annotate writeup/nips2010_submission.tex @ 517:0a5945249f2b

section 2, quick first pass
author Dumitru Erhan <dumitru.erhan@gmail.com>
date Tue, 01 Jun 2010 11:14:48 -0700
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1 \documentclass{article} % For LaTeX2e
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2 \usepackage{nips10submit_e,times}
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3
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4 \usepackage{amsthm,amsmath,amssymb,bbold,bbm}
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5 \usepackage{algorithm,algorithmic}
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6 \usepackage[utf8]{inputenc}
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7 \usepackage{graphicx,subfigure}
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8 \usepackage[numbers]{natbib}
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9
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10 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
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11 \author{The IFT6266 Gang}
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13 \begin{document}
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15 %\makeanontitle
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16 \maketitle
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17
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18 \vspace*{-2mm}
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19 \begin{abstract}
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20 Recent theoretical and empirical work in statistical machine learning has
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21 demonstrated the importance of learning algorithms for deep
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22 architectures, i.e., function classes obtained by composing multiple
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23 non-linear transformations. Self-taught learning (exploiting unlabeled
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24 examples or examples from other distributions) has already been applied
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25 to deep learners, but mostly to show the advantage of unlabeled
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26 examples. Here we explore the advantage brought by {\em out-of-distribution
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27 examples} and show that {\em deep learners benefit more from them than a
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28 corresponding shallow learner}, in the area
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29 of handwritten character recognition. In fact, we show that they reach
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30 human-level performance on both handwritten digit classification and
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31 62-class handwritten character recognition. For this purpose we
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32 developed a powerful generator of stochastic variations and noise
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33 processes character images, including not only affine transformations but
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34 also slant, local elastic deformations, changes in thickness, background
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35 images, grey level changes, contrast, occlusion, and various types of pixel and
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36 spatially correlated noise. The out-of-distribution examples are
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37 obtained by training with these highly distorted images or
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38 by including object classes different from those in the target test set.
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39 \end{abstract}
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40 \vspace*{-2mm}
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41
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42 \section{Introduction}
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43 \vspace*{-1mm}
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44
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45 Deep Learning has emerged as a promising new area of research in
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46 statistical machine learning (see~\citet{Bengio-2009} for a review).
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47 Learning algorithms for deep architectures are centered on the learning
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48 of useful representations of data, which are better suited to the task at hand.
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49 This is in great part inspired by observations of the mammalian visual cortex,
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50 which consists of a chain of processing elements, each of which is associated with a
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51 different representation of the raw visual input. In fact,
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52 it was found recently that the features learnt in deep architectures resemble
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53 those observed in the first two of these stages (in areas V1 and V2
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54 of visual cortex)~\citep{HonglakL2008}, and that they become more and
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55 more invariant to factors of variation (such as camera movement) in
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56 higher layers~\citep{Goodfellow2009}.
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57 Learning a hierarchy of features increases the
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58 ease and practicality of developing representations that are at once
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59 tailored to specific tasks, yet are able to borrow statistical strength
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60 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
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61 feature representation can lead to higher-level (more abstract, more
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62 general) features that are more robust to unanticipated sources of
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63 variance extant in real data.
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64
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65 Whereas a deep architecture can in principle be more powerful than a
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66 shallow one in terms of representation, depth appears to render the
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67 training problem more difficult in terms of optimization and local minima.
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68 It is also only recently that successful algorithms were proposed to
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69 overcome some of these difficulties. All are based on unsupervised
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70 learning, often in an greedy layer-wise ``unsupervised pre-training''
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71 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
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72 applied here, is the Denoising
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73 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which
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74 performed similarly or better than previously proposed Restricted Boltzmann
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75 Machines in terms of unsupervised extraction of a hierarchy of features
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76 useful for classification. The principle is that each layer starting from
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77 the bottom is trained to encode its input (the output of the previous
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78 layer) and to reconstruct it from a corrupted version of it. After this
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79 unsupervised initialization, the stack of denoising auto-encoders can be
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80 converted into a deep supervised feedforward neural network and fine-tuned by
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81 stochastic gradient descent.
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82
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83 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
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84 of semi-supervised and multi-task learning: the learner can exploit examples
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85 that are unlabeled and/or come from a distribution different from the target
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86 distribution, e.g., from other classes that those of interest. Whereas
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87 it has already been shown that deep learners can clearly take advantage of
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88 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small}
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89 and multi-task learning, not much has been done yet to explore the impact
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90 of {\em out-of-distribution} examples and of the multi-task setting
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91 (but see~\citep{CollobertR2008}). In particular the {\em relative
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92 advantage} of deep learning for this settings has not been evaluated.
