annotate writeup/nips2010_submission.tex @ 487:21787ac4e5a0

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author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Mon, 31 May 2010 22:04:44 -0400
parents 877af97ee193
children ee9836baade3 d6cf4912abb0
rev   line source
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1 \documentclass{article} % For LaTeX2e
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2 \usepackage{nips10submit_e,times}
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4 \usepackage{amsthm,amsmath,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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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. The self-taught learning (exploitng 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, color, 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~\cite{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 their input (the output of the previous
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78 layer) and try 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}
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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-short}). 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 In this paper we ask the following questions:
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95
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96 %\begin{enumerate}
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97 $\bullet$ %\item
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98 Do the good results previously obtained with deep architectures on the
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99 MNIST digit images generalize to the setting of a much larger and richer (but similar)
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100 dataset, the NIST special database 19, with 62 classes and around 800k examples?
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101
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102 $\bullet$ %\item
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103 To what extent does the perturbation of input images (e.g. adding
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104 noise, affine transformations, background images) make the resulting
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105 classifiers better not only on similarly perturbed images but also on
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106 the {\em original clean examples}?
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107
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108 $\bullet$ %\item
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109 Do deep architectures {\em benefit more from such out-of-distribution}
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110 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
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111
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112 $\bullet$ %\item
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113 Similarly, does the feature learning step in deep learning algorithms benefit more
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114 training with similar but different classes (i.e. a multi-task learning scenario) than
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115 a corresponding shallow and purely supervised architecture?
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116 %\end{enumerate}
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117
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118 The experimental results presented here provide positive evidence towards all of these questions.
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119
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120 \vspace*{-1mm}
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121 \section{Perturbation and Transformation of Character Images}
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122 \vspace*{-1mm}
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123
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124 This section describes the different transformations we used to stochastically
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125 transform source images in order to obtain data. More details can
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126 be found in this technical report~\citep{ift6266-tr-anonymous}.
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127 The code for these transformations (mostly python) is available at
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128 {\tt http://anonymous.url.net}. All the modules in the pipeline share
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129 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
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130 amount of deformation or noise introduced.
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131
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132 There are two main parts in the pipeline. The first one,
Yoshua Bengio <bengioy@iro.umontreal.ca>
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133 from slant to pinch below, performs transformations. The second
Yoshua Bengio <bengioy@iro.umontreal.ca>
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134 part, from blur to contrast, adds different kinds of noise.
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135
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136 {\large\bf Transformations}
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137
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138 \vspace*{2mm}
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139
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140 {\bf Slant.}
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141 We mimic slant by shifting each row of the image
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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142 proportionnaly to its height: $shift = round(slant \times height)$.
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143 The $slant$ coefficient can be negative or positive with equal probability
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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144 and its value is randomly sampled according to the complexity level:
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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145 e $slant \sim U[0,complexity]$, so the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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146 maximum displacement for the lowest or highest pixel line is of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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147 $round(complexity \times 32)$.\\
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148 {\bf Thickness.}
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149 Morpholigical operators of dilation and erosion~\citep{Haralick87,Serra82}
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150 are applied. The neighborhood of each pixel is multiplied
Yoshua Bengio <bengioy@iro.umontreal.ca>
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151 element-wise with a {\em structuring element} matrix.
Yoshua Bengio <bengioy@iro.umontreal.ca>
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152 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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153 matrix, respectively for dilation or erosion. Ten different structural elements with
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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154 increasing dimensions (largest is $5\times5$) were used. For each image,
Yoshua Bengio <bengioy@iro.umontreal.ca>
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155 randomly sample the operator type (dilation or erosion) with equal probability and one structural
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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156 element from a subset of the $n$ smallest structuring elements where $n$ is
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
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157 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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158 for erosion. A neutral element is always present in the set, and if it is
Yoshua Bengio <bengioy@iro.umontreal.ca>
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159 chosen no transformation is applied. Erosion allows only the six
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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160 smallest structural elements because when the character is too thin it may
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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161 be completely erased.\\
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162 {\bf Affine Transformations.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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163 A $2 \times 3$ affine transform matrix (with
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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164 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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165 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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166 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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167 produces scaling, translation, rotation and shearing.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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168 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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169 forbid important rotations (not to confuse classes) but to give good
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
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170 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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171 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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172 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
Yoshua Bengio <bengioy@iro.umontreal.ca>
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173 complexity]$.\\
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174 {\bf Local Elastic Deformations.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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175 This filter induces a "wiggly" effect in the image, following~\citet{SimardSP03},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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176 which provides more details.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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177 Two "displacements" fields are generated and applied, for horizontal
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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178 and vertical displacements of pixels.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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179 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>
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180 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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181 multiplied by a constant $\alpha$ which controls the intensity of the
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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182 displacements (larger $\alpha$ translates into larger wiggles).
