Mercurial > ift6266
annotate writeup/nips2010_submission.tex @ 486:877af97ee193
section resultats et appendice
| author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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| date | Mon, 31 May 2010 22:03:35 -0400 |
| parents | 6beaf3328521 |
| children | 21787ac4e5a0 |
| 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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3 |
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4 \usepackage{amsthm,amsmath,amssymb,bbold,bbm} |
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5 \usepackage{algorithm,algorithmic} |
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6 \usepackage[utf8]{inputenc} |
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7 \usepackage{graphicx,subfigure} |
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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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17 |
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18 \vspace*{-2mm} |
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19 \begin{abstract} |
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20 Recent theoretical and empirical work in statistical machine learning has |
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21 demonstrated the importance of learning algorithms for deep |
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22 architectures, i.e., function classes obtained by composing multiple |
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23 non-linear transformations. The self-taught learning (exploitng unlabeled |
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24 examples or examples from other distributions) has already been applied |
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25 to deep learners, but mostly to show the advantage of unlabeled |
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26 examples. Here we explore the advantage brought by {\em out-of-distribution |
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27 examples} and show that {\em deep learners benefit more from them than a |
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28 corresponding shallow learner}, in the area |
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29 of handwritten character recognition. In fact, we show that they reach |
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30 human-level performance on both handwritten digit classification and |
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31 62-class handwritten character recognition. For this purpose we |
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32 developed a powerful generator of stochastic variations and noise |
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33 processes character images, including not only affine transformations but |
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34 also slant, local elastic deformations, changes in thickness, background |
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35 images, color, contrast, occlusion, and various types of pixel and |
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36 spatially correlated noise. The out-of-distribution examples are |
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37 obtained by training with these highly distorted images or |
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38 by including object classes different from those in the target test set. |
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39 \end{abstract} |
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40 \vspace*{-2mm} |
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41 |
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42 \section{Introduction} |
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43 \vspace*{-1mm} |
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44 |
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45 Deep Learning has emerged as a promising new area of research in |
| 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 |
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56 higher layers~\cite{Goodfellow2009}. |
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57 Learning a hierarchy of features increases the |
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58 ease and practicality of developing representations that are at once |
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59 tailored to specific tasks, yet are able to borrow statistical strength |
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60 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the |
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61 feature representation can lead to higher-level (more abstract, more |
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62 general) features that are more robust to unanticipated sources of |
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63 variance extant in real data. |
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64 |
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65 Whereas a deep architecture can in principle be more powerful than a |
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66 shallow one in terms of representation, depth appears to render the |
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67 training problem more difficult in terms of optimization and local minima. |
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68 It is also only recently that successful algorithms were proposed to |
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69 overcome some of these difficulties. All are based on unsupervised |
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70 learning, often in an greedy layer-wise ``unsupervised pre-training'' |
| 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} |
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89 and multi-task learning, not much has been done yet to explore the impact |
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90 of {\em out-of-distribution} examples and of the multi-task setting |
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91 (but see~\citep{CollobertR2008-short}). In particular the {\em relative |
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92 advantage} of deep learning for this settings has not been evaluated. |
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93 |
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94 In this paper we ask the following questions: |
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95 |
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96 %\begin{enumerate} |
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97 $\bullet$ %\item |
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98 Do the good results previously obtained with deep architectures on the |
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99 MNIST digit images generalize to the setting of a much larger and richer (but similar) |
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100 dataset, the NIST special database 19, with 62 classes and around 800k examples? |
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101 |
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102 $\bullet$ %\item |
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103 To what extent does the perturbation of input images (e.g. adding |
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104 noise, affine transformations, background images) make the resulting |
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105 classifiers better not only on similarly perturbed images but also on |