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93
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94 % TODO: why we care to evaluate this relative advantage
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95
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96 In this paper we ask the following questions:
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97
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98 %\begin{enumerate}
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99 $\bullet$ %\item
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100 Do the good results previously obtained with deep architectures on the
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101 MNIST digit images generalize to the setting of a much larger and richer (but similar)
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102 dataset, the NIST special database 19, with 62 classes and around 800k examples?
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103
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104 $\bullet$ %\item
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105 To what extent does the perturbation of input images (e.g. adding
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106 noise, affine transformations, background images) make the resulting
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107 classifiers better not only on similarly perturbed images but also on
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108 the {\em original clean examples}?
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109
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110 $\bullet$ %\item
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111 Do deep architectures {\em benefit more from such out-of-distribution}
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112 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
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113
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114 $\bullet$ %\item
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115 Similarly, does the feature learning step in deep learning algorithms benefit more
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116 training with similar but different classes (i.e. a multi-task learning scenario) than
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117 a corresponding shallow and purely supervised architecture?
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118 %\end{enumerate}
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119
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120 Our experimental results provide positive evidence towards all of these questions.
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121
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122 \vspace*{-1mm}
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123 \section{Perturbation and Transformation of Character Images}
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124 \vspace*{-1mm}
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125
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126 This section describes the different transformations we used to stochastically
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127 transform source images in order to obtain data. More details can
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128 be found in this technical report~\citep{ift6266-tr-anonymous}.
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129 The code for these transformations (mostly python) is available at
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130 {\tt http://anonymous.url.net}. All the modules in the pipeline share
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131 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
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132 amount of deformation or noise introduced.
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133
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134 There are two main parts in the pipeline. The first one,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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135 from slant to pinch below, performs transformations. The second
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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136 part, from blur to contrast, adds different kinds of noise.
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137
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138 \begin{figure}[h]
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139 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\
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140 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE
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141 \caption{Illustration of each transformation applied alone to the same image
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
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142 of an upper-case h (top left). First row (from left to right) : original image, slant,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
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143 thickness, affine transformation (translation, rotation, shear),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
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144 local elastic deformation; second row (from left to right) :
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
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145 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to right) :
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
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146 background image, salt and pepper noise, spatially Gaussian noise, scratches,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
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147 grey level and contrast changes.}
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148 \label{fig:transfo}
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149 \end{figure}
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150
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151 {\large\bf Transformations}
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152
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153 \vspace*{2mm}
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154
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155 {\bf Slant.}
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156 We mimic slant by shifting each row of the image
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157 proportionally to its height: $shift = round(slant \times height)$.
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158 The $slant$ coefficient can be negative or positive with equal probability
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159 and its value is randomly sampled according to the complexity level:
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160 $slant \sim U[0,complexity]$, so the
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parents:
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161 maximum displacement for the lowest or highest pixel line is of
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parents: 466
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162 $round(complexity \times 32)$.\\
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163 {\bf Thickness.}
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164 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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165 are applied. The neighborhood of each pixel is multiplied
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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166 element-wise with a {\em structuring element} matrix.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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167 The pixel value is replaced by the maximum or the minimum of the resulting
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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168 matrix, respectively for dilation or erosion. Ten different structural elements with
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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169 increasing dimensions (largest is $5\times5$) were used. For each image,
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170 randomly sample the operator type (dilation or erosion) with equal probability and one structural
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parents:
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171 element from a subset of the $n$ smallest structuring elements where $n$ is
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172 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
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173 for erosion. A neutral element is always present in the set, and if it is
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174 chosen no transformation is applied. Erosion allows only the six
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parents:
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175 smallest structural elements because when the character is too thin it may
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176 be completely erased.\\
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177 {\bf Affine Transformations.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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178 A $2 \times 3$ affine transform matrix (with
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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179 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
Yoshua Bengio <bengioy@iro.umontreal.ca>
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180 Each pixel $(x,y)$ of the output image takes the value of the pixel
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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181 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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182 produces scaling, translation, rotation and shearing.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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183 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
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parents:
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184 forbid important rotations (not to confuse classes) but to give good
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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185 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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186 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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187 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
Yoshua Bengio <bengioy@iro.umontreal.ca>
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188 complexity]$.\\
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189 {\bf Local Elastic Deformations.}
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190 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
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parents: 466
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191 which provides more details.