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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183 Each field is convoluted with a Gaussian 2D kernel of
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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184 standard deviation $\sigma$. Visually, this results in a blur.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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185 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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186 \sqrt[3]{complexity}$.\\
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187 {\bf Pinch.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
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188 This GIMP filter is named "Whirl and
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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189 pinch", but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
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190 surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}.
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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191 For a square input image, think of drawing a circle of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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192 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
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193 that disk (region inside circle) will have its value recalculated by taking
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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194 the value of another "source" pixel in the original image. The position of
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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195 that source pixel is found on the line thats goes through $C$ and $P$, but
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
196 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:
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197 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
198 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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199 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
200 around the (non-integer) source position thus found.
484
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201 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
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202
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
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203 \vspace*{1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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204
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205 {\large\bf Injecting Noise}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
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206
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
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207 \vspace*{1mm}
483
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208
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209 {\bf Motion Blur.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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210 This GIMP filter is a ``linear motion blur'' in GIMP
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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211 terminology, with two parameters, $length$ and $angle$. The value of
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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212 a pixel in the final image is the approximately mean value of the $length$ first pixels
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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213 found by moving in the $angle$ direction.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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214 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.\\
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215 {\bf Occlusion.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
216 This filter selects a random rectangle from an {\em occluder} character
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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217 images and places it over the original {\em occluded} character
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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218 image. Pixels are combined by taking the max(occluder,occluded),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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219 closer to black. The corners of the occluder The rectangle corners
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
220 are sampled so that larger complexity gives larger rectangles.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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221 The destination position in the occluded image are also sampled
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
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222 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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223 It has has a probability of not being applied at all of 60\%.\\
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224 {\bf Pixel Permutation.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
225 This filter permutes neighbouring pixels. It selects first
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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226 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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227 sequentially exchanged to one other pixel in its $V4$ neighbourhood. Number
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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228 of exchanges to the left, right, top, bottom are equal or does not differ
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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229 from more than 1 if the number of selected pixels is not a multiple of 4.
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
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230 It has has a probability of not being applied at all of 80\%.\\
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231 {\bf Gaussian Noise.}
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24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
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232 This filter simply adds, to each pixel of the image independently, a
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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233 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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234 It has has a probability of not being applied at all of 70\%.\\
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235 {\bf Background Images.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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236 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
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24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
237 background behind the letter. The background is chosen by first selecting,
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
238 at random, an image from a set of images. Then a 32$\times$32 subregion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
239 of that image is chosen as the background image (by sampling position
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
240 uniformly while making sure not to cross image borders).
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
241 To combine the original letter image and the background image, contrast
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
242 adjustments are made. We first get the maximal values (i.e. maximal
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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243 intensity) for both the original image and the background image, $maximage$
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
244 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
245 Each background pixel value is multiplied by $\frac{max(maximage -
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
246 contrast, 0)}{maxbg}$ (higher contrast yield darker
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
247 background). The output image pixels are max(background,original).\\
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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248 {\bf Salt and Pepper Noise.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
249 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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250 The number of selected pixels is $0.2 \times complexity$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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251 This filter has a probability of not being applied at all of 75\%.\\
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252 {\bf Spatially Gaussian Noise.}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
253 Different regions of the image are spatially smoothed.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
254 The image is convolved with a symmetric Gaussian kernel of
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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255 size and variance choosen uniformly in the ranges $[12,12 + 20 \times
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24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
256 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
257 between $0$ and $1$. We also create a symmetric averaging window, of the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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258 kernel size, with maximum value at the center. For each image we sample
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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259 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
260 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
261 initialize to zero a mask matrix of the image size. For each selected pixel
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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262 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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263 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
264 image \times mask}{mask+1}$.