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106 the {\em original clean examples}? |
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107 |
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108 $\bullet$ %\item |
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109 Do deep architectures {\em benefit more from such out-of-distribution} |
| 469 | 110 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? |
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111 |
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112 $\bullet$ %\item |
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113 Similarly, does the feature learning step in deep learning algorithms benefit more |
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114 training with similar but different classes (i.e. a multi-task learning scenario) than |
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115 a corresponding shallow and purely supervised architecture? |
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116 %\end{enumerate} |
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117 |
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118 The experimental results presented here provide positive evidence towards all of these questions. |
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119 |
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120 \vspace*{-1mm} |
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121 \section{Perturbation and Transformation of Character Images} |
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122 \vspace*{-1mm} |
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123 |
| 467 | 124 This section describes the different transformations we used to stochastically |
| 125 transform source images in order to obtain data. More details can | |
| 469 | 126 be found in this technical report~\citep{ift6266-tr-anonymous}. |
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127 The code for these transformations (mostly python) is available at |
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128 {\tt http://anonymous.url.net}. All the modules in the pipeline share |
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129 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the |
| 467 | 130 amount of deformation or noise introduced. |
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131 |
| 467 | 132 There are two main parts in the pipeline. The first one, |
| 133 from slant to pinch below, performs transformations. The second | |
| 134 part, from blur to contrast, adds different kinds of noise. | |
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135 |
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136 {\large\bf Transformations} |
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137 |
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138 \vspace*{2mm} |
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139 |
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140 {\bf Slant.} |
| 467 | 141 We mimic slant by shifting each row of the image |
| 142 proportionnaly to its height: $shift = round(slant \times height)$. | |
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143 The $slant$ coefficient can be negative or positive with equal probability |
| 467 | 144 and its value is randomly sampled according to the complexity level: |
| 145 e $slant \sim U[0,complexity]$, so the | |
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146 maximum displacement for the lowest or highest pixel line is of |
| 467 | 147 $round(complexity \times 32)$.\\ |
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148 {\bf Thickness.} |
| 469 | 149 Morpholigical operators of dilation and erosion~\citep{Haralick87,Serra82} |
| 467 | 150 are applied. The neighborhood of each pixel is multiplied |
| 151 element-wise with a {\em structuring element} matrix. | |
| 152 The pixel value is replaced by the maximum or the minimum of the resulting | |
| 153 matrix, respectively for dilation or erosion. Ten different structural elements with | |
| 154 increasing dimensions (largest is $5\times5$) were used. For each image, | |
| 155 randomly sample the operator type (dilation or erosion) with equal probability and one structural | |
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156 element from a subset of the $n$ smallest structuring elements where $n$ is |
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157 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$ |
| 467 | 158 for erosion. A neutral element is always present in the set, and if it is |
| 159 chosen no transformation is applied. Erosion allows only the six | |
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160 smallest structural elements because when the character is too thin it may |
| 467 | 161 be completely erased.\\ |
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162 {\bf Affine Transformations.} |
| 467 | 163 A $2 \times 3$ affine transform matrix (with |
| 164 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level. | |
| 165 Each pixel $(x,y)$ of the output image takes the value of the pixel | |
| 166 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This | |
| 167 produces scaling, translation, rotation and shearing. | |
| 168 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to | |
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169 forbid important rotations (not to confuse classes) but to give good |
| 467 | 170 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times |
| 171 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3 | |
| 172 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times | |
| 173 complexity]$.\\ | |
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174 {\bf Local Elastic Deformations.} |
| 469 | 175 This filter induces a "wiggly" effect in the image, following~\citet{SimardSP03}, |
| 467 | 176 which provides more details. |
| 177 Two "displacements" fields are generated and applied, for horizontal | |
| 178 and vertical displacements of pixels. | |
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179 To generate a pixel in either field, first a value between -1 and 1 is |
| 467 | 180 chosen from a uniform distribution. Then all the pixels, in both fields, are |
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181 multiplied by a constant $\alpha$ which controls the intensity of the |
| 467 | 182 displacements (larger $\alpha$ translates into larger wiggles). |
| 183 Each field is convoluted with a Gaussian 2D kernel of | |
| 184 standard deviation $\sigma$. Visually, this results in a blur. | |
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185 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times |
| 467 | 186 \sqrt[3]{complexity}$.\\ |
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187 {\bf Pinch.} |
| 467 | 188 This GIMP filter is named "Whirl and |
| 189 pinch", but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic | |
| 469 | 190 surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}. |
| 467 | 191 For a square input image, think of drawing a circle of |
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192 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to |
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193 that disk (region inside circle) will have its value recalculated by taking |
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194 the value of another "source" pixel in the original image. The position of |
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195 that source pixel is found on the line thats goes through $C$ and $P$, but |