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192 Two ``displacements'' fields are generated and applied, for horizontal
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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193 and vertical displacements of pixels.
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parents:
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194 To generate a pixel in either field, first a value between -1 and 1 is
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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195 chosen from a uniform distribution. Then all the pixels, in both fields, are
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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196 multiplied by a constant $\alpha$ which controls the intensity of the
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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197 displacements (larger $\alpha$ translates into larger wiggles).
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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198 Each field is convoluted with a Gaussian 2D kernel of
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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199 standard deviation $\sigma$. Visually, this results in a blur.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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200 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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201 \sqrt[3]{complexity}$.\\
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202 {\bf Pinch.}
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203 This is a GIMP filter called ``Whirl and
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
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204 pinch'', but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
509
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
205 surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}.
517
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parents: 511
diff changeset
206 For a square input image, this is akin to drawing a circle of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
207 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
208 that disk (region inside circle) will have its value recalculated by taking
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
209 the value of another ``source'' pixel in the original image. The position of
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
210 that source pixel is found on the line that goes through $C$ and $P$, but
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
211 at some other distance $d_2$. Define $d_1$ to be the distance between $P$
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
212 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
213 d_1$, where $pinch$ is a parameter to the filter.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
214 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
215 around the (non-integer) source position thus found.
484
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parents: 483
diff changeset
216 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
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parents: 483
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217
9a757d565e46 reduction de taille
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parents: 483
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218 \vspace*{1mm}
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parents:
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219
484
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220 {\large\bf Injecting Noise}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
221
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
222 \vspace*{1mm}
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parents: 482
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223
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224 {\bf Motion Blur.}
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parents: 511
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225 This is a ``linear motion blur'' in GIMP
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
226 terminology, with two parameters, $length$ and $angle$. The value of
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
227 a pixel in the final image is approximately the mean value of the $length$ first pixels
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
228 found by moving in the $angle$ direction.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
229 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.\\
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230 {\bf Occlusion.}
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
231 Selects a random rectangle from an {\em occluder} character
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
232 images and places it over the original {\em occluded} character
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
233 image. Pixels are combined by taking the max(occluder,occluded),
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
234 closer to black. The rectangle corners
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
235 are sampled so that larger complexity gives larger rectangles.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
236 The destination position in the occluded image are also sampled
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
237 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
238 This filter has a probability of 60\% of not being applied.\\
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parents: 472
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239 {\bf Pixel Permutation.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
240 This filter permutes neighbouring pixels. It selects first
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
241 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
517
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
242 sequentially exchanged with one other pixel in its $V4$ neighbourhood. The number
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
243 of exchanges to the left, right, top, bottom is equal or does not differ
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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244 from more than 1 if the number of selected pixels is not a multiple of 4.
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
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245 % TODO: The previous sentence is hard to parse
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
246 This filter has a probability of 80\% of not being applied.\\
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247 {\bf Gaussian Noise.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
248 This filter simply adds, to each pixel of the image independently, a
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
249 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
517
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Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
250 It has a probability of 70\% of not being applied.\\
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251 {\bf Background Images.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
252 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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253 background behind the letter. The background is chosen by first selecting,
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
254 at random, an image from a set of images. Then a 32$\times$32 sub-region
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
255 of that image is chosen as the background image (by sampling position
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
256 uniformly while making sure not to cross image borders).
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
257 To combine the original letter image and the background image, contrast
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
258 adjustments are made. We first get the maximal values (i.e. maximal
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
259 intensity) for both the original image and the background image, $maximage$
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
260 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
261 Each background pixel value is multiplied by $\frac{max(maximage -
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
262 contrast, 0)}{maxbg}$ (higher contrast yield darker
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
263 background). The output image pixels are max(background,original).\\
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parents: 472
diff changeset
264 {\bf Salt and Pepper Noise.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
265 This filter adds noise $\sim U[0,1]$ to random subsets of pixels.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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266 The number of selected pixels is $0.2 \times complexity$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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267 This filter has a probability of not being applied at all of 75\%.\\
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268 {\bf Spatially Gaussian Noise.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
269 Different regions of the image are spatially smoothed.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
270 The image is convolved with a symmetric Gaussian kernel of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
271 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
272 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
273 between $0$ and $1$. We also create a symmetric averaging window, of the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
274 kernel size, with maximum value at the center. For each image we sample
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
275 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
276 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
277 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:
diff changeset
278 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
279 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
280 image \times mask}{mask+1}$.
