Mercurial > ift6266
annotate writeup/nips2010_submission.tex @ 513:66a905508e34
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| author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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| date | Tue, 01 Jun 2010 14:05:02 -0400 |
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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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9 |
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10 \title{Deep Self-Taught Learning for Handwritten Character Recognition} |
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11 \author{The IFT6266 Gang} |
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12 |
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13 \begin{document} |
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14 |
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15 %\makeanontitle |
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16 \maketitle |
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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 (exploiting unlabeled |
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24 examples or examples from other distributions) has already been applied |
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25 to deep learners, but mostly to show the advantage of unlabeled |
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26 examples. Here we explore the advantage brought by {\em out-of-distribution |
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27 examples} and show that {\em deep learners benefit more from them than a |
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28 corresponding shallow learner}, in the area |
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29 of handwritten character recognition. In fact, we show that they reach |
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30 human-level performance on both handwritten digit classification and |
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31 62-class handwritten character recognition. For this purpose we |
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32 developed a powerful generator of stochastic variations and noise |
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33 processes character images, including not only affine transformations but |
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34 also slant, local elastic deformations, changes in thickness, background |
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35 images, grey level changes, contrast, occlusion, and various types of pixel and |
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36 spatially correlated noise. The out-of-distribution examples are |
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37 obtained by training with these highly distorted images or |
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38 by including object classes different from those in the target test set. |
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39 \end{abstract} |
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40 \vspace*{-2mm} |
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41 |
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42 \section{Introduction} |
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43 \vspace*{-1mm} |
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44 |
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45 Deep Learning has emerged as a promising new area of research in |
| 469 | 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 |
| 501 | 56 higher layers~\citep{Goodfellow2009}. |
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57 Learning a hierarchy of features increases the |
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58 ease and practicality of developing representations that are at once |
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59 tailored to specific tasks, yet are able to borrow statistical strength |
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60 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the |
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61 feature representation can lead to higher-level (more abstract, more |
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62 general) features that are more robust to unanticipated sources of |
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63 variance extant in real data. |
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64 |
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65 Whereas a deep architecture can in principle be more powerful than a |
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66 shallow one in terms of representation, depth appears to render the |
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67 training problem more difficult in terms of optimization and local minima. |
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68 It is also only recently that successful algorithms were proposed to |
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69 overcome some of these difficulties. All are based on unsupervised |
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70 learning, often in an greedy layer-wise ``unsupervised pre-training'' |
| 469 | 71 stage~\citep{Bengio-2009}. One of these layer initialization techniques, |
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72 applied here, is the Denoising |
| 469 | 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-small} |
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89 and multi-task learning, not much has been done yet to explore the impact |
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90 of {\em out-of-distribution} examples and of the multi-task setting |
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91 (but see~\citep{CollobertR2008}). In particular the {\em relative |
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92 advantage} of deep learning for this settings has not been evaluated. |
| 512 | 93 The hypothesis explored here is that a deep hierarchy of features |
| 94 may be better able to provide sharing of statistical strength | |
| 95 between different regions in input space or different tasks, | |
| 96 as discussed in the conclusion. | |
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97 |
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98 In this paper we ask the following questions: |
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99 |
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100 %\begin{enumerate} |
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101 $\bullet$ %\item |
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102 Do the good results previously obtained with deep architectures on the |
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103 MNIST digit images generalize to the setting of a much larger and richer (but similar) |
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104 dataset, the NIST special database 19, with 62 classes and around 800k examples? |
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105 |
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106 $\bullet$ %\item |
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107 To what extent does the perturbation of input images (e.g. adding |
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108 noise, affine transformations, background images) make the resulting |
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109 classifiers better not only on similarly perturbed images but also on |
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110 the {\em original clean examples}? |