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
265 This filter has a probability of not being applied at all of 75\%.\\
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266 {\bf Scratches.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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267 The scratches module places line-like white patches on the image. The
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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268 lines are heavily transformed images of the digit "1" (one), chosen
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
269 at random among five thousands such 1 images. The 1 image is
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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270 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
271 complexity)^2$, using bicubic interpolation,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
272 Two passes of a greyscale morphological erosion filter
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
273 are applied, reducing the width of the line
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
274 by an amount controlled by $complexity$.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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275 This filter is only applied only 15\% of the time. When it is applied, 50\%
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276 of the time, only one patch image is generated and applied. In 30\% of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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277 cases, two patches are generated, and otherwise three patches are
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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278 generated. The patch is applied by taking the maximal value on any given
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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279 patch or the original image, for each of the 32x32 pixel locations.\\
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280 {\bf Color and Contrast Changes.}
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281 This filter changes the constrast and may invert the image polarity (white
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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282 on black to black on white). The contrast $C$ is defined here as the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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283 difference between the maximum and the minimum pixel value of the image.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
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284 Contrast $\sim U[1-0.85 \times complexity,1]$ (so constrast $\geq 0.15$).
Yoshua Bengio <bengioy@iro.umontreal.ca>
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285 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
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286 polarity is inverted with $0.5$ probability.
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287
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288
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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289 \begin{figure}[h]
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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290 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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291 \caption{Illustration of the pipeline of stochastic
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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292 transformations applied to the image of a lower-case t
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
293 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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294 left to right, first top line, then bottom line) shows the result
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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295 of applying one of the modules in the pipeline. The last image
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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296 (bottom right) is used as training example.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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297 \label{fig:pipeline}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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298 \end{figure}
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299
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300
479
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301 \begin{figure}[h]
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302 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\
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parents: 480
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303 \caption{Illustration of each transformation applied alone to the same image
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
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304 of an upper-case h (top left). First row (from left to rigth) : original image, slant,
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parents: 476
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305 thickness, affine transformation, local elastic deformation; second row (from left to rigth) :
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parents: 480
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306 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to rigth) :
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
307 background image, salt and pepper noise, spatially Gaussian noise, scratches,
479
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308 color and contrast changes.}
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309 \label{fig:transfo}
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310 \end{figure}
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311
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312
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313 \vspace*{-1mm}
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314 \section{Experimental Setup}
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315 \vspace*{-1mm}
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316
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parents: 469
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317 Whereas much previous work on deep learning algorithms had been performed on
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
318 the MNIST digits classification task~\citep{Hinton06,ranzato-07,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
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319 with 60~000 examples, and variants involving 10~000
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
320 examples~\cite{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
321 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
322 to 1000 times larger. The larger datasets are obtained by first sampling from
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
323 a {\em data source} (NIST characters, scanned machine printed characters, characters
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
324 from fonts, or characters from captchas) and then optionally applying some of the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
325 above transformations and/or noise processes.
464
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326
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327 \vspace*{-1mm}
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diff changeset
328 \subsection{Data Sources}
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329 \vspace*{-1mm}
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330
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331 %\begin{itemize}
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332 %\item
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333 {\bf NIST.}
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334 Our main source of characters is the NIST Special Database 19~\cite{Grother-1995},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
335 widely used for training and testing character
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parents: 469
diff changeset
336 recognition systems~\cite{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
337 The dataset is composed with 8????? digits and characters (upper and lower cases), with hand checked classifications,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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338 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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339 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity.
472
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parents: 469
diff changeset
340 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one is recommended
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
341 by NIST as testing set and is used in our work and some previous work~\cite{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
342 for that purpose. We randomly split the remainder into a training set and a validation set for
480
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Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 479
diff changeset
343 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
344 and 82587 for testing.
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
345 The performances reported by previous work on that dataset mostly use only the digits.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
346 Here we use all the classes both in the training and testing phase. This is especially
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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347 useful to estimate the effect of a multi-task setting.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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348 Note that the distribution of the classes in the NIST training and test sets differs
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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349 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
350 of letters in the test set, not in the training set (more like the natural distribution
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
351 of letters in text).