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
281 This filter has a probability of not being applied at all of 75\%.\\
474
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 472
diff changeset
282 {\bf Scratches.}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
283 The 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
284 lines are heavily transformed images of the digit ``1'' (one), chosen
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
285 at random among five thousands such 1 images. The 1 image is
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
286 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
287 complexity)^2$, using bi-cubic interpolation,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
288 Two passes of a grey-scale morphological erosion filter
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
289 are applied, reducing the width of the line
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
290 by an amount controlled by $complexity$.
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
291 This filter is only applied only 15\% of the time. When it is applied, 50\%
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
292 of the time, only one patch image is generated and applied. In 30\% of
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
293 cases, two patches are generated, and otherwise three patches are
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
294 generated. The patch is applied by taking the maximal value on any given
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
295 patch or the original image, for each of the 32x32 pixel locations.\\
499
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
296 {\bf Grey Level and Contrast Changes.}
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
297 This filter changes the contrast and may invert the image polarity (white
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
298 on black to black on white). The contrast $C$ is defined here as the
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
299 difference between the maximum and the minimum pixel value of the image.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
300 Contrast $\sim U[1-0.85 \times complexity,1]$ (so contrast $\geq 0.15$).
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
301 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
302 polarity is inverted with $0.5$ probability.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
303
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
304 \iffalse
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
305 \begin{figure}[h]
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
306 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
307 \caption{Illustration of the pipeline of stochastic
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
308 transformations applied to the image of a lower-case t
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
309 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
310 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
311 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
312 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
313 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
314 \end{figure}
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
315 \fi
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
316
479
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Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
317
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318 \vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
319 \section{Experimental Setup}
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
320 \vspace*{-1mm}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
321
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
322 Whereas much previous work on deep learning algorithms had been performed on
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
323 the MNIST digits classification task~\citep{Hinton06,ranzato-07,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
324 with 60~000 examples, and variants involving 10~000
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
325 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
326 to focus here on the case of much larger training sets, from 10 times to
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
327 to 1000 times larger. The larger datasets are obtained by first sampling from
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
328 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
329 and {\bf OCR data} (scanned machine printed characters). Once a character
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
330 is sampled from one of these sources (chosen randomly), a pipeline of
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
331 the above transformations and/or noise processes is applied to the
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
332 image.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
333
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
334 We compare the best MLP (according to validation set error) that we found against
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
335 the best SDA (again according to validation set error), along with a precise estimate
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
336 of human performance obtained via Amazon's Mechanical Turk (AMT)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
337 service\footnote{http://mturk.com}.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
338 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
339 of money to perform tasks for which human intelligence is required.
509
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
340 Mechanical Turk has been used extensively in natural language
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
341 processing \citep{SnowEtAl2008} and vision
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
342 \citep{SorokinAndForsyth2008,whitehill09}.
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
343 AMT users where presented
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
344 with 10 character images and asked to type 10 corresponding ASCII
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
345 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
346 62 or 10 character classes (all classes or digits only).
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
347 Three users classified each image, allowing
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
348 to estimate inter-human variability.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
349
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
350 \vspace*{-1mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
351 \subsection{Data Sources}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
352 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
353
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
354 %\begin{itemize}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
355 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
356 {\bf NIST.}
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
357 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
358 widely used for training and testing character
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
359 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
360 The dataset is composed with 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
361 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
362 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity.
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
363 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one is recommended
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
364 by NIST as testing set and is used in our work and some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
365 for that purpose. We randomly split the remainder into a training set and a validation set for
480
150203d2b5c3 added number of train test and valid for NIST
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 479
diff changeset
366 model selection. The sizes of these data sets are: 651668 for training, 80000 for validation,
150203d2b5c3 added number of train test and valid for NIST
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 479
diff changeset
367 and 82587 for testing.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
368 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
369 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
370 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
371 Note that the distribution of the classes in the NIST training and test sets differs
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
372 substantially, with relatively many more digits in the test set, and uniform distribution
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
373 of letters in the test set, not in the training set (more like the natural distribution
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
374 of letters in text).
