Mercurial > ift6266
annotate writeup/nips2010_submission.tex @ 529:4354c3c8f49c
longer conclusion
| author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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| date | Tue, 01 Jun 2010 20:48:05 -0400 |
| parents | 07bc0ca8d246 |
| children | 85f2337d47d2 2e33885730cf |
| 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} |
| 469 | 8 \usepackage[numbers]{natbib} |
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12 \title{Deep Self-Taught Learning for Handwritten Character Recognition} |
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13 \author{The IFT6266 Gang} |
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14 |
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15 \begin{document} |
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16 |
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17 %\makeanontitle |
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18 \maketitle |
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19 |
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20 \vspace*{-2mm} |
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21 \begin{abstract} |
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22 Recent theoretical and empirical work in statistical machine learning has |
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23 demonstrated the importance of learning algorithms for deep |
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24 architectures, i.e., function classes obtained by composing multiple |
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25 non-linear transformations. Self-taught learning (exploiting unlabeled |
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26 examples or examples from other distributions) has already been applied |
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27 to deep learners, but mostly to show the advantage of unlabeled |
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28 examples. Here we explore the advantage brought by {\em out-of-distribution |
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29 examples} and show that {\em deep learners benefit more from them than a |
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30 corresponding shallow learner}, in the area |
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31 of handwritten character recognition. In fact, we show that they reach |
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32 human-level performance on both handwritten digit classification and |
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33 62-class handwritten character recognition. For this purpose we |
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34 developed a powerful generator of stochastic variations and noise |
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35 processes character images, including not only affine transformations but |
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36 also slant, local elastic deformations, changes in thickness, background |
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37 images, grey level changes, contrast, occlusion, and various types of pixel and |
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38 spatially correlated noise. The out-of-distribution examples are |
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39 obtained by training with these highly distorted images or |
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40 by including object classes different from those in the target test set. |
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41 \end{abstract} |
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42 \vspace*{-2mm} |
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43 |
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44 \section{Introduction} |
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45 \vspace*{-1mm} |
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46 |
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47 Deep Learning has emerged as a promising new area of research in |
| 469 | 48 statistical machine learning (see~\citet{Bengio-2009} for a review). |
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49 Learning algorithms for deep architectures are centered on the learning |
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50 of useful representations of data, which are better suited to the task at hand. |
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51 This is in great part inspired by observations of the mammalian visual cortex, |
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52 which consists of a chain of processing elements, each of which is associated with a |
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53 different representation of the raw visual input. In fact, |
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54 it was found recently that the features learnt in deep architectures resemble |
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55 those observed in the first two of these stages (in areas V1 and V2 |
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56 of visual cortex)~\citep{HonglakL2008}, and that they become more and |
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57 more invariant to factors of variation (such as camera movement) in |
| 501 | 58 higher layers~\citep{Goodfellow2009}. |
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59 Learning a hierarchy of features increases the |
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60 ease and practicality of developing representations that are at once |
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61 tailored to specific tasks, yet are able to borrow statistical strength |
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62 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the |
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63 feature representation can lead to higher-level (more abstract, more |
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64 general) features that are more robust to unanticipated sources of |
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65 variance extant in real data. |
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66 |
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67 Whereas a deep architecture can in principle be more powerful than a |
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68 shallow one in terms of representation, depth appears to render the |
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69 training problem more difficult in terms of optimization and local minima. |
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70 It is also only recently that successful algorithms were proposed to |
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71 overcome some of these difficulties. All are based on unsupervised |
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72 learning, often in an greedy layer-wise ``unsupervised pre-training'' |
| 469 | 73 stage~\citep{Bengio-2009}. One of these layer initialization techniques, |
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74 applied here, is the Denoising |
| 469 | 75 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which |
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76 performed similarly or better than previously proposed Restricted Boltzmann |
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77 Machines in terms of unsupervised extraction of a hierarchy of features |
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78 useful for classification. The principle is that each layer starting from |
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79 the bottom is trained to encode its input (the output of the previous |
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80 layer) and to reconstruct it from a corrupted version of it. After this |
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81 unsupervised initialization, the stack of denoising auto-encoders can be |
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82 converted into a deep supervised feedforward neural network and fine-tuned by |
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83 stochastic gradient descent. |
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84 |
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85 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles |
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86 of semi-supervised and multi-task learning: the learner can exploit examples |