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196 at some other distance $d_2$. Define $d_1$ to be the distance between $P$ |
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197 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times |
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198 d_1$, where $pinch$ is a parameter to the filter. |
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199 The actual value is given by bilinear interpolation considering the pixels |
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200 around the (non-integer) source position thus found. |
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201 Here $pinch \sim U[-complexity, 0.7 \times complexity]$. |
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202 |
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203 \vspace*{1mm} |
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204 |
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205 {\large\bf Injecting Noise} |
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206 |
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207 \vspace*{1mm} |
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208 |
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209 {\bf Motion Blur.} |
| 467 | 210 This GIMP filter is a ``linear motion blur'' in GIMP |
| 211 terminology, with two parameters, $length$ and $angle$. The value of | |
| 212 a pixel in the final image is the approximately mean value of the $length$ first pixels | |
| 213 found by moving in the $angle$ direction. | |
| 214 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.\\ | |
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215 {\bf Occlusion.} |
| 467 | 216 This filter selects a random rectangle from an {\em occluder} character |
| 217 images and places it over the original {\em occluded} character | |
| 218 image. Pixels are combined by taking the max(occluder,occluded), | |
| 219 closer to black. The corners of the occluder The rectangle corners | |
| 220 are sampled so that larger complexity gives larger rectangles. | |
| 221 The destination position in the occluded image are also sampled | |
| 469 | 222 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}). |
| 467 | 223 It has has a probability of not being applied at all of 60\%.\\ |
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224 {\bf Pixel Permutation.} |
| 467 | 225 This filter permutes neighbouring pixels. It selects first |
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226 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then |
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227 sequentially exchanged to one other pixel in its $V4$ neighbourhood. Number |
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228 of exchanges to the left, right, top, bottom are equal or does not differ |
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229 from more than 1 if the number of selected pixels is not a multiple of 4. |
| 467 | 230 It has has a probability of not being applied at all of 80\%.\\ |
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231 {\bf Gaussian Noise.} |
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232 This filter simply adds, to each pixel of the image independently, a |
| 467 | 233 noise $\sim Normal(0(\frac{complexity}{10})^2)$. |
| 234 It has has a probability of not being applied at all of 70\%.\\ | |
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235 {\bf Background Images.} |
| 469 | 236 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random |
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237 background behind the letter. The background is chosen by first selecting, |
| 467 | 238 at random, an image from a set of images. Then a 32$\times$32 subregion |
| 239 of that image is chosen as the background image (by sampling position | |
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240 uniformly while making sure not to cross image borders). |
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241 To combine the original letter image and the background image, contrast |
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242 adjustments are made. We first get the maximal values (i.e. maximal |
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243 intensity) for both the original image and the background image, $maximage$ |
| 467 | 244 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$. |
| 245 Each background pixel value is multiplied by $\frac{max(maximage - | |
| 246 contrast, 0)}{maxbg}$ (higher contrast yield darker | |
| 247 background). The output image pixels are max(background,original).\\ | |
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248 {\bf Salt and Pepper Noise.} |
| 467 | 249 This filter adds noise $\sim U[0,1]$ to random subsets of pixels. |
| 250 The number of selected pixels is $0.2 \times complexity$. | |
| 251 This filter has a probability of not being applied at all of 75\%.\\ | |
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252 {\bf Spatially Gaussian Noise.} |
| 467 | 253 Different regions of the image are spatially smoothed. |
| 254 The image is convolved with a symmetric Gaussian kernel of | |
| 255 size and variance choosen uniformly in the ranges $[12,12 + 20 \times | |
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256 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized |
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257 between $0$ and $1$. We also create a symmetric averaging window, of the |
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258 kernel size, with maximum value at the center. For each image we sample |
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259 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be |
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260 averaging centers between the original image and the filtered one. We |
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261 initialize to zero a mask matrix of the image size. For each selected pixel |
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262 we add to the mask the averaging window centered to it. The final image is |
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263 computed from the following element-wise operation: $\frac{image + filtered |
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264 image \times mask}{mask+1}$. |
| 467 | 265 This filter has a probability of not being applied at all of 75\%.\\ |
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266 {\bf Scratches.} |
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267 The scratches module places line-like white patches on the image. The |
| 467 | 268 lines are heavily transformed images of the digit "1" (one), chosen |
| 269 at random among five thousands such 1 images. The 1 image is | |
| 270 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times | |
| 271 complexity)^2$, using bicubic interpolation, | |
| 272 Two passes of a greyscale morphological erosion filter | |
| 273 are applied, reducing the width of the line | |
| 274 by an amount controlled by $complexity$. | |
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275 This filter is only applied only 15\% of the time. When it is applied, 50\% |
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276 of the time, only one patch image is generated and applied. In 30\% of |
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277 cases, two patches are generated, and otherwise three patches are |
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278 generated. The patch is applied by taking the maximal value on any given |
| 467 | 279 patch or the original image, for each of the 32x32 pixel locations.\\ |