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
375
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
376 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
377 {\bf Fonts.}
479
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Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
378 In order to have a good variety of sources we downloaded an important number of free fonts from: {\tt http://anonymous.url.net}
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
379 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html}
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
380 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
381 The {\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
382 directly as input to our models.
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
383
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
384 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
385 {\bf Captchas.}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
386 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
387 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
388 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
389 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
390 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
391 depending on the value of the complexity parameter provided by the user of the data source. Two levels of complexity are
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
392 allowed and can be controlled via an easy to use facade class.
484
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
393
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
394 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
395 {\bf OCR data.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
396 A large set (2 million) of scanned, OCRed and manually verified machine-printed
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
397 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
398 additional source. This set is part of a larger corpus being collected by the Image Understanding
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
399 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
400 ({\tt http://www.iupr.com}), and which will be publicly released.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
401 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
402
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
403 \vspace*{-1mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
404 \subsection{Data Sets}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
405 \vspace*{-1mm}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
406
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
407 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
408 from one of the 62 character classes.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
409 %\begin{itemize}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
410
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
411 %\item
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
412 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
413
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
414 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
415 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
416 and sending them through the above transformation pipeline.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
417 For each new example to generate, a source is selected with probability $10\%$ from the fonts,
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
418 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
419 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
420
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
421 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
422 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion)
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
423 except that we only apply
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
424 transformations from slant to pinch. Therefore, the character is
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
425 transformed but no additional noise is added to the image, giving images
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
426 closer to the NIST dataset.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
427 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
428
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
429 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
430 \subsection{Models and their Hyperparameters}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
431 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
432
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
433 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
434 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
435 All hyper-parameters are selected based on performance on the NISTP validation set.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
436
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
437 {\bf Multi-Layer Perceptrons (MLP).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
438 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
439 SVMs, we only compared to MLPs here because of the very large datasets used
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
440 (making the use of SVMs computationally inconvenient because of their quadratic
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
441 scaling behavior).
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
442 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
443 exponentials) on the output layer for estimating P(class | image).
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
444 The hyper-parameters are the following: number of hidden units, taken in
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
445 $\{300,500,800,1000,1500\}$. The optimization procedure is as follows. Training
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
446 examples are presented in minibatches of size 20. A constant learning
474
bcf024e6ab23 fits now, but still now graphics
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 472
diff changeset
447 rate is chosen in $10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
448 through preliminary experiments, and 0.1 was selected.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
449
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
450 {\bf Stacked Denoising Auto-Encoders (SDA).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
451 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
452 can be used to initialize the weights of each layer of a deep MLP (with many hidden
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
453 layers)~\citep{Hinton06,ranzato-07,Bengio-nips-2006}
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
454 enabling better generalization, apparently setting parameters in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
455 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
456 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
457 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
458 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
459 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
460 $P(y|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
461 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
462 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
463 compositions of simpler ones through a deep hierarchy).
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
464 Here we chose to use the Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
465 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
466 % AJOUTER UNE IMAGE?
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
467 these deep hierarchies of features, as it is very simple to train and
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
468 teach (see tutorial and code there: {\tt http://deeplearning.net/tutorial}),
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
469 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
470 comparable or better than RBMs in series of experiments
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
471 \citep{VincentPLarochelleH2008}. During training of a Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
472 Auto-Encoder, it is presented with a stochastically corrupted version
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
473 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
474 forcing the hidden units to represent the leading regularities in
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
475 the data. Once it is trained, its hidden units activations can
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
476 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
477 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
478 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
479 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
480 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
481 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
482 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
483 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
484 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
485 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
486 of hidden layers but it was fixed to 3 based on previous work with
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
487 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
488
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
489 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
490 \section{Experimental Results}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
491
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
492 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
493 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
494 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
495
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
496 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
497 comparing Humans, three MLPs (MLP0, MLP1, MLP2) and three SDAs (SDA0, SDA1,
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
498 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
499 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
500 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
501 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002}, and SVMs
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
502 ~\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
503 (figures and tables, including standard errors on the error rates) can be
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
504 found in the supplementary material. The 3 kinds of model differ in the
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
505 training sets used: NIST only (MLP0,SDA0), NISTP (MLP1, SDA1), or P07
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
506 (MLP2, SDA2). The deep learner not only outperformed the shallow ones and
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
507 previously published performance (in a statistically and qualitatively
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
508 significant way) but reaches human performance on both the 62-class task
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
509 and the 10-class (digits) task. In addition, as shown in the left of
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
510 Figure~\ref{fig:fig:improvements-charts}, the relative improvement in error
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
511 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
512 differences with the MLP are statistically and qualitatively
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
513 significant.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
514 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
515 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
516 (i.e. the perturbed examples examples from NISTP or P07).