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87 that are unlabeled and/or come from a distribution different from the target |
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88 distribution, e.g., from other classes that those of interest. Whereas |
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89 it has already been shown that deep learners can clearly take advantage of |
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90 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small} |
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91 and multi-task learning, not much has been done yet to explore the impact |
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92 of {\em out-of-distribution} examples and of the multi-task setting |
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93 (but see~\citep{CollobertR2008}). In particular the {\em relative |
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94 advantage} of deep learning for this settings has not been evaluated. |
| 512 | 95 The hypothesis explored here is that a deep hierarchy of features |
| 96 may be better able to provide sharing of statistical strength | |
| 97 between different regions in input space or different tasks, | |
| 98 as discussed in the conclusion. | |
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99 |
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100 % TODO: why we care to evaluate this relative advantage |
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101 |
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102 In this paper we ask the following questions: |
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103 |
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104 %\begin{enumerate} |
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105 $\bullet$ %\item |
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106 Do the good results previously obtained with deep architectures on the |
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107 MNIST digit images generalize to the setting of a much larger and richer (but similar) |
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108 dataset, the NIST special database 19, with 62 classes and around 800k examples? |
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109 |
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110 $\bullet$ %\item |
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111 To what extent does the perturbation of input images (e.g. adding |
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112 noise, affine transformations, background images) make the resulting |
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113 classifiers better not only on similarly perturbed images but also on |
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114 the {\em original clean examples}? |
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115 |
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116 $\bullet$ %\item |
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117 Do deep architectures {\em benefit more from such out-of-distribution} |
| 469 | 118 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? |
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119 |
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120 $\bullet$ %\item |
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121 Similarly, does the feature learning step in deep learning algorithms benefit more |
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122 training with similar but different classes (i.e. a multi-task learning scenario) than |
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123 a corresponding shallow and purely supervised architecture? |
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124 %\end{enumerate} |
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125 |
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126 Our experimental results provide positive evidence towards all of these questions. |
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127 |
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128 \vspace*{-1mm} |
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129 \section{Perturbation and Transformation of Character Images} |
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130 \vspace*{-1mm} |
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131 |
| 467 | 132 This section describes the different transformations we used to stochastically |
| 133 transform source images in order to obtain data. More details can | |
| 469 | 134 be found in this technical report~\citep{ift6266-tr-anonymous}. |
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135 The code for these transformations (mostly python) is available at |
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136 {\tt http://anonymous.url.net}. All the modules in the pipeline share |
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137 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the |
| 467 | 138 amount of deformation or noise introduced. |
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139 |
| 467 | 140 There are two main parts in the pipeline. The first one, |
| 141 from slant to pinch below, performs transformations. The second | |
| 142 part, from blur to contrast, adds different kinds of noise. | |
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143 |
| 523 | 144 \begin{figure}[ht] |
| 145 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}} | |
| 506 | 146 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE |
| 501 | 147 \caption{Illustration of each transformation applied alone to the same image |
| 148 of an upper-case h (top left). First row (from left to right) : original image, slant, | |
| 149 thickness, affine transformation (translation, rotation, shear), | |
| 150 local elastic deformation; second row (from left to right) : | |
| 151 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to right) : | |
| 152 background image, salt and pepper noise, spatially Gaussian noise, scratches, | |
| 153 grey level and contrast changes.} | |
| 154 \label{fig:transfo} | |
| 155 \end{figure} | |
| 156 | |
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157 {\large\bf Transformations} |
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158 |
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159 \vspace*{2mm} |
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160 |
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161 {\bf Slant.} |
| 467 | 162 We mimic slant by shifting each row of the image |
| 495 | 163 proportionally to its height: $shift = round(slant \times height)$. |
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164 The $slant$ coefficient can be negative or positive with equal probability |
| 467 | 165 and its value is randomly sampled according to the complexity level: |
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166 $slant \sim U[0,complexity]$, so the |
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167 maximum displacement for the lowest or highest pixel line is of |
| 523 | 168 $round(complexity \times 32)$. |
| 169 \vspace*{0mm} | |
| 170 | |
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171 {\bf Thickness.} |
| 495 | 172 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82} |
| 467 | 173 are applied. The neighborhood of each pixel is multiplied |
| 174 element-wise with a {\em structuring element} matrix. | |
| 175 The pixel value is replaced by the maximum or the minimum of the resulting | |
| 176 matrix, respectively for dilation or erosion. Ten different structural elements with | |
| 177 increasing dimensions (largest is $5\times5$) were used. For each image, | |
| 178 randomly sample the operator type (dilation or erosion) with equal probability and one structural | |
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179 element from a subset of the $n$ smallest structuring elements where $n$ is |
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180 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$ |
| 467 | 181 for erosion. A neutral element is always present in the set, and if it is |
| 182 chosen no transformation is applied. Erosion allows only the six | |
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183 smallest structural elements because when the character is too thin it may |
| 523 | 184 be completely erased. |
| 185 \vspace*{0mm} | |
| 186 | |
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187 {\bf Affine Transformations.} |
| 467 | 188 A $2 \times 3$ affine transform matrix (with |