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111 |
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112 $\bullet$ %\item |
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113 Do deep architectures {\em benefit more from such out-of-distribution} |
| 469 | 114 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? |
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115 |
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116 $\bullet$ %\item |
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117 Similarly, does the feature learning step in deep learning algorithms benefit more |
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118 training with similar but different classes (i.e. a multi-task learning scenario) than |
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119 a corresponding shallow and purely supervised architecture? |
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120 %\end{enumerate} |
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121 |
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122 The experimental results presented here provide positive evidence towards all of these questions. |
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123 |
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124 \vspace*{-1mm} |
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125 \section{Perturbation and Transformation of Character Images} |
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126 \vspace*{-1mm} |
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127 |
| 467 | 128 This section describes the different transformations we used to stochastically |
| 129 transform source images in order to obtain data. More details can | |
| 469 | 130 be found in this technical report~\citep{ift6266-tr-anonymous}. |
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131 The code for these transformations (mostly python) is available at |
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132 {\tt http://anonymous.url.net}. All the modules in the pipeline share |
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133 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the |
| 467 | 134 amount of deformation or noise introduced. |
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135 |
| 467 | 136 There are two main parts in the pipeline. The first one, |
| 137 from slant to pinch below, performs transformations. The second | |
| 138 part, from blur to contrast, adds different kinds of noise. | |
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139 |
| 501 | 140 \begin{figure}[h] |
| 141 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\ | |
| 506 | 142 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE |
| 501 | 143 \caption{Illustration of each transformation applied alone to the same image |
| 144 of an upper-case h (top left). First row (from left to right) : original image, slant, | |
| 145 thickness, affine transformation (translation, rotation, shear), | |
| 146 local elastic deformation; second row (from left to right) : | |
| 147 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to right) : | |
| 148 background image, salt and pepper noise, spatially Gaussian noise, scratches, | |
| 149 grey level and contrast changes.} | |
| 150 \label{fig:transfo} | |
| 151 \end{figure} | |
| 152 | |
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153 {\large\bf Transformations} |
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154 |
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155 \vspace*{2mm} |
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156 |
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157 {\bf Slant.} |
| 467 | 158 We mimic slant by shifting each row of the image |
| 495 | 159 proportionally to its height: $shift = round(slant \times height)$. |
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160 The $slant$ coefficient can be negative or positive with equal probability |
| 467 | 161 and its value is randomly sampled according to the complexity level: |
| 162 e $slant \sim U[0,complexity]$, so the | |
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163 maximum displacement for the lowest or highest pixel line is of |
| 467 | 164 $round(complexity \times 32)$.\\ |
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165 {\bf Thickness.} |
| 495 | 166 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82} |
| 467 | 167 are applied. The neighborhood of each pixel is multiplied |
| 168 element-wise with a {\em structuring element} matrix. | |
| 169 The pixel value is replaced by the maximum or the minimum of the resulting | |
| 170 matrix, respectively for dilation or erosion. Ten different structural elements with | |
| 171 increasing dimensions (largest is $5\times5$) were used. For each image, | |
| 172 randomly sample the operator type (dilation or erosion) with equal probability and one structural | |
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173 element from a subset of the $n$ smallest structuring elements where $n$ is |
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174 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$ |
| 467 | 175 for erosion. A neutral element is always present in the set, and if it is |
| 176 chosen no transformation is applied. Erosion allows only the six | |
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177 smallest structural elements because when the character is too thin it may |
| 467 | 178 be completely erased.\\ |
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179 {\bf Affine Transformations.} |
| 467 | 180 A $2 \times 3$ affine transform matrix (with |
| 181 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level. | |
| 182 Each pixel $(x,y)$ of the output image takes the value of the pixel | |
| 183 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This | |
| 184 produces scaling, translation, rotation and shearing. | |
| 185 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to | |
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186 forbid important rotations (not to confuse classes) but to give good |
| 467 | 187 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times |
| 188 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3 | |
| 189 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times | |
| 190 complexity]$.\\ | |
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191 {\bf Local Elastic Deformations.} |
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192 This filter induces a "wiggly" effect in the image, following~\citet{SimardSP03-short}, |
| 467 | 193 which provides more details. |
| 194 Two "displacements" fields are generated and applied, for horizontal | |
| 195 and vertical displacements of pixels. | |
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196 To generate a pixel in either field, first a value between -1 and 1 is |
| 467 | 197 chosen from a uniform distribution. Then all the pixels, in both fields, are |
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198 multiplied by a constant $\alpha$ which controls the intensity of the |
| 467 | 199 displacements (larger $\alpha$ translates into larger wiggles). |
| 200 Each field is convoluted with a Gaussian 2D kernel of | |
| 201 standard deviation $\sigma$. Visually, this results in a blur. | |
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202 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times |
| 467 | 203 \sqrt[3]{complexity}$.\\ |
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204 {\bf Pinch.} |
| 467 | 205 This GIMP filter is named "Whirl and |
| 206 pinch", but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic | |