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280 {\bf Color and Contrast Changes.} |
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281 This filter changes the constrast and may invert the image polarity (white |
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282 on black to black on white). The contrast $C$ is defined here as the |
| 467 | 283 difference between the maximum and the minimum pixel value of the image. |
| 284 Contrast $\sim U[1-0.85 \times complexity,1]$ (so constrast $\geq 0.15$). | |
| 285 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The | |
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286 polarity is inverted with $0.5$ probability. |
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287 |
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288 |
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289 \begin{figure}[h] |
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290 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\ |
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291 \caption{Illustration of the pipeline of stochastic |
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292 transformations applied to the image of a lower-case t |
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293 (the upper left image). Each image in the pipeline (going from |
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294 left to right, first top line, then bottom line) shows the result |
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295 of applying one of the modules in the pipeline. The last image |
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296 (bottom right) is used as training example.} |
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297 \label{fig:pipeline} |
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298 \end{figure} |
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299 |
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300 |
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301 \begin{figure}[h] |
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302 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\ |
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303 \caption{Illustration of each transformation applied alone to the same image |
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304 of an upper-case h (top left). First row (from left to rigth) : original image, slant, |
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305 thickness, affine transformation, local elastic deformation; second row (from left to rigth) : |
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306 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to rigth) : |
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307 background image, salt and pepper noise, spatially Gaussian noise, scratches, |
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308 color and contrast changes.} |
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309 \label{fig:transfo} |
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310 \end{figure} |
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311 |
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312 |
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313 \vspace*{-1mm} |
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314 \section{Experimental Setup} |
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315 \vspace*{-1mm} |
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316 |
| 472 | 317 Whereas much previous work on deep learning algorithms had been performed on |
| 318 the MNIST digits classification task~\citep{Hinton06,ranzato-07,Bengio-nips-2006,Salakhutdinov+Hinton-2009}, | |
| 319 with 60~000 examples, and variants involving 10~000 | |
| 320 examples~\cite{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want | |
| 321 to focus here on the case of much larger training sets, from 10 times to | |
| 322 to 1000 times larger. The larger datasets are obtained by first sampling from | |
| 323 a {\em data source} (NIST characters, scanned machine printed characters, characters | |
| 324 from fonts, or characters from captchas) and then optionally applying some of the | |
| 325 above transformations and/or noise processes. | |
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326 |
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327 \vspace*{-1mm} |
| 472 | 328 \subsection{Data Sources} |
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329 \vspace*{-1mm} |
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330 |
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331 %\begin{itemize} |
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332 %\item |
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333 {\bf NIST.} |
| 472 | 334 Our main source of characters is the NIST Special Database 19~\cite{Grother-1995}, |
| 335 widely used for training and testing character | |
| 336 recognition systems~\cite{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}. | |
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337 The dataset is composed with 8????? digits and characters (upper and lower cases), with hand checked classifications, |
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338 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes |
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339 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity. |
| 472 | 340 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one is recommended |
| 341 by NIST as testing set and is used in our work and some previous work~\cite{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005} | |
| 342 for that purpose. We randomly split the remainder into a training set and a validation set for | |
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343 model selection. The sizes of these data sets are: 651668 for training, 80000 for validation, |
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344 and 82587 for testing. |
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345 The performances reported by previous work on that dataset mostly use only the digits. |
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346 Here we use all the classes both in the training and testing phase. This is especially |
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347 useful to estimate the effect of a multi-task setting. |
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348 Note that the distribution of the classes in the NIST training and test sets differs |
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349 substantially, with relatively many more digits in the test set, and uniform distribution |
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350 of letters in the test set, not in the training set (more like the natural distribution |
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351 of letters in text). |
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352 |
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353 %\item |
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354 {\bf Fonts.} |
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355 In order to have a good variety of sources we downloaded an important number of free fonts from: {\tt http://anonymous.url.net} |
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356 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html} |
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357 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly. |
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358 The ttf file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image, |