| 189 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level. | |
| 190 Each pixel $(x,y)$ of the output image takes the value of the pixel | |
| 191 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This | |
| 192 produces scaling, translation, rotation and shearing. | |
| 193 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to | |
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194 forbid important rotations (not to confuse classes) but to give good |
| 467 | 195 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times |
| 196 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3 | |
| 197 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times | |
| 523 | 198 complexity]$. |
| 199 \vspace*{0mm} | |
| 200 | |
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201 {\bf Local Elastic Deformations.} |
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202 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short}, |
| 467 | 203 which provides more details. |
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204 Two ``displacements'' fields are generated and applied, for horizontal |
| 467 | 205 and vertical displacements of pixels. |
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206 To generate a pixel in either field, first a value between -1 and 1 is |
| 467 | 207 chosen from a uniform distribution. Then all the pixels, in both fields, are |
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208 multiplied by a constant $\alpha$ which controls the intensity of the |
| 467 | 209 displacements (larger $\alpha$ translates into larger wiggles). |
| 210 Each field is convoluted with a Gaussian 2D kernel of | |
| 211 standard deviation $\sigma$. Visually, this results in a blur. | |
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212 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times |
| 523 | 213 \sqrt[3]{complexity}$. |
| 214 \vspace*{0mm} | |
| 215 | |
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216 {\bf Pinch.} |
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217 This is a GIMP filter called ``Whirl and |
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218 pinch'', but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic |
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219 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual). |
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220 For a square input image, this is akin to drawing a circle of |
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221 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to |
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222 that disk (region inside circle) will have its value recalculated by taking |
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223 the value of another ``source'' pixel in the original image. The position of |
| 495 | 224 that source pixel is found on the line that goes through $C$ and $P$, but |
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225 at some other distance $d_2$. Define $d_1$ to be the distance between $P$ |
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226 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times |
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227 d_1$, where $pinch$ is a parameter to the filter. |
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228 The actual value is given by bilinear interpolation considering the pixels |
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229 around the (non-integer) source position thus found. |
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230 Here $pinch \sim U[-complexity, 0.7 \times complexity]$. |
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231 |
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232 \vspace*{1mm} |
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233 |
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234 {\large\bf Injecting Noise} |
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235 |
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236 \vspace*{1mm} |
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237 |
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238 {\bf Motion Blur.} |
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239 This is a ``linear motion blur'' in GIMP |
| 467 | 240 terminology, with two parameters, $length$ and $angle$. The value of |
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241 a pixel in the final image is approximately the mean value of the $length$ first pixels |
| 467 | 242 found by moving in the $angle$ direction. |
| 523 | 243 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$. |
| 244 \vspace*{0mm} | |
| 245 | |
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246 {\bf Occlusion.} |
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247 Selects a random rectangle from an {\em occluder} character |
| 467 | 248 images and places it over the original {\em occluded} character |
| 249 image. Pixels are combined by taking the max(occluder,occluded), | |
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250 closer to black. The rectangle corners |
| 467 | 251 are sampled so that larger complexity gives larger rectangles. |
| 252 The destination position in the occluded image are also sampled | |
| 469 | 253 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}). |
| 523 | 254 This filter has a probability of 60\% of not being applied. |
| 255 \vspace*{0mm} | |
| 256 | |
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257 {\bf Pixel Permutation.} |
| 467 | 258 This filter permutes neighbouring pixels. It selects first |
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259 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then |
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260 sequentially exchanged with one other pixel in its $V4$ neighbourhood. The number |
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261 of exchanges to the left, right, top, bottom is equal or does not differ |
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262 from more than 1 if the number of selected pixels is not a multiple of 4. |
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263 % TODO: The previous sentence is hard to parse |
| 523 | 264 This filter has a probability of 80\% of not being applied. |
| 265 \vspace*{0mm} | |
| 266 | |
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267 {\bf Gaussian Noise.} |
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268 This filter simply adds, to each pixel of the image independently, a |
| 467 | 269 noise $\sim Normal(0(\frac{complexity}{10})^2)$. |
| 523 | 270 It has a probability of 70\% of not being applied. |
| 271 \vspace*{0mm} | |
| 272 | |
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273 {\bf Background Images.} |
| 469 | 274 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random |
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275 background behind the letter. The background is chosen by first selecting, |
| 495 | 276 at random, an image from a set of images. Then a 32$\times$32 sub-region |
| 467 | 277 of that image is chosen as the background image (by sampling position |
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278 uniformly while making sure not to cross image borders). |
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279 To combine the original letter image and the background image, contrast |
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280 adjustments are made. We first get the maximal values (i.e. maximal |
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281 intensity) for both the original image and the background image, $maximage$ |
| 467 | 282 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$. |
| 283 Each background pixel value is multiplied by $\frac{max(maximage - | |
| 284 contrast, 0)}{maxbg}$ (higher contrast yield darker | |
| 523 | 285 background). The output image pixels are max(background,original). |
| 286 \vspace*{0mm} | |
| 287 | |
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288 {\bf Salt and Pepper Noise.} |
| 467 | 289 This filter adds noise $\sim U[0,1]$ to random subsets of pixels. |
| 290 The number of selected pixels is $0.2 \times complexity$. | |
| 523 | 291 This filter has a probability of not being applied at all of 75\%. |
| 292 \vspace*{0mm} | |
| 293 | |
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294 {\bf Spatially Gaussian Noise.} |
| 467 | 295 Different regions of the image are spatially smoothed. |
| 296 The image is convolved with a symmetric Gaussian kernel of | |