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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352
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353 %\item
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354 {\bf Fonts.}
479
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355 In order to have a good variety of sources we downloaded an important number of free fonts from: {\tt http://anonymous.url.net}
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356 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html}
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parents: 476
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357 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly.
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parents: 476
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358 The ttf file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
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Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
359 directly as input to our models.
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parents: 476
diff changeset
360
484
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361 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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362 {\bf Captchas.}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
363 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
364 generating characters of the same format as the NIST dataset. This software is based on
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
365 a random character class generator and various kinds of tranformations similar to those described in the previous sections.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
366 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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367 Transformations (slant, distorsions, rotation, translation) are applied to each randomly generated character with a complexity
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
368 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:
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369 allowed and can be controlled via an easy to use facade class.
484
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370
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parents: 483
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371 %\item
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diff changeset
372 {\bf OCR data.}
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
373 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
374 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
375 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
376 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
377 ({\tt http://www.iupr.com}), and which will be publically released.
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diff changeset
378 %\end{itemize}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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diff changeset
379
484
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380 \vspace*{-1mm}
472
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diff changeset
381 \subsection{Data Sets}
484
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382 \vspace*{-1mm}
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383
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
384 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
385 from one of the 62 character classes.
484
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386 %\begin{itemize}
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parents: 483
diff changeset
387
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diff changeset
388 %\item
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parents: 483
diff changeset
389 {\bf NIST.} This is the raw NIST special database 19.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
390
9a757d565e46 reduction de taille
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diff changeset
391 %\item
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parents: 483
diff changeset
392 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
472
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
393 and sending them through the above transformation pipeline.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
394 For each new exemple to generate, a source is selected with probability $10\%$ from the fonts,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
395 $25\%$ 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
396 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$.
484
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diff changeset
397
9a757d565e46 reduction de taille
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parents: 483
diff changeset
398 %\item
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parents: 483
diff changeset
399 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion)
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
400 except that we only apply
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
401 transformations from slant to pinch. Therefore, the character is
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
402 transformed but no additionnal noise is added to the image, giving images
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
403 closer to the NIST dataset.
484
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diff changeset
404 %\end{itemize}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
405
484
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diff changeset
406 \vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
407 \subsection{Models and their Hyperparameters}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
408 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
409
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
410 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
411
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
412 {\bf Multi-Layer Perceptrons (MLP).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
413 Whereas previous work had compared deep architectures to both shallow MLPs and
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
414 SVMs, we only compared to MLPs here because of the very large datasets used.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
415 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
416 exponentials) on the output layer for estimating P(class | image).
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
417 The hyper-parameters are the following: number of hidden units, taken in
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
418 $\{300,500,800,1000,1500\}$. The optimization procedure is as follows. Training
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
419 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
420 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
421 through preliminary experiments, and 0.1 was selected.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
422
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
423 {\bf Stacked Denoising Auto-Encoders (SDAE).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
424 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
425 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
426 layers)~\citep{Hinton06,ranzato-07,Bengio-nips-2006}
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
427 enabling better generalization, apparently setting parameters in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
428 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
429 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
430 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
431 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
432 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
433 $P(y|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
434 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
435 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
436 compositions of simpler ones through a deep hierarchy).
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
437 Here we chose to use the Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
438 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
439 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
440 teach (see tutorial and code there: {\tt http://deeplearning.net/tutorial}),
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
441 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
442 comparable or better than RBMs in series of experiments
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
443 \citep{VincentPLarochelleH2008}. During training of a Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
444 Auto-Encoder, it is presented with a stochastically corrupted version
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
445 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
446 forcing the hidden units to represent the leading regularities in
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
447 the data. Once it is trained, its hidden units activations can
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
448 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
449 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
450 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
451 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
452 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
453 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
454 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
455 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
456 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
457 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
458 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
459 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
460
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
461 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
462 \section{Experimental Results}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
463
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
464 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
465 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
466 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
467
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
468 We compare the best MLP (according to validation set error) that we found against
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
469 the best SDA (again according to validation set error), along with a precise estimate
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
470 of human performance obtained via Amazon's Mechanical Turk (AMT)
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
471 service\footnote{http://mturk.com}.
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
472 %AMT users are paid small amounts
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
473 %of money to perform tasks for which human intelligence is required.
