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
704 \caption{SDAx are the {\bf deep} models. 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
705 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
548
34cb28249de0 suggestions de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 547
diff changeset
706 of all models, on NIST and NISTP test sets.
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
707 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
708 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
709 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
710 \label{fig:error-rates-charts}
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
711 \vspace*{-2mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
712 \end{figure}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
713
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
714
557
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
715 \begin{figure}[ht]
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
716 \vspace*{-3mm}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
717 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
718 \vspace*{-3mm}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
719 \caption{Relative improvement in error rate due to self-taught learning.
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
720 Left: Improvement (or loss, when negative)
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
721 induced by out-of-distribution examples (perturbed data).
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
722 Right: Improvement (or loss, when negative) induced by multi-task
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
723 learning (training on all classes and testing only on either digits,
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
724 upper case, or lower-case). The deep learner (SDA) benefits more from
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
725 both self-taught learning scenarios, compared to the shallow MLP.}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
726 \label{fig:improvements-charts}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
727 \vspace*{-2mm}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
728 \end{figure}
17d16700e0c8 encore du visuel de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 555
diff changeset
729
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
730 \section{Experimental Results}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
731 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
732
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
733 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
734 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
735 %\vspace*{-1mm}
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
736 The models are either trained on NIST (MLP0 and SDA0),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
737 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
738 on either NIST, NISTP or P07, either on the 62-class task
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
739 or on the 10-digits task.
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
740 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
741 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
742 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
743 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
744 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
745 ~\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
746 ~\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
747 (figures and tables, including standard errors on the error rates) can be
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
748 found in Appendix I of the supplementary material.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
749 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
750 previously published performance (in a statistically and qualitatively
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
751 significant way) but when trained with perturbed data
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
752 reaches human performance on both the 62-class task
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
753 and the 10-class (digits) task.
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
754 17\% error (SDA1) or 18\% error (humans) may seem large but a large
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
755 majority of the errors from humans and from SDA1 are from out-of-context
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
756 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
757 ``c'' and a ``C'' are often indistinguishible).
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
758
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
759 In addition, as shown in the left of
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
760 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
761 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
762 differences with the MLP are statistically and qualitatively
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
763 significant.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
764 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
765 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
766 (i.e. the perturbed examples examples from NISTP or P07).
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
767 Relative percent change is measured by taking
548
34cb28249de0 suggestions de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 547
diff changeset
768 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
769 The right side of
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
770 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
771 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
772 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
773 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
774 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
775 multi-task setting is marginal or negative for the MLP, it is substantial
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
776 for the SDA. Note that to simplify these multi-task experiments, only the original
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
777 NIST dataset is used. For example, the MLP-digits bar shows the relative
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
778 percent improvement in MLP error rate on the NIST digits test set
548
34cb28249de0 suggestions de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 547
diff changeset
779 is $100\% \times$ (1 - single-task
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
780 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
781 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
782 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
783 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
784 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
785 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
786 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
787 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
788 and upper case characters).
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
789 %\vspace*{-1mm}
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
790 %\subsection{Perturbed Training Data More Helpful for SDA}
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
791 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
792
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
793 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
794 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
795 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
796
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
797 \iffalse
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
798 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
799 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
800 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
801 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
802 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
803 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
804 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
805 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
806 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
807 (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
808 shallow learner.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
809
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
810 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
811 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
812 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
813
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
814 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
815 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
816 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
817 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
818 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
819 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
820 \fi
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
821
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
822
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
823 \vspace*{-2mm}
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
824 \section{Conclusions and Discussion}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
825 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
826
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
827 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
828 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
829 supervised learner. More precisely,
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
830 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
831 %\begin{itemize}
487
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 486
diff changeset
832
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
833 $\bullet$ %\item
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
834 {\bf Do the good results previously obtained with deep architectures on the
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
835 MNIST digits generalize to a much larger and richer (but similar)
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
836 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
837 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
838 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
839 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
840
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
841 $\bullet$ %\item
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
842 {\bf To what extent do self-taught learning scenarios help deep learners,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
843 and do they help them more than shallow supervised ones}?
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
844 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
845 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
846 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
847 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
848 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
849 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
850 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
851 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
852 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
853 were very significantly boosted by these out-of-distribution examples.
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
854 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
855 negative for the MLP (from +5.6\% to -3.6\% relative change),
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
856 it was very significant for the SDA (from +13\% to +27\% relative change),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
857 which may be explained by the arguments below.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
858 %\end{itemize}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
859
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
860 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
861 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
862 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
863 scenario. However, many of the results by \citet{RainaR2007} (who used a
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
864 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
865 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
866 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
867 architectures, our experiments show that such a positive effect is accomplished
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
868 even in a scenario with a \emph{very large number of labeled examples},
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
869 i.e., here, the relative gain of self-taught learning is probably preserved
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
870 in the asymptotic regime.
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
871
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
872 {\bf Why would deep learners benefit more from the self-taught learning framework}?
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
873 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
874 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
875 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
876 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
877 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
878 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
879 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
880 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
881 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
882 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
883 experiments could attempt at teasing apart these factors.
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
884 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
885 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
886 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
887 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
888 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
889 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
890 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
891 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
892 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
893 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
894 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
895 (with or without self-taught settings), and more labeled examples
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
896 does not allow the model to go from the poorer basins of attraction discovered
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
897 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
898 with deep learning and self-taught learning.
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
899
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
900 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
901 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
902
498
7ff00c27c976 add missing file for bibtex and make it smaller.
Frederic Bastien <nouiz@nouiz.org>
parents: 496
diff changeset
903 \newpage
496
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
904 {
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
905 \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
906 %\bibliographystyle{plainnat}
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
907 \bibliographystyle{unsrtnat}
464
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parents:
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908 %\bibliographystyle{apalike}
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9a757d565e46 reduction de taille
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909 }
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910
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6beaf3328521 les tables enlevées
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912 \end{document}