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359 directly as input to our models. |
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360 |
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361 %\item |
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362 {\bf Captchas.} |
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363 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for |
| 472 | 364 generating characters of the same format as the NIST dataset. This software is based on |
| 365 a random character class generator and various kinds of tranformations similar to those described in the previous sections. | |
| 366 In order to increase the variability of the data generated, many different fonts are used for generating the characters. | |
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367 Transformations (slant, distorsions, rotation, translation) are applied to each randomly generated character with a complexity |
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368 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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369 allowed and can be controlled via an easy to use facade class. |
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370 |
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371 %\item |
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372 {\bf OCR data.} |
| 472 | 373 A large set (2 million) of scanned, OCRed and manually verified machine-printed |
| 374 characters (from various documents and books) where included as an | |
| 375 additional source. This set is part of a larger corpus being collected by the Image Understanding | |
| 376 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern | |
| 377 ({\tt http://www.iupr.com}), and which will be publically released. | |
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378 %\end{itemize} |
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379 |
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380 \vspace*{-1mm} |
| 472 | 381 \subsection{Data Sets} |
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382 \vspace*{-1mm} |
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383 |
| 472 | 384 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label |
| 385 from one of the 62 character classes. | |
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386 %\begin{itemize} |
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387 |
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388 %\item |
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389 {\bf NIST.} This is the raw NIST special database 19. |
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390 |
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391 %\item |
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392 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources |
| 472 | 393 and sending them through the above transformation pipeline. |
| 394 For each new exemple to generate, a source is selected with probability $10\%$ from the fonts, | |
| 395 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the | |
| 396 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$. | |
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397 |
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398 %\item |
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399 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion) |
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400 except that we only apply |
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401 transformations from slant to pinch. Therefore, the character is |
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402 transformed but no additionnal noise is added to the image, giving images |
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403 closer to the NIST dataset. |
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404 %\end{itemize} |
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405 |
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406 \vspace*{-1mm} |
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407 \subsection{Models and their Hyperparameters} |
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408 \vspace*{-1mm} |
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409 |
| 472 | 410 All hyper-parameters are selected based on performance on the NISTP validation set. |
| 411 | |
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412 {\bf Multi-Layer Perceptrons (MLP).} |
| 472 | 413 Whereas previous work had compared deep architectures to both shallow MLPs and |
| 414 SVMs, we only compared to MLPs here because of the very large datasets used. | |
| 415 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized | |
| 416 exponentials) on the output layer for estimating P(class | image). | |
| 417 The hyper-parameters are the following: number of hidden units, taken in | |
| 418 $\{300,500,800,1000,1500\}$. The optimization procedure is as follows. Training | |
| 419 examples are presented in minibatches of size 20. A constant learning | |
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420 rate is chosen in $10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$ |
| 472 | 421 through preliminary experiments, and 0.1 was selected. |
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422 |
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423 {\bf Stacked Denoising Auto-Encoders (SDAE).} |
| 472 | 424 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs) |
| 425 can be used to initialize the weights of each layer of a deep MLP (with many hidden | |
| 426 layers)~\citep{Hinton06,ranzato-07,Bengio-nips-2006} | |
| 427 enabling better generalization, apparently setting parameters in the | |
| 428 basin of attraction of supervised gradient descent yielding better | |
| 429 generalization~\citep{Erhan+al-2010}. It is hypothesized that the | |
| 430 advantage brought by this procedure stems from a better prior, | |
| 431 on the one hand taking advantage of the link between the input | |
| 432 distribution $P(x)$ and the conditional distribution of interest | |
| 433 $P(y|x)$ (like in semi-supervised learning), and on the other hand | |
| 434 taking advantage of the expressive power and bias implicit in the | |
| 435 deep architecture (whereby complex concepts are expressed as | |
| 436 compositions of simpler ones through a deep hierarchy). | |
| 437 Here we chose to use the Denoising | |
| 438 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for | |
| 439 these deep hierarchies of features, as it is very simple to train and | |
| 440 teach (see tutorial and code there: {\tt http://deeplearning.net/tutorial}), | |
| 441 provides immediate and efficient inference, and yielded results | |
| 442 comparable or better than RBMs in series of experiments | |
| 443 \citep{VincentPLarochelleH2008}. During training of a Denoising | |
| 444 Auto-Encoder, it is presented with a stochastically corrupted version | |
| 445 of the input and trained to reconstruct the uncorrupted input, | |
| 446 forcing the hidden units to represent the leading regularities in | |
| 447 the data. Once it is trained, its hidden units activations can | |
| 448 be used as inputs for training a second one, etc. | |
| 449 After this unsupervised pre-training stage, the parameters | |
| 450 are used to initialize a deep MLP, which is fine-tuned by | |
| 451 the same standard procedure used to train them (see previous section). | |
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452 The SDA hyper-parameters are the same as for the MLP, with the addition of the |
| 472 | 453 amount of corruption noise (we used the masking noise process, whereby a |