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
474 %Mechanical Turk has been used extensively in natural language
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
475 %processing \citep{SnowEtAl2008} and vision
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
476 %\citep{SorokinAndForsyth2008,whitehill09}.
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
477 AMT users where presented
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
478 with 10 character images and asked to type 10 corresponding ascii
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
479 characters. They were forced to make a hard choice among the
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
480 62 or 10 character classes (all classes or digits only).
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
481 Three users classified each image, allowing
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
482 to estimate inter-human variability (shown as +/- in parenthesis below).
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
483
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
484 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
485 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
486 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
487 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
488 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
489 ~\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
490 ~\citep{Milgram+al-2005}. More detailed and complete numerical results
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
491 (figures and tables) can be found in the appendix. The 3 kinds of model
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
492 differ in the training sets used: NIST only (MLP0,SDA0), NISTP (MLP1,
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
493 SDA1), or P07 (MLP2, SDA2). The deep learner not only outperformed the
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
494 shallow ones and previously published performance but reaches human
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
495 performance on both the 62-class task and the 10-class (digits) task. In
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
496 addition, as shown in the left of Figure~\ref{fig:fig:improvements-charts},
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
497 the relative improvement in error rate brought by self-taught learning is
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
498 greater for the SDA. The left side shows the improvement to the clean NIST
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
499 test set error brought by the use of out-of-distribution examples (i.e. the
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
500 perturbed examples examples from NISTP or P07). The right side of
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
501 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
502 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
503 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
504 with all 62 classes when the target classes are respectively the digits,
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
505 lower-case, or upper-case characters). Again, whereas the gain is marginal
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
506 or negative for the MLP, it is substantial for the SDA. Note that for
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
507 these multi-task experiment, only the original NIST dataset is used. For
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
508 example, the MLP-digits bar shows the relative improvement in MLP error
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
509 rate on the NIST digits test set (1 - single-task model's error /
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
510 multi-task model's error). The single-task model is trained with only 10
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
511 outputs (one per digit), seeing only digit examples, whereas the multi-task
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
512 model is trained with 62 outputs, with all 62 character classes as
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
513 examples. For the multi-task model, the digit error rate is measured by
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
514 comparing the correct digit class with the output class associated with
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
515 the maximum conditional probability among only the digit classes outputs.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
516
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
517 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
518 \resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}\\
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
519 \caption{Charts corresponding to table \ref{tab:sda-vs-mlp-vs-humans}. Left: overall results; error bars indicate a 95\% confidence interval. Right: error rates on NIST test digits only, with results from litterature. }
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
520 \label{fig:error-rates-charts}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
521 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
522
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
523 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
524 %\subsection{Perturbed Training Data More Helpful for SDAE}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
525 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
526
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
527 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
528 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
529 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
530
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
531 \iffalse
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
532 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
533 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
534 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
535 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
536 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
537 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
538 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
539 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
540 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
541 (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
542 shallow learner.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
543
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
544 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
545 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
546 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
547
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
548 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
549 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
550 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
551 On the other hand the SDA benefitted from the multi-task setting, with relative
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
552 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
553 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
485
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
554 \fi
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
555
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
556
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
557 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
558 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
559 \caption{Charts corresponding to tables \ref{tab:perturbation-effect} (left) and \ref{tab:multi-task} (right).}
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
560 \label{fig:improvements-charts}
ead3085c1c66 Added charts to nips2010_submission.tex
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parents: 469
diff changeset
561 \end{figure}
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fsavard
parents: 469
diff changeset
562
484
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parents: 483
diff changeset
563 \vspace*{-1mm}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
564 \section{Conclusions}
484
9a757d565e46 reduction de taille
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parents: 483
diff changeset
565 \vspace*{-1mm}
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
566
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
567 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
568 %\begin{itemize}
487
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 486
diff changeset
569
484
9a757d565e46 reduction de taille
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parents: 483
diff changeset
570 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
571 Do the good results previously obtained with deep architectures on the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
572 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
573 dataset, the NIST special database 19, with 62 classes and around 800k examples?
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
574 Yes, the SDA systematically outperformed the MLP and all the previously
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
575 published results on this dataset (as far as we know), in fact reaching human-level
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
576 performance.