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
517 Relative change is measured by taking
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
518 (original model's error / perturbed-data model's error - 1).
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
519 The right side of
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
520 Figure~\ref{fig:fig:improvements-charts} shows the relative improvement
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
521 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
522 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
523 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
524 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
525 multi-task setting is marginal or negative for the MLP, it is substantial
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
526 for the SDA. Note that for these multi-task experiment, only the original
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
527 NIST dataset is used. For example, the MLP-digits bar shows the relative
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
528 improvement in MLP error rate on the NIST digits test set (1 - single-task
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
529 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
530 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
531 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
532 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
533 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
534 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
535 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
536 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
537 and upper case characters).
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
538
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
539 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
540 \resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}\\
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
541 \caption{Error bars indicate a 95\% confidence interval. 0 indicates training
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
542 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
543 of all models, on 3 different test sets corresponding to the three
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
544 datasets.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
545 Right: error rates on NIST test digits only, along with the previous results from
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
546 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
547 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
548
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
549 \label{fig:error-rates-charts}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
550 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
551
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
552 %\vspace*{-1mm}
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
553 %\subsection{Perturbed Training Data More Helpful for SDA}
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
554 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
555
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
556 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
557 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
558 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
559
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
560 \iffalse
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
561 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
562 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
563 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
564 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
565 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
566 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
567 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
568 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
569 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
570 (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
571 shallow learner.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
572
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
573 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
574 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
575 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
576
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
577 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
578 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
579 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
580 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
581 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
582 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
583 \fi
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
584
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
585
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
586 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
587 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\
509
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
588 \caption{Relative improvement in error rate due to self-taught learning.
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
589 Left: Improvement (or loss, when negative)
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
590 induced by out-of-distribution examples (perturbed data).
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
591 Right: Improvement (or loss, when negative) induced by multi-task
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
592 learning (training on all classes and testing only on either digits,
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
593 upper case, or lower-case). The deep learner (SDA) benefits more from
860c755ddcff argh, sorry about that
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 505
diff changeset
594 both self-taught learning scenarios, compared to the shallow MLP.}
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
595 \label{fig:improvements-charts}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
596 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
597
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
598 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
599 \section{Conclusions}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
600 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
601
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
602 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
603 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
604 supervised learner. More precisely,
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
605 the conclusions 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
606 %\begin{itemize}
487
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 486
diff changeset
607
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
608 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
609 Do the good results previously obtained with deep architectures on the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
610 MNIST digits generalize to the setting of a much larger and richer (but similar)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
611 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
612 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
613 published results on this dataset (as far as we know), in fact reaching human-level
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
614 performance} at round 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
615
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
616 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
617 To what extent does the perturbation of input images (e.g. adding
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
618 noise, affine transformations, background images) make the resulting
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
619 classifier better not only on similarly perturbed images but also on
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
620 the {\em original clean examples}? Do deep architectures benefit more from such {\em out-of-distribution}
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
621 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
622 MLPs were helped by perturbed training examples when tested on perturbed input
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
623 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
624 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
625 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
626 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
627 were very significantly boosted by these out-of-distribution examples.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
628
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
629 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
630 Similarly, does the feature learning step in deep learning algorithms benefit more
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
631 training with similar but different classes (i.e. a multi-task learning scenario) than
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
632 a corresponding shallow and purely supervised architecture?
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
633 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
634 negative for the MLP (from +5.6\% to -3.6\% relative change),
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
635 it was very significant for the SDA (from +13\% to +27\% relative change).
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
636 %\end{itemize}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
637
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
638 Why would deep learners benefit more from the self-taught learning framework?
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
639 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
640 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
641 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
642 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
643 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
644 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
645 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
646 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
647 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
648 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
649 experiments could attempt at teasing apart these factors.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
650
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
651 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
652 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
653
498
7ff00c27c976 add missing file for bibtex and make it smaller.
Frederic Bastien <nouiz@nouiz.org>
parents: 496
diff changeset
654 \newpage
496
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
655 {
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
656 \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
657 %\bibliographystyle{plainnat}
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
658 \bibliographystyle{unsrtnat}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
659 %\bibliographystyle{apalike}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
660 }
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
661
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
662
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
663 \end{document}