| 454 fixed proportion of the input values, randomly selected, are zeroed), and a | |
| 455 separate learning rate for the unsupervised pre-training stage (selected | |
| 456 from the same above set). The fraction of inputs corrupted was selected | |
| 457 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number | |
| 458 of hidden layers but it was fixed to 3 based on previous work with | |
| 459 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}. | |
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460 |
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461 \vspace*{-1mm} |
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462 \section{Experimental Results} |
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463 |
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464 %\vspace*{-1mm} |
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465 %\subsection{SDA vs MLP vs Humans} |
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466 %\vspace*{-1mm} |
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467 |
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468 We compare the best MLP (according to validation set error) that we found against |
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469 the best SDA (again according to validation set error), along with a precise estimate |
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470 of human performance obtained via Amazon's Mechanical Turk (AMT) |
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471 service\footnote{http://mturk.com}. |
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472 %AMT users are paid small amounts |
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473 %of money to perform tasks for which human intelligence is required. |
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474 %Mechanical Turk has been used extensively in natural language |
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475 %processing \citep{SnowEtAl2008} and vision |
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476 %\citep{SorokinAndForsyth2008,whitehill09}. |
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477 AMT users where presented |
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478 with 10 character images and asked to type 10 corresponding ascii |
|
484
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479 characters. They were forced to make a hard choice among the |
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480 62 or 10 character classes (all classes or digits only). |
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481 Three users classified each image, allowing |
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482 to estimate inter-human variability (shown as +/- in parenthesis below). |
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483 |
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484 Figure~\ref{fig:error-rates-charts} summarizes the results obtained, |
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485 comparing Humans, three MLPs (MLP0, MLP1, MLP2) and three SDAs (SDA0, SDA1, |
|
486
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486 SDA2), along with the previous results on the digits NIST special database |
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487 19 test set from the literature respectively based on ARTMAP neural |
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488 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search |
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489 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002}, and SVMs |
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490 ~\citep{Milgram+al-2005}. More detailed and complete numerical results |
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491 (figures and tables) can be found in the appendix. The 3 kinds of model |
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492 differ in the training sets used: NIST only (MLP0,SDA0), NISTP (MLP1, |
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493 SDA1), or P07 (MLP2, SDA2). The deep learner not only outperformed the |
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494 shallow ones and previously published performance but reaches human |
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495 performance on both the 62-class task and the 10-class (digits) task. In |
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496 addition, as shown in the left of Figure~\ref{fig:fig:improvements-charts}, |
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497 the relative improvement in error rate brought by self-taught learning is |
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498 greater for the SDA. The left side shows the improvement to the clean NIST |
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499 test set error brought by the use of out-of-distribution examples (i.e. the |
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500 perturbed examples examples from NISTP or P07). The right side of |
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501 Figure~\ref{fig:fig:improvements-charts} shows the relative improvement |
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502 brought by the use of a multi-task setting, in which the same model is |
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503 trained for more classes than the target classes of interest (i.e. training |
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504 with all 62 classes when the target classes are respectively the digits, |
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505 lower-case, or upper-case characters). Again, whereas the gain is marginal |
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506 or negative for the MLP, it is substantial for the SDA. Note that for |
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507 these multi-task experiment, only the original NIST dataset is used. For |
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508 example, the MLP-digits bar shows the relative improvement in MLP error |
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509 rate on the NIST digits test set (1 - single-task model's error / |
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510 multi-task model's error). The single-task model is trained with only 10 |
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511 outputs (one per digit), seeing only digit examples, whereas the multi-task |
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512 model is trained with 62 outputs, with all 62 character classes as |
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513 examples. For the multi-task model, the digit error rate is measured by |
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514 comparing the correct digit class with the output class associated with |
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515 the maximum conditional probability among only the digit classes outputs. |
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516 |
| 475 | 517 \begin{figure}[h] |
| 518 \resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}\\ | |
| 519 \caption{Charts corresponding to table \ref{tab:sda-vs-mlp-vs-humans}. Left: overall results; error bars indicate a 95\% confidence interval. Right: error rates on NIST test digits only, with results from litterature. } | |
| 520 \label{fig:error-rates-charts} | |
| 521 \end{figure} | |
| 522 | |
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523 %\vspace*{-1mm} |
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524 %\subsection{Perturbed Training Data More Helpful for SDAE} |