484
9a757d565e46 reduction de taille
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parents: 483
diff changeset
577
9a757d565e46 reduction de taille
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parents: 483
diff changeset
578 $\bullet$ %\item
9a757d565e46 reduction de taille
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parents: 483
diff changeset
579 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
580 noise, affine transformations, background images) make the resulting
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
581 classifier better not only on similarly perturbed images but also on
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
582 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
583 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
584 MLPs were helped by perturbed training examples when tested on perturbed input images,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
585 but only marginally helped wrt clean examples. On the other hand, the deep SDAs
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
586 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
587
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
588 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
589 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
590 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
591 a corresponding shallow and purely supervised architecture?
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
592 Whereas the improvement due to the multi-task setting was marginal or
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
593 negative for the MLP, it was very significant for the SDA.
484
9a757d565e46 reduction de taille
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parents: 483
diff changeset
594 %\end{itemize}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
595
484
9a757d565e46 reduction de taille
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parents: 483
diff changeset
596 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
597 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
598
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
599
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
600 {\small
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
601 \bibliography{strings,ml,aigaion,specials}
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
602 %\bibliographystyle{plainnat}
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
603 \bibliographystyle{unsrtnat}
464
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parents:
diff changeset
604 %\bibliographystyle{apalike}
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9a757d565e46 reduction de taille
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parents: 483
diff changeset
605 }
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
606
485
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
607 \newpage
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
608
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
609 \centerline{APPENDIX FOR {\bf Deep Self-Taught Learning for Handwritten Character Recognition}}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
610
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
611 \vspace*{1cm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
612
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
613 \begin{table}[h]
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
614 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
615 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
616 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
617 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
618 and using a validation set to select hyper-parameters and other training choices.
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
619 \{SDA,MLP\}0 are trained on NIST,
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
620 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
621 The human error rate on digits is a lower bound because it does not count digits that were
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
622 recognized as letters. For comparison, the results found in the literature
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
623 on NIST digits classification using the same test set are included.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
624 \label{tab:sda-vs-mlp-vs-humans}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
625 \begin{center}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
626 \begin{tabular}{|l|r|r|r|r|} \hline
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parents: 484
diff changeset
627 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
628 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
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parents: 484
diff changeset
629 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
630 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
631 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
632 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
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parents: 484
diff changeset
633 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
6beaf3328521 les tables enlevées
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parents: 484
diff changeset
634 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
635 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
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parents: 484
diff changeset
636 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
637 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
638 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
639 \end{tabular}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
640 \end{center}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
641 \end{table}
6beaf3328521 les tables enlevées
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parents: 484
diff changeset
642
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
643 \begin{table}[h]
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
644 \caption{Relative change in error rates due to the use of perturbed training data,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
645 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
646 A positive value indicates that training on the perturbed data helped for the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
647 given test set (the first 3 columns on the 62-class tasks and the last one is
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
648 on the clean 10-class digits). Clearly, the deep learning models did benefit more
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
649 from perturbed training data, even when testing on clean data, whereas the MLP
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
650 trained on perturbed data performed worse on the clean digits and about the same
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
651 on the clean characters. }
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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652 \label{tab:perturbation-effect}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
653 \begin{center}
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parents: 484
diff changeset
654 \begin{tabular}{|l|r|r|r|r|} \hline
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parents: 484
diff changeset
655 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
656 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
657 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
658 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
659 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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diff changeset
660 \end{tabular}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
661 \end{center}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
662 \end{table}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
663
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
664 \begin{table}[h]
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
665 \caption{Test error rates and relative change in error rates due to the use of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
666 a multi-task setting, i.e., training on each task in isolation vs training
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
667 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
668 more from the multi-task setting. All experiments on only on the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
669 unperturbed NIST data, using validation error for model selection.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
670 Relative improvement is 1 - single-task error / multi-task error.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
671 \label{tab:multi-task}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
672 \begin{center}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
673 \begin{tabular}{|l|r|r|r|} \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
674 & single-task & multi-task & relative \\
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
675 & setting & setting & improvement \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
676 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
677 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
678 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
679 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
680 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
681 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
682 \end{tabular}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
683 \end{center}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
684 \end{table}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
685
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
686
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
687 \end{document}