| 495 | 297 size and variance chosen uniformly in the ranges $[12,12 + 20 \times |
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298 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized |
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299 between $0$ and $1$. We also create a symmetric averaging window, of the |
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300 kernel size, with maximum value at the center. For each image we sample |
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301 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be |
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302 averaging centers between the original image and the filtered one. We |
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303 initialize to zero a mask matrix of the image size. For each selected pixel |
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304 we add to the mask the averaging window centered to it. The final image is |
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305 computed from the following element-wise operation: $\frac{image + filtered |
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306 image \times mask}{mask+1}$. |
| 523 | 307 This filter has a probability of not being applied at all of 75\%. |
| 308 \vspace*{0mm} | |
| 309 | |
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310 {\bf Scratches.} |
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311 The scratches module places line-like white patches on the image. The |
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312 lines are heavily transformed images of the digit ``1'' (one), chosen |
| 467 | 313 at random among five thousands such 1 images. The 1 image is |
| 314 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times | |
| 495 | 315 complexity)^2$, using bi-cubic interpolation, |
| 316 Two passes of a grey-scale morphological erosion filter | |
| 467 | 317 are applied, reducing the width of the line |
| 318 by an amount controlled by $complexity$. | |
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319 This filter is only applied only 15\% of the time. When it is applied, 50\% |
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320 of the time, only one patch image is generated and applied. In 30\% of |
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321 cases, two patches are generated, and otherwise three patches are |
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322 generated. The patch is applied by taking the maximal value on any given |
| 523 | 323 patch or the original image, for each of the 32x32 pixel locations. |
| 324 \vspace*{0mm} | |
| 325 | |
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326 {\bf Grey Level and Contrast Changes.} |
| 495 | 327 This filter changes the contrast and may invert the image polarity (white |
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328 on black to black on white). The contrast $C$ is defined here as the |
| 467 | 329 difference between the maximum and the minimum pixel value of the image. |
| 495 | 330 Contrast $\sim U[1-0.85 \times complexity,1]$ (so contrast $\geq 0.15$). |
| 467 | 331 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The |
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332 polarity is inverted with $0.5$ probability. |
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333 |
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334 \iffalse |
| 523 | 335 \begin{figure}[ht] |
| 336 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}}\\ | |
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337 \caption{Illustration of the pipeline of stochastic |
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338 transformations applied to the image of a lower-case \emph{t} |
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339 (the upper left image). Each image in the pipeline (going from |
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340 left to right, first top line, then bottom line) shows the result |
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341 of applying one of the modules in the pipeline. The last image |
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342 (bottom right) is used as training example.} |
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343 \label{fig:pipeline} |
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344 \end{figure} |
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345 \fi |
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346 |
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347 |
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348 \vspace*{-1mm} |
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349 \section{Experimental Setup} |
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350 \vspace*{-1mm} |
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351 |
| 472 | 352 Whereas much previous work on deep learning algorithms had been performed on |
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353 the MNIST digits classification task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009}, |
| 472 | 354 with 60~000 examples, and variants involving 10~000 |
| 501 | 355 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want |
| 472 | 356 to focus here on the case of much larger training sets, from 10 times to |
| 357 to 1000 times larger. The larger datasets are obtained by first sampling from | |
|
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358 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas}, |
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359 and {\bf OCR data} (scanned machine printed characters). Once a character |
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360 is sampled from one of these sources (chosen randomly), a pipeline of |
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361 the above transformations and/or noise processes is applied to the |
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362 image. |
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363 |
|
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364 We compare the best MLP (according to validation set error) that we found against |
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365 the best SDA (again according to validation set error), along with a precise estimate |
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366 of human performance obtained via Amazon's Mechanical Turk (AMT) |
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367 service\footnote{http://mturk.com}. |
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368 AMT users are paid small amounts |
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369 of money to perform tasks for which human intelligence is required. |
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370 Mechanical Turk has been used extensively in natural language processing and vision. |
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371 %processing \citep{SnowEtAl2008} and vision |
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372 %\citep{SorokinAndForsyth2008,whitehill09}. |
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373 AMT users where presented |
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374 with 10 character images and asked to type 10 corresponding ASCII |
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375 characters. They were forced to make a hard choice among the |
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376 62 or 10 character classes (all classes or digits only). |
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377 Three users classified each image, allowing |
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378 to estimate inter-human variability. |
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379 |
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380 \vspace*{-1mm} |
| 472 | 381 \subsection{Data Sources} |
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382 \vspace*{-1mm} |
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383 |
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384 %\begin{itemize} |
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385 %\item |
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386 {\bf NIST.} |
| 501 | 387 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995}, |
| 472 | 388 widely used for training and testing character |
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389 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}. |