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207 surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}. |
| 467 | 208 For a square input image, think of drawing a circle of |
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209 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to |
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210 that disk (region inside circle) will have its value recalculated by taking |
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211 the value of another "source" pixel in the original image. The position of |
| 495 | 212 that source pixel is found on the line that goes through $C$ and $P$, but |
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213 at some other distance $d_2$. Define $d_1$ to be the distance between $P$ |
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214 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times |
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215 d_1$, where $pinch$ is a parameter to the filter. |
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216 The actual value is given by bilinear interpolation considering the pixels |
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217 around the (non-integer) source position thus found. |
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218 Here $pinch \sim U[-complexity, 0.7 \times complexity]$. |
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219 |
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220 \vspace*{1mm} |
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221 |
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222 {\large\bf Injecting Noise} |
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223 |
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224 \vspace*{1mm} |
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225 |
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226 {\bf Motion Blur.} |
| 467 | 227 This GIMP filter is a ``linear motion blur'' in GIMP |
| 228 terminology, with two parameters, $length$ and $angle$. The value of | |
| 229 a pixel in the final image is the approximately mean value of the $length$ first pixels | |
| 230 found by moving in the $angle$ direction. | |
| 231 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.\\ | |
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232 {\bf Occlusion.} |
| 467 | 233 This filter selects a random rectangle from an {\em occluder} character |
| 234 images and places it over the original {\em occluded} character | |
| 235 image. Pixels are combined by taking the max(occluder,occluded), | |
| 236 closer to black. The corners of the occluder The rectangle corners | |
| 237 are sampled so that larger complexity gives larger rectangles. | |
| 238 The destination position in the occluded image are also sampled | |
| 469 | 239 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}). |
| 467 | 240 It has has a probability of not being applied at all of 60\%.\\ |
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241 {\bf Pixel Permutation.} |
| 467 | 242 This filter permutes neighbouring pixels. It selects first |
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243 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then |
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244 sequentially exchanged to one other pixel in its $V4$ neighbourhood. Number |
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245 of exchanges to the left, right, top, bottom are equal or does not differ |
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246 from more than 1 if the number of selected pixels is not a multiple of 4. |
| 467 | 247 It has has a probability of not being applied at all of 80\%.\\ |
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248 {\bf Gaussian Noise.} |
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249 This filter simply adds, to each pixel of the image independently, a |
| 467 | 250 noise $\sim Normal(0(\frac{complexity}{10})^2)$. |
| 251 It has has a probability of not being applied at all of 70\%.\\ | |
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252 {\bf Background Images.} |
| 469 | 253 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random |
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254 background behind the letter. The background is chosen by first selecting, |
| 495 | 255 at random, an image from a set of images. Then a 32$\times$32 sub-region |
| 467 | 256 of that image is chosen as the background image (by sampling position |
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257 uniformly while making sure not to cross image borders). |
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258 To combine the original letter image and the background image, contrast |
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259 adjustments are made. We first get the maximal values (i.e. maximal |
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260 intensity) for both the original image and the background image, $maximage$ |
| 467 | 261 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$. |
| 262 Each background pixel value is multiplied by $\frac{max(maximage - | |
| 263 contrast, 0)}{maxbg}$ (higher contrast yield darker | |
| 264 background). The output image pixels are max(background,original).\\ | |
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265 {\bf Salt and Pepper Noise.} |
| 467 | 266 This filter adds noise $\sim U[0,1]$ to random subsets of pixels. |
| 267 The number of selected pixels is $0.2 \times complexity$. | |
| 268 This filter has a probability of not being applied at all of 75\%.\\ | |
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269 {\bf Spatially Gaussian Noise.} |
| 467 | 270 Different regions of the image are spatially smoothed. |
| 271 The image is convolved with a symmetric Gaussian kernel of | |
| 495 | 272 size and variance chosen uniformly in the ranges $[12,12 + 20 \times |
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273 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized |
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274 between $0$ and $1$. We also create a symmetric averaging window, of the |
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275 kernel size, with maximum value at the center. For each image we sample |
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276 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be |
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277 averaging centers between the original image and the filtered one. We |
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278 initialize to zero a mask matrix of the image size. For each selected pixel |
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279 we add to the mask the averaging window centered to it. The final image is |
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280 computed from the following element-wise operation: $\frac{image + filtered |
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281 image \times mask}{mask+1}$. |
| 467 | 282 This filter has a probability of not being applied at all of 75\%.\\ |
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283 {\bf Scratches.} |
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284 The scratches module places line-like white patches on the image. The |
| 467 | 285 lines are heavily transformed images of the digit "1" (one), chosen |
| 286 at random among five thousands such 1 images. The 1 image is | |
| 287 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times | |
| 495 | 288 complexity)^2$, using bi-cubic interpolation, |
| 289 Two passes of a grey-scale morphological erosion filter | |