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525 %\vspace*{-1mm} |
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526 |
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527 %\vspace*{-1mm} |
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528 %\subsection{Multi-Task Learning Effects} |
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529 %\vspace*{-1mm} |
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530 |
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531 \iffalse |
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532 As previously seen, the SDA is better able to benefit from the |
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533 transformations applied to the data than the MLP. In this experiment we |
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534 define three tasks: recognizing digits (knowing that the input is a digit), |
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535 recognizing upper case characters (knowing that the input is one), and |
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536 recognizing lower case characters (knowing that the input is one). We |
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537 consider the digit classification task as the target task and we want to |
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538 evaluate whether training with the other tasks can help or hurt, and |
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539 whether the effect is different for MLPs versus SDAs. The goal is to find |
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540 out if deep learning can benefit more (or less) from multiple related tasks |
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541 (i.e. the multi-task setting) compared to a corresponding purely supervised |
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542 shallow learner. |
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543 |
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544 We use a single hidden layer MLP with 1000 hidden units, and a SDA |
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545 with 3 hidden layers (1000 hidden units per layer), pre-trained and |
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546 fine-tuned on NIST. |
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547 |
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548 Our results show that the MLP benefits marginally from the multi-task setting |
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549 in the case of digits (5\% relative improvement) but is actually hurt in the case |
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parents:
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550 of characters (respectively 3\% and 4\% worse for lower and upper class characters). |
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551 On the other hand the SDA benefitted from the multi-task setting, with relative |
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parents:
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552 error rate improvements of 27\%, 15\% and 13\% respectively for digits, |
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parents:
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553 lower and upper case characters, as shown in Table~\ref{tab:multi-task}. |
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554 \fi |
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555 |
| 475 | 556 |
| 557 \begin{figure}[h] | |
| 558 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\ | |
| 559 \caption{Charts corresponding to tables \ref{tab:perturbation-effect} (left) and \ref{tab:multi-task} (right).} | |
| 560 \label{fig:improvements-charts} | |
| 561 \end{figure} | |
| 562 | |
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563 \vspace*{-1mm} |
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564 \section{Conclusions} |
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565 \vspace*{-1mm} |
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566 |
| 472 | 567 The conclusions are positive for all the questions asked in the introduction. |
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568 %\begin{itemize} |
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569 $\bullet$ %\item |
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570 Do the good results previously obtained with deep architectures on the |
| 472 | 571 MNIST digits generalize to the setting of a much larger and richer (but similar) |
| 572 dataset, the NIST special database 19, with 62 classes and around 800k examples? | |
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486
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573 Yes, the SDA systematically outperformed the MLP and all the previously |
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574 published results on this dataset (as far as we know), in fact reaching human-level |
| 472 | 575 performance. |
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576 |
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577 $\bullet$ %\item |
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578 To what extent does the perturbation of input images (e.g. adding |
| 472 | 579 noise, affine transformations, background images) make the resulting |
| 580 classifier better not only on similarly perturbed images but also on | |
| 581 the {\em original clean examples}? Do deep architectures benefit more from such {\em out-of-distribution} | |
| 582 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? | |
| 583 MLPs were helped by perturbed training examples when tested on perturbed input images, | |
| 584 but only marginally helped wrt clean examples. On the other hand, the deep SDAs | |
| 585 were very significantly boosted by these out-of-distribution examples. | |
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586 |
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587 $\bullet$ %\item |
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588 Similarly, does the feature learning step in deep learning algorithms benefit more |
| 472 | 589 training with similar but different classes (i.e. a multi-task learning scenario) than |
| 590 a corresponding shallow and purely supervised architecture? | |
| 591 Whereas the improvement due to the multi-task setting was marginal or | |
| 592 negative for the MLP, it was very significant for the SDA. | |
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593 %\end{itemize} |
| 472 | 594 |
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595 A Flash demo of the recognizer (where both the MLP and the SDA can be compared) |
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596 can be executed on-line at {\tt http://deep.host22.com}. |
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597 |
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598 |
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599 {\small |
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600 \bibliography{strings,ml,aigaion,specials} |
| 469 | 601 %\bibliographystyle{plainnat} |
| 602 \bibliographystyle{unsrtnat} | |
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603 %\bibliographystyle{apalike} |
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604 } |
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605 |
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606 \newpage |
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607 |
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608 \centerline{APPENDIX FOR {\bf Deep Self-Taught Learning for Handwritten Character Recognition}} |
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609 |