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390 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications, |
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391 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes |
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392 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity. |
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393 The fourth partition, $hsf_4$, experimentally recognized to be the most difficult one, is the one recommended |
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394 by NIST as a testing set and is used in our work as well as some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005} |
| 472 | 395 for that purpose. We randomly split the remainder into a training set and a validation set for |
|
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396 model selection. The sizes of these data sets are: 651668 for training, 80000 for validation, |
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397 and 82587 for testing. |
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398 The performances reported by previous work on that dataset mostly use only the digits. |
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399 Here we use all the classes both in the training and testing phase. This is especially |
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400 useful to estimate the effect of a multi-task setting. |
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401 Note that the distribution of the classes in the NIST training and test sets differs |
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402 substantially, with relatively many more digits in the test set, and more uniform distribution |
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403 of letters in the test set, compared to the training set (in the latter, the letters are distributed |
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404 more like the natural distribution of letters in text). |
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405 |
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406 %\item |
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407 {\bf Fonts.} |
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408 In order to have a good variety of sources we downloaded an important number of free fonts from: |
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409 {\tt http://cg.scs.carleton.ca/~luc/freefonts.html} |
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410 % TODO: pointless to anonymize, it's not pointing to our work |
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411 Including operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from. |
| 495 | 412 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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413 directly as input to our models. |
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414 |
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415 %\item |
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416 {\bf Captchas.} |
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417 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for |
| 472 | 418 generating characters of the same format as the NIST dataset. This software is based on |
| 495 | 419 a random character class generator and various kinds of transformations similar to those described in the previous sections. |
| 472 | 420 In order to increase the variability of the data generated, many different fonts are used for generating the characters. |
| 495 | 421 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity |
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422 depending on the value of the complexity parameter provided by the user of the data source. |
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423 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class? |
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424 |
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425 %\item |
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426 {\bf OCR data.} |
| 472 | 427 A large set (2 million) of scanned, OCRed and manually verified machine-printed |
| 428 characters (from various documents and books) where included as an | |
| 429 additional source. This set is part of a larger corpus being collected by the Image Understanding | |
| 430 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern | |
| 495 | 431 ({\tt http://www.iupr.com}), and which will be publicly released. |
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432 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this |
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433 %\end{itemize} |
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434 |
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435 \vspace*{-1mm} |
| 472 | 436 \subsection{Data Sets} |
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437 \vspace*{-1mm} |
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438 |
| 472 | 439 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label |
| 440 from one of the 62 character classes. | |
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441 %\begin{itemize} |
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442 |
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443 %\item |
| 501 | 444 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. |
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445 |
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446 %\item |
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447 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources |
| 472 | 448 and sending them through the above transformation pipeline. |
| 495 | 449 For each new example to generate, a source is selected with probability $10\%$ from the fonts, |
| 472 | 450 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the |
| 451 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$. | |
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452 |
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453 %\item |
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454 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion) |
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455 except that we only apply |
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456 transformations from slant to pinch. Therefore, the character is |
| 495 | 457 transformed but no additional noise is added to the image, giving images |
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458 closer to the NIST dataset. |
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459 %\end{itemize} |
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460 |
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461 \vspace*{-1mm} |
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462 \subsection{Models and their Hyperparameters} |
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463 \vspace*{-1mm} |
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464 |
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465 The experiments are performed with Multi-Layer Perceptrons (MLP) with a single |
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466 hidden layer and with Stacked Denoising Auto-Encoders (SDA). |
| 472 | 467 All hyper-parameters are selected based on performance on the NISTP validation set. |
| 468 | |
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469 {\bf Multi-Layer Perceptrons (MLP).} |
| 472 | 470 Whereas previous work had compared deep architectures to both shallow MLPs and |
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471 SVMs, we only compared to MLPs here because of the very large datasets used |
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472 (making the use of SVMs computationally inconvenient because of their quadratic |
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473 scaling behavior). |
| 472 | 474 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized |
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475 exponentials) on the output layer for estimating $P(class | image)$. |
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476 The number of hidden units is taken in $\{300,500,800,1000,1500\}$. |
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477 The optimization procedure is as follows: training |
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478 examples are presented in minibatches of size 20, a constant learning |
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479 rate is chosen in $\{10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$ |