| 467 | 290 are applied, reducing the width of the line |
| 291 by an amount controlled by $complexity$. | |
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292 This filter is only applied only 15\% of the time. When it is applied, 50\% |
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293 of the time, only one patch image is generated and applied. In 30\% of |
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294 cases, two patches are generated, and otherwise three patches are |
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295 generated. The patch is applied by taking the maximal value on any given |
| 467 | 296 patch or the original image, for each of the 32x32 pixel locations.\\ |
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297 {\bf Grey Level and Contrast Changes.} |
| 495 | 298 This filter changes the contrast and may invert the image polarity (white |
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299 on black to black on white). The contrast $C$ is defined here as the |
| 467 | 300 difference between the maximum and the minimum pixel value of the image. |
| 495 | 301 Contrast $\sim U[1-0.85 \times complexity,1]$ (so contrast $\geq 0.15$). |
| 467 | 302 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The |
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303 polarity is inverted with $0.5$ probability. |
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304 |
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305 \iffalse |
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306 \begin{figure}[h] |
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307 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\ |
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308 \caption{Illustration of the pipeline of stochastic |
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309 transformations applied to the image of a lower-case t |
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310 (the upper left image). Each image in the pipeline (going from |
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311 left to right, first top line, then bottom line) shows the result |
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312 of applying one of the modules in the pipeline. The last image |
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313 (bottom right) is used as training example.} |
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314 \label{fig:pipeline} |
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315 \end{figure} |
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316 \fi |
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317 |
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318 |
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319 \vspace*{-1mm} |
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320 \section{Experimental Setup} |
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321 \vspace*{-1mm} |
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322 |
| 472 | 323 Whereas much previous work on deep learning algorithms had been performed on |
| 324 the MNIST digits classification task~\citep{Hinton06,ranzato-07,Bengio-nips-2006,Salakhutdinov+Hinton-2009}, | |
| 325 with 60~000 examples, and variants involving 10~000 | |
| 501 | 326 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want |
| 472 | 327 to focus here on the case of much larger training sets, from 10 times to |
| 328 to 1000 times larger. The larger datasets are obtained by first sampling from | |
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329 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas}, |
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330 and {\bf OCR data} (scanned machine printed characters). Once a character |
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331 is sampled from one of these sources (chosen randomly), a pipeline of |
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332 the above transformations and/or noise processes is applied to the |
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333 image. |
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334 |
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335 We compare the best MLP (according to validation set error) that we found against |
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336 the best SDA (again according to validation set error), along with a precise estimate |
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337 of human performance obtained via Amazon's Mechanical Turk (AMT) |
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338 service\footnote{http://mturk.com}. |
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339 AMT users are paid small amounts |
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340 of money to perform tasks for which human intelligence is required. |
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341 Mechanical Turk has been used extensively in natural language |
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342 processing \citep{SnowEtAl2008} and vision |
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343 \citep{SorokinAndForsyth2008,whitehill09}. |
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344 AMT users where presented |
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345 with 10 character images and asked to type 10 corresponding ASCII |
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346 characters. They were forced to make a hard choice among the |
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347 62 or 10 character classes (all classes or digits only). |
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348 Three users classified each image, allowing |
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349 to estimate inter-human variability. |
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350 |
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351 \vspace*{-1mm} |
| 472 | 352 \subsection{Data Sources} |
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353 \vspace*{-1mm} |
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354 |
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355 %\begin{itemize} |
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356 %\item |
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357 {\bf NIST.} |
| 501 | 358 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995}, |
| 472 | 359 widely used for training and testing character |
| 501 | 360 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}. |
| 361 The dataset is composed with 814255 digits and characters (upper and lower cases), with hand checked classifications, | |
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362 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes |
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363 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity. |
| 472 | 364 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one is recommended |
| 501 | 365 by NIST as testing set and is used in our work and some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005} |
| 472 | 366 for that purpose. We randomly split the remainder into a training set and a validation set for |
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367 model selection. The sizes of these data sets are: 651668 for training, 80000 for validation, |
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368 and 82587 for testing. |
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369 The performances reported by previous work on that dataset mostly use only the digits. |
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370 Here we use all the classes both in the training and testing phase. This is especially |