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480 through preliminary experiments (measuring performance on a validation set), |
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481 and $0.1$ was then selected. |
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482 |
| 523 | 483 \begin{figure}[ht] |
| 484 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}} | |
|
521
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485 \caption{Illustration of the computations and training criterion for the denoising |
| 523 | 486 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of |
| 487 the layer (i.e. raw input or output of previous layer) | |
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488 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$. |
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489 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which |
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490 is compared to the uncorrupted input $x$ through the loss function |
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491 $L_H(x,z)$, whose expected value is approximately minimized during training |
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492 by tuning $\theta$ and $\theta'$.} |
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493 \label{fig:da} |
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494 \end{figure} |
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495 |
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496 {\bf Stacked Denoising Auto-Encoders (SDA).} |
| 472 | 497 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs) |
| 498 can be used to initialize the weights of each layer of a deep MLP (with many hidden | |
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499 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006}, |
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500 apparently setting parameters in the |
| 472 | 501 basin of attraction of supervised gradient descent yielding better |
| 502 generalization~\citep{Erhan+al-2010}. It is hypothesized that the | |
| 503 advantage brought by this procedure stems from a better prior, | |
| 504 on the one hand taking advantage of the link between the input | |
| 505 distribution $P(x)$ and the conditional distribution of interest | |
| 506 $P(y|x)$ (like in semi-supervised learning), and on the other hand | |
| 507 taking advantage of the expressive power and bias implicit in the | |
| 508 deep architecture (whereby complex concepts are expressed as | |
| 509 compositions of simpler ones through a deep hierarchy). | |
| 510 Here we chose to use the Denoising | |
| 511 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for | |
| 512 these deep hierarchies of features, as it is very simple to train and | |
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513 teach (see Figure~\ref{fig:da}, as well as |
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514 tutorial and code there: {\tt http://deeplearning.net/tutorial}), |
| 472 | 515 provides immediate and efficient inference, and yielded results |
| 516 comparable or better than RBMs in series of experiments | |
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517 \citep{VincentPLarochelleH2008}. During training, a Denoising |
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518 Auto-Encoder is presented with a stochastically corrupted version |
| 472 | 519 of the input and trained to reconstruct the uncorrupted input, |
| 520 forcing the hidden units to represent the leading regularities in | |
| 521 the data. Once it is trained, its hidden units activations can | |
| 522 be used as inputs for training a second one, etc. | |
| 523 After this unsupervised pre-training stage, the parameters | |
| 524 are used to initialize a deep MLP, which is fine-tuned by | |
| 525 the same standard procedure used to train them (see previous section). | |
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526 The SDA hyper-parameters are the same as for the MLP, with the addition of the |
| 472 | 527 amount of corruption noise (we used the masking noise process, whereby a |
| 528 fixed proportion of the input values, randomly selected, are zeroed), and a | |
| 529 separate learning rate for the unsupervised pre-training stage (selected | |
| 530 from the same above set). The fraction of inputs corrupted was selected | |
| 531 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number | |
| 532 of hidden layers but it was fixed to 3 based on previous work with | |
| 533 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}. | |
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534 |
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535 \vspace*{-1mm} |
| 523 | 536 |
| 537 \begin{figure}[ht] | |
| 538 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}} | |
| 539 \caption{Error bars indicate a 95\% confidence interval. 0 indicates training | |
| 540 on NIST, 1 on NISTP, and 2 on P07. Left: overall results | |
| 541 of all models, on 3 different test sets corresponding to the three | |
| 542 datasets. | |
| 543 Right: error rates on NIST test digits only, along with the previous results from | |
| 544 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005} | |
| 545 respectively based on ART, nearest neighbors, MLPs, and SVMs.} | |
| 546 | |
| 547 \label{fig:error-rates-charts} | |
| 548 \vspace*{-1mm} | |
| 549 \end{figure} | |
| 550 | |
| 551 | |
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552 \section{Experimental Results} |
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553 |
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554 %\vspace*{-1mm} |
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555 %\subsection{SDA vs MLP vs Humans} |
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556 %\vspace*{-1mm} |
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557 |
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558 Figure~\ref{fig:error-rates-charts} summarizes the results obtained, |
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559 comparing Humans, three MLPs (MLP0, MLP1, MLP2) and three SDAs (SDA0, SDA1, |
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560 SDA2), along with the previous results on the digits NIST special database |
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561 19 test set from the literature respectively based on ARTMAP neural |
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562 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search |
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516
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563 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs |
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564 ~\citep{Milgram+al-2005}. More detailed and complete numerical results |
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565 (figures and tables, including standard errors on the error rates) can be |
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566 found in Appendix I of the supplementary material. The 3 kinds of model differ in the |
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567 training sets used: NIST only (MLP0,SDA0), NISTP (MLP1, SDA1), or P07 |
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568 (MLP2, SDA2). The deep learner not only outperformed the shallow ones and |
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569 previously published performance (in a statistically and qualitatively |
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570 significant way) but reaches human performance on both the 62-class task |
| 523 | 571 and the 10-class (digits) task. |
| 572 | |
| 573 \begin{figure}[ht] | |
| 574 \vspace*{-2mm} | |
| 575 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}} | |
| 576 \caption{Relative improvement in error rate due to self-taught learning. | |
| 577 Left: Improvement (or loss, when negative) | |
| 578 induced by out-of-distribution examples (perturbed data). | |
| 579 Right: Improvement (or loss, when negative) induced by multi-task | |
| 580 learning (training on all classes and testing only on either digits, | |
| 581 upper case, or lower-case). The deep learner (SDA) benefits more from | |
| 582 both self-taught learning scenarios, compared to the shallow MLP.} | |
| 583 \label{fig:improvements-charts} | |
| 584 \vspace*{-2mm} | |
| 585 \end{figure} | |
| 586 | |
| 587 In addition, as shown in the left of | |
| 588 Figure~\ref{fig:improvements-charts}, the relative improvement in error | |
|
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589 rate brought by self-taught learning is greater for the SDA, and these |
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590 differences with the MLP are statistically and qualitatively |
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591 significant. |
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592 The left side of the figure shows the improvement to the clean |
|
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593 NIST test set error brought by the use of out-of-distribution examples |
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594 (i.e. the perturbed examples examples from NISTP or P07). |
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595 Relative change is measured by taking |
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596 (original model's error / perturbed-data model's error - 1). |
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597 The right side of |
| 523 | 598 Figure~\ref{fig:improvements-charts} shows the relative improvement |
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599 brought by the use of a multi-task setting, in which the same model is |
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600 trained for more classes than the target classes of interest (i.e. training |
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601 with all 62 classes when the target classes are respectively the digits, |
|
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602 lower-case, or upper-case characters). Again, whereas the gain from the |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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491
diff
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|
603 multi-task setting is marginal or negative for the MLP, it is substantial |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
604 for the SDA. Note that for these multi-task experiment, only the original |
|
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difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
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|
605 NIST dataset is used. For example, the MLP-digits bar shows the relative |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
606 improvement in MLP error rate on the NIST digits test set (1 - single-task |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
607 model's error / multi-task model's error). The single-task model is |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
608 trained with only 10 outputs (one per digit), seeing only digit examples, |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
609 whereas the multi-task model is trained with 62 outputs, with all 62 |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
610 character classes as examples. Hence the hidden units are shared across |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
611 all tasks. For the multi-task model, the digit error rate is measured by |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
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|
612 comparing the correct digit class with the output class associated with the |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
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|
613 maximum conditional probability among only the digit classes outputs. The |
|
a194ce5a4249
difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
614 setting is similar for the other two target classes (lower case characters |
|
a194ce5a4249
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
491
diff
changeset
|
615 and upper case characters). |
|
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff
changeset
|
616 |
|
485
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|
617 %\vspace*{-1mm} |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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|
618 %\subsection{Perturbed Training Data More Helpful for SDA} |
|
485
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
484
diff
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|
619 %\vspace*{-1mm} |
|
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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|
620 |
|
485
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parents:
484
diff
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|
621 %\vspace*{-1mm} |
|
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diff
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|
622 %\subsection{Multi-Task Learning Effects} |
|
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parents:
484
diff
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|
623 %\vspace*{-1mm} |
|
464
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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|
624 |
|
485
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parents:
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diff
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|
625 \iffalse |
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff
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|
626 As previously seen, the SDA is better able to benefit from the |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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|
627 transformations applied to the data than the MLP. In this experiment we |
|
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parents:
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|
628 define three tasks: recognizing digits (knowing that the input is a digit), |
|
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parents:
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|
629 recognizing upper case characters (knowing that the input is one), and |
|
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parents:
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|
630 recognizing lower case characters (knowing that the input is one). We |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff
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|
631 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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|
632 evaluate whether training with the other tasks can help or hurt, and |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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633 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:
diff
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|
634 out if deep learning can benefit more (or less) from multiple related tasks |
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parents:
diff
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|
635 (i.e. the multi-task setting) compared to a corresponding purely supervised |
|
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parents:
diff
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|
636 shallow learner. |
|
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parents:
diff
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|
637 |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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|
638 We use a single hidden layer MLP with 1000 hidden units, and a SDA |
|
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parents:
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639 with 3 hidden layers (1000 hidden units per layer), pre-trained and |
|
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parents:
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640 fine-tuned on NIST. |
|
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parents:
diff
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|
641 |
|
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|
642 Our results show that the MLP benefits marginally from the multi-task setting |
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parents:
diff
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|
643 in the case of digits (5\% relative improvement) but is actually hurt in the case |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff
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|
644 of characters (respectively 3\% and 4\% worse for lower and upper class characters). |
| 495 | 645 On the other hand the SDA benefited from the multi-task setting, with relative |
|
464
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parents:
diff
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|
646 error rate improvements of 27\%, 15\% and 13\% respectively for digits, |
|
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff