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371 useful to estimate the effect of a multi-task setting. |
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372 Note that the distribution of the classes in the NIST training and test sets differs |
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373 substantially, with relatively many more digits in the test set, and uniform distribution |
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374 of letters in the test set, not in the training set (more like the natural distribution |
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375 of letters in text). |
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376 |
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377 %\item |
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378 {\bf Fonts.} |
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379 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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380 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html} |
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381 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly. |
| 495 | 382 The {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image, |
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383 directly as input to our models. |
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384 |
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385 %\item |
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386 {\bf Captchas.} |
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387 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for |
| 472 | 388 generating characters of the same format as the NIST dataset. This software is based on |
| 495 | 389 a random character class generator and various kinds of transformations similar to those described in the previous sections. |
| 472 | 390 In order to increase the variability of the data generated, many different fonts are used for generating the characters. |
| 495 | 391 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity |
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392 depending on the value of the complexity parameter provided by the user of the data source. Two levels of complexity are |
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393 allowed and can be controlled via an easy to use facade class. |
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394 |
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395 %\item |
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396 {\bf OCR data.} |
| 472 | 397 A large set (2 million) of scanned, OCRed and manually verified machine-printed |
| 398 characters (from various documents and books) where included as an | |
| 399 additional source. This set is part of a larger corpus being collected by the Image Understanding | |
| 400 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern | |
| 495 | 401 ({\tt http://www.iupr.com}), and which will be publicly released. |
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402 %\end{itemize} |
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403 |
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404 \vspace*{-1mm} |
| 472 | 405 \subsection{Data Sets} |
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406 \vspace*{-1mm} |
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407 |
| 472 | 408 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label |
| 409 from one of the 62 character classes. | |
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410 %\begin{itemize} |
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411 |
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412 %\item |
| 501 | 413 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. |
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414 |
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415 %\item |
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416 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources |
| 472 | 417 and sending them through the above transformation pipeline. |
| 495 | 418 For each new example to generate, a source is selected with probability $10\%$ from the fonts, |
| 472 | 419 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the |
| 420 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$. | |
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421 |
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422 %\item |
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423 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion) |
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424 except that we only apply |
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425 transformations from slant to pinch. Therefore, the character is |
| 495 | 426 transformed but no additional noise is added to the image, giving images |
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427 closer to the NIST dataset. |
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428 %\end{itemize} |
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429 |
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430 \vspace*{-1mm} |
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431 \subsection{Models and their Hyperparameters} |
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432 \vspace*{-1mm} |
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433 |
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434 The experiments are performed with Multi-Layer Perceptrons (MLP) with a single |
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435 hidden layer and with Stacked Denoising Auto-Encoders (SDA). |
| 472 | 436 All hyper-parameters are selected based on performance on the NISTP validation set. |
| 437 | |
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438 {\bf Multi-Layer Perceptrons (MLP).} |
| 472 | 439 Whereas previous work had compared deep architectures to both shallow MLPs and |
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440 SVMs, we only compared to MLPs here because of the very large datasets used |
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441 (making the use of SVMs computationally inconvenient because of their quadratic |
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442 scaling behavior). |
| 472 | 443 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized |
| 444 exponentials) on the output layer for estimating P(class | image). | |
| 445 The hyper-parameters are the following: number of hidden units, taken in | |
| 446 $\{300,500,800,1000,1500\}$. The optimization procedure is as follows. Training | |
| 447 examples are presented in minibatches of size 20. A constant learning | |
|
474
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448 rate is chosen in $10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$ |
| 472 | 449 through preliminary experiments, and 0.1 was selected. |
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450 |
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451 {\bf Stacked Denoising Auto-Encoders (SDA).} |
| 472 | 452 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs) |
| 453 can be used to initialize the weights of each layer of a deep MLP (with many hidden | |
| 454 layers)~\citep{Hinton06,ranzato-07,Bengio-nips-2006} | |
| 455 enabling better generalization, apparently setting parameters in the | |
| 456 basin of attraction of supervised gradient descent yielding better | |
| 457 generalization~\citep{Erhan+al-2010}. It is hypothesized that the | |
| 458 advantage brought by this procedure stems from a better prior, | |