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|
647 lower and upper case characters, as shown in Table~\ref{tab:multi-task}. |
|
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484
diff
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|
648 \fi |
|
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parents:
diff
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|
649 |
| 475 | 650 |
|
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651 \vspace*{-1mm} |
| 529 | 652 \section{Conclusions and Discussion} |
|
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653 \vspace*{-1mm} |
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|
654 |
|
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655 We have found that the self-taught learning framework is more beneficial |
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656 to a deep learner than to a traditional shallow and purely |
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657 supervised learner. More precisely, |
|
520
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658 the answers are positive for all the questions asked in the introduction. |
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659 %\begin{itemize} |
| 487 | 660 |
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661 $\bullet$ %\item |
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662 Do the good results previously obtained with deep architectures on the |
| 472 | 663 MNIST digits generalize to the setting of a much larger and richer (but similar) |
| 664 dataset, the NIST special database 19, with 62 classes and around 800k examples? | |
|
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665 Yes, the SDA {\bf systematically outperformed the MLP and all the previously |
| 529 | 666 published results on this dataset} (the ones that we are aware of), {\bf in fact reaching human-level |
| 667 performance} at around 17\% error on the 62-class task and 1.4\% on the digits. | |
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668 |
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669 $\bullet$ %\item |
| 529 | 670 To what extent do self-taught learning scenarios help deep learners, |
| 671 and do they help them more than shallow supervised ones? | |
| 672 We found that distorted training examples not only made the resulting | |
| 673 classifier better on similarly perturbed images but also on | |
| 674 the {\em original clean examples}, and more importantly and more novel, | |
| 675 that deep architectures benefit more from such {\em out-of-distribution} | |
| 676 examples. MLPs were helped by perturbed training examples when tested on perturbed input | |
|
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677 images (65\% relative improvement on NISTP) |
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678 but only marginally helped (5\% relative improvement on all classes) |
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679 or even hurt (10\% relative loss on digits) |
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680 with respect to clean examples . On the other hand, the deep SDAs |
| 472 | 681 were very significantly boosted by these out-of-distribution examples. |
| 529 | 682 Similarly, whereas the improvement due to the multi-task setting was marginal or |
|
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683 negative for the MLP (from +5.6\% to -3.6\% relative change), |
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684 it was very significant for the SDA (from +13\% to +27\% relative change). |
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685 %\end{itemize} |
| 472 | 686 |
|
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687 In the original self-taught learning framework~\citep{RainaR2007}, the |
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688 out-of-sample examples were used as a source of unsupervised data, and |
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689 experiments showed its positive effects in a \emph{limited labeled data} |
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690 scenario. However, many of the results by \citet{RainaR2007} (who used a |
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691 shallow, sparse coding approach) suggest that the relative gain of self-taught |
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692 learning diminishes as the number of labeled examples increases, (essentially, |
| 529 | 693 a ``diminishing returns'' scenario occurs). We note instead that, for deep |
|
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694 architectures, our experiments show that such a positive effect is accomplished |
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695 even in a scenario with a \emph{very large number of labeled examples}. |
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696 |
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697 Why would deep learners benefit more from the self-taught learning framework? |
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698 The key idea is that the lower layers of the predictor compute a hierarchy |
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699 of features that can be shared across tasks or across variants of the |
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700 input distribution. Intermediate features that can be used in different |
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701 contexts can be estimated in a way that allows to share statistical |
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702 strength. Features extracted through many levels are more likely to |
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703 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest), |
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704 increasing the likelihood that they would be useful for a larger array |
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705 of tasks and input conditions. |
|
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706 Therefore, we hypothesize that both depth and unsupervised |
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707 pre-training play a part in explaining the advantages observed here, and future |
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|
708 experiments could attempt at teasing apart these factors. |
| 529 | 709 And why would deep learners benefit from the self-taught learning |
| 710 scenarios even when the number of labeled examples is very large? | |
| 711 We hypothesize that this is related to the hypotheses studied | |
| 712 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010} | |
| 713 it was found that online learning on a huge dataset did not make the | |
| 714 advantage of the deep learning bias vanish, a similar phenomenon | |
| 715 may be happening here. We hypothesize that unsupervised pre-training | |
| 716 of a deep hierarchy with self-taught learning initializes the | |
| 717 model in the basin of attraction of supervised gradient descent | |
| 718 that corresponds to better generalization. Furthermore, such good | |
| 719 basins of attraction are not discovered by pure supervised learning | |
| 720 (with or without self-taught settings), and more labeled examples | |
| 721 does not allow to go from the poorer basins of attraction discovered | |
| 722 by the purely supervised shallow models to the kind of better basins associated | |
| 723 with deep learning and self-taught learning. | |
|
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724 |
|
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725 A Flash demo of the recognizer (where both the MLP and the SDA can be compared) |
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726 can be executed on-line at {\tt http://deep.host22.com}. |
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727 |
|
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728 \newpage |
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729 { |
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730 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,aigaion-shorter,specials} |
| 469 | 731 %\bibliographystyle{plainnat} |
| 732 \bibliographystyle{unsrtnat} | |
|
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733 %\bibliographystyle{apalike} |
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734 } |
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735 |
|
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736 |
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737 \end{document} |