| 459 on the one hand taking advantage of the link between the input | |
| 460 distribution $P(x)$ and the conditional distribution of interest | |
| 461 $P(y|x)$ (like in semi-supervised learning), and on the other hand | |
| 462 taking advantage of the expressive power and bias implicit in the | |
| 463 deep architecture (whereby complex concepts are expressed as | |
| 464 compositions of simpler ones through a deep hierarchy). | |
| 465 Here we chose to use the Denoising | |
| 466 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for | |
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467 % AJOUTER UNE IMAGE? |
| 472 | 468 these deep hierarchies of features, as it is very simple to train and |
| 469 teach (see tutorial and code there: {\tt http://deeplearning.net/tutorial}), | |
| 470 provides immediate and efficient inference, and yielded results | |
| 471 comparable or better than RBMs in series of experiments | |
| 472 \citep{VincentPLarochelleH2008}. During training of a Denoising | |
| 473 Auto-Encoder, it is presented with a stochastically corrupted version | |
| 474 of the input and trained to reconstruct the uncorrupted input, | |
| 475 forcing the hidden units to represent the leading regularities in | |
| 476 the data. Once it is trained, its hidden units activations can | |
| 477 be used as inputs for training a second one, etc. | |
| 478 After this unsupervised pre-training stage, the parameters | |
| 479 are used to initialize a deep MLP, which is fine-tuned by | |
| 480 the same standard procedure used to train them (see previous section). | |
|
484
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481 The SDA hyper-parameters are the same as for the MLP, with the addition of the |
| 472 | 482 amount of corruption noise (we used the masking noise process, whereby a |
| 483 fixed proportion of the input values, randomly selected, are zeroed), and a | |
| 484 separate learning rate for the unsupervised pre-training stage (selected | |
| 485 from the same above set). The fraction of inputs corrupted was selected | |
| 486 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number | |
| 487 of hidden layers but it was fixed to 3 based on previous work with | |
| 488 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}. | |
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489 |
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490 \vspace*{-1mm} |
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491 \section{Experimental Results} |
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492 |
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493 %\vspace*{-1mm} |
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494 %\subsection{SDA vs MLP vs Humans} |
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495 %\vspace*{-1mm} |
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496 |
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497 Figure~\ref{fig:error-rates-charts} summarizes the results obtained, |
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498 comparing Humans, three MLPs (MLP0, MLP1, MLP2) and three SDAs (SDA0, SDA1, |
|
486
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499 SDA2), along with the previous results on the digits NIST special database |
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500 19 test set from the literature respectively based on ARTMAP neural |
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501 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search |
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502 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002}, and SVMs |
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503 ~\citep{Milgram+al-2005}. More detailed and complete numerical results |
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493
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504 (figures and tables, including standard errors on the error rates) can be |
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505 found in the supplementary material. The 3 kinds of model differ in the |
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491
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506 training sets used: NIST only (MLP0,SDA0), NISTP (MLP1, SDA1), or P07 |
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507 (MLP2, SDA2). The deep learner not only outperformed the shallow ones and |
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491
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508 previously published performance (in a statistically and qualitatively |
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491
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509 significant way) but reaches human performance on both the 62-class task |
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510 and the 10-class (digits) task. In addition, as shown in the left of |
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511 Figure~\ref{fig:fig:improvements-charts}, the relative improvement in error |
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512 rate brought by self-taught learning is greater for the SDA, and these |
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513 differences with the MLP are statistically and qualitatively |
|
502
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514 significant. |
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515 The left side of the figure shows the improvement to the clean |
|
493
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parents:
491
diff
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516 NIST test set error brought by the use of out-of-distribution examples |
|
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517 (i.e. the perturbed examples examples from NISTP or P07). |
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diff
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518 Relative change is measured by taking |
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diff
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519 (original model's error / perturbed-data model's error - 1). |
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520 The right side of |
|
486
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521 Figure~\ref{fig:fig:improvements-charts} shows the relative improvement |
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522 brought by the use of a multi-task setting, in which the same model is |
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523 trained for more classes than the target classes of interest (i.e. training |
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524 with all 62 classes when the target classes are respectively the digits, |
|
493
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diff
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525 lower-case, or upper-case characters). Again, whereas the gain from the |
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parents:
491
diff
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|
526 multi-task setting is marginal or negative for the MLP, it is substantial |
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527 for the SDA. Note that for these multi-task experiment, only the original |
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528 NIST dataset is used. For example, the MLP-digits bar shows the relative |
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parents:
491
diff
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|
529 improvement in MLP error rate on the NIST digits test set (1 - single-task |
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diff
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530 model's error / multi-task model's error). The single-task model is |
|
a194ce5a4249
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parents:
491
diff
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|
531 trained with only 10 outputs (one per digit), seeing only digit examples, |
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parents:
491
diff
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|
532 whereas the multi-task model is trained with 62 outputs, with all 62 |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
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|
533 character classes as examples. Hence the hidden units are shared across |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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diff
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|
534 all tasks. For the multi-task model, the digit error rate is measured by |
|
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parents:
491
diff
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|
535 comparing the correct digit class with the output class associated with the |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
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|
536 maximum conditional probability among only the digit classes outputs. The |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
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|
537 setting is similar for the other two target classes (lower case characters |
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491
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538 and upper case characters). |
|
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|
539 |
| 475 | 540 \begin{figure}[h] |
| 541 \resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}\\ | |
|
502
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501
diff
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|
542 \caption{Error bars indicate a 95\% confidence interval. 0 indicates training |
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parents:
501
diff
changeset
|
543 on NIST, 1 on NISTP, and 2 on P07. Left: overall results |
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|
544 of all models, on 3 different test sets corresponding to the three |
|
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|
545 datasets. |
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parents:
501
diff
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|
546 Right: error rates on NIST test digits only, along with the previous results from |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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diff
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547 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005} |
|
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parents:
501
diff
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|
548 respectively based on ART, nearest neighbors, MLPs, and SVMs.} |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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549 |
| 475 | 550 \label{fig:error-rates-charts} |
| 551 \end{figure} | |
| 552 | |
|
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|
553 %\vspace*{-1mm} |
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554 %\subsection{Perturbed Training Data More Helpful for SDA} |
|
485
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555 %\vspace*{-1mm} |
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parents:
diff
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|
556 |
|
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parents:
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diff
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|
557 %\vspace*{-1mm} |
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parents:
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diff
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558 %\subsection{Multi-Task Learning Effects} |
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559 %\vspace*{-1mm} |
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560 |
|
485
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561 \iffalse |
|
464
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parents:
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|
562 As previously seen, the SDA is better able to benefit from the |
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parents:
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563 transformations applied to the data than the MLP. In this experiment we |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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564 define three tasks: recognizing digits (knowing that the input is a digit), |
|
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parents:
diff
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|
565 recognizing upper case characters (knowing that the input is one), and |
|
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parents:
diff
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|
566 recognizing lower case characters (knowing that the input is one). We |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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567 consider the digit classification task as the target task and we want to |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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|
568 evaluate whether training with the other tasks can help or hurt, and |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff
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|
569 whether the effect is different for MLPs versus SDAs. The goal is to find |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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570 out if deep learning can benefit more (or less) from multiple related tasks |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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571 (i.e. the multi-task setting) compared to a corresponding purely supervised |
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572 shallow learner. |
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573 |
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574 We use a single hidden layer MLP with 1000 hidden units, and a SDA |
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575 with 3 hidden layers (1000 hidden units per layer), pre-trained and |
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576 fine-tuned on NIST. |
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577 |
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578 Our results show that the MLP benefits marginally from the multi-task setting |
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579 in the case of digits (5\% relative improvement) but is actually hurt in the case |
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580 of characters (respectively 3\% and 4\% worse for lower and upper class characters). |
| 495 | 581 On the other hand the SDA benefited from the multi-task setting, with relative |
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582 error rate improvements of 27\%, 15\% and 13\% respectively for digits, |
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583 lower and upper case characters, as shown in Table~\ref{tab:multi-task}. |
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485
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584 \fi |
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585 |
| 475 | 586 |
| 587 \begin{figure}[h] | |
| 588 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\ | |
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509
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589 \caption{Relative improvement in error rate due to self-taught learning. |
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590 Left: Improvement (or loss, when negative) |
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591 induced by out-of-distribution examples (perturbed data). |
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592 Right: Improvement (or loss, when negative) induced by multi-task |
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593 learning (training on all classes and testing only on either digits, |
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594 upper case, or lower-case). The deep learner (SDA) benefits more from |
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595 both self-taught learning scenarios, compared to the shallow MLP.} |
| 475 | 596 \label{fig:improvements-charts} |
| 597 \end{figure} | |
| 598 | |
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599 \vspace*{-1mm} |
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600 \section{Conclusions} |
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484
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601 \vspace*{-1mm} |
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602 |
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502
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603 We have found that the self-taught learning framework is more beneficial |
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604 to a deep learner than to a traditional shallow and purely |
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605 supervised learner. More precisely, |
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606 the conclusions are positive for all the questions asked in the introduction. |
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484
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607 %\begin{itemize} |
| 487 | 608 |
|
484
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609 $\bullet$ %\item |
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610 Do the good results previously obtained with deep architectures on the |
| 472 | 611 MNIST digits generalize to the setting of a much larger and richer (but similar) |
| 612 dataset, the NIST special database 19, with 62 classes and around 800k examples? | |
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502
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613 Yes, the SDA {\bf systematically outperformed the MLP and all the previously |
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486
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614 published results on this dataset (as far as we know), in fact reaching human-level |
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615 performance} at round 17\% error on the 62-class task and 1.4\% on the digits. |
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616 |
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617 $\bullet$ %\item |
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618 To what extent does the perturbation of input images (e.g. adding |
| 472 | 619 noise, affine transformations, background images) make the resulting |
| 620 classifier better not only on similarly perturbed images but also on | |
| 621 the {\em original clean examples}? Do deep architectures benefit more from such {\em out-of-distribution} | |
| 622 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? | |
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623 MLPs were helped by perturbed training examples when tested on perturbed input |
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624 images (65\% relative improvement on NISTP) |
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625 but only marginally helped (5\% relative improvement on all classes) |
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626 or even hurt (10\% relative loss on digits) |
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627 with respect to clean examples . On the other hand, the deep SDAs |
| 472 | 628 were very significantly boosted by these out-of-distribution examples. |
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629 |
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630 $\bullet$ %\item |
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631 Similarly, does the feature learning step in deep learning algorithms benefit more |
| 472 | 632 training with similar but different classes (i.e. a multi-task learning scenario) than |
| 633 a corresponding shallow and purely supervised architecture? | |
| 634 Whereas the improvement due to the multi-task setting was marginal or | |
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635 negative for the MLP (from +5.6\% to -3.6\% relative change), |
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636 it was very significant for the SDA (from +13\% to +27\% relative change). |
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637 %\end{itemize} |
| 472 | 638 |
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639 Why would deep learners benefit more from the self-taught learning framework? |
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640 The key idea is that the lower layers of the predictor compute a hierarchy |
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641 of features that can be shared across tasks or across variants of the |
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642 input distribution. Intermediate features that can be used in different |
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643 contexts can be estimated in a way that allows to share statistical |
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644 strength. Features extracted through many levels are more likely to |
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645 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest), |
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646 increasing the likelihood that they would be useful for a larger array |
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647 of tasks and input conditions. |
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648 Therefore, we hypothesize that both depth and unsupervised |
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649 pre-training play a part in explaining the advantages observed here, and future |
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650 experiments could attempt at teasing apart these factors. |
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651 |
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652 A Flash demo of the recognizer (where both the MLP and the SDA can be compared) |
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653 can be executed on-line at {\tt http://deep.host22.com}. |
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654 |
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655 \newpage |
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656 { |
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657 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,aigaion-shorter,specials} |
| 469 | 658 %\bibliographystyle{plainnat} |
| 659 \bibliographystyle{unsrtnat} | |
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660 %\bibliographystyle{apalike} |
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661 } |
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662 |
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663 |
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664 \end{document} |