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610 \vspace*{1cm} |
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611 |
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612 \begin{table}[h] |
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613 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits + |
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614 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training |
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615 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture |
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616 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07) |
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617 and using a validation set to select hyper-parameters and other training choices. |
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618 \{SDA,MLP\}0 are trained on NIST, |
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619 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07. |
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620 The human error rate on digits is a lower bound because it does not count digits that were |
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621 recognized as letters. For comparison, the results found in the literature |
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622 on NIST digits classification using the same test set are included.} |
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623 \label{tab:sda-vs-mlp-vs-humans} |
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624 \begin{center} |
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625 \begin{tabular}{|l|r|r|r|r|} \hline |
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626 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline |
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627 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline |
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628 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline |
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629 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline |
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630 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline |
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631 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline |
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632 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline |
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633 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline |
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634 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline |
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635 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline |
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636 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline |
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637 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline |
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638 \end{tabular} |
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639 \end{center} |
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640 \end{table} |
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641 |
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642 \begin{table}[h] |
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643 \caption{Relative change in error rates due to the use of perturbed training data, |
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644 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models. |
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645 A positive value indicates that training on the perturbed data helped for the |
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646 given test set (the first 3 columns on the 62-class tasks and the last one is |
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647 on the clean 10-class digits). Clearly, the deep learning models did benefit more |
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648 from perturbed training data, even when testing on clean data, whereas the MLP |
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649 trained on perturbed data performed worse on the clean digits and about the same |
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650 on the clean characters. } |
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651 \label{tab:perturbation-effect} |
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652 \begin{center} |
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653 \begin{tabular}{|l|r|r|r|r|} \hline |
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654 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline |
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655 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline |
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656 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline |
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657 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline |
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658 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline |
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659 \end{tabular} |
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660 \end{center} |
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661 \end{table} |
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662 |
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663 \begin{table}[h] |
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664 \caption{Test error rates and relative change in error rates due to the use of |
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665 a multi-task setting, i.e., training on each task in isolation vs training |
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666 for all three tasks together, for MLPs vs SDAs. The SDA benefits much |
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667 more from the multi-task setting. All experiments on only on the |
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668 unperturbed NIST data, using validation error for model selection. |
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669 Relative improvement is 1 - single-task error / multi-task error.} |
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670 \label{tab:multi-task} |
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671 \begin{center} |
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672 \begin{tabular}{|l|r|r|r|} \hline |
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673 & single-task & multi-task & relative \\ |
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674 & setting & setting & improvement \\ \hline |
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675 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline |
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676 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline |
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677 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline |
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678 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline |
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679 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline |
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680 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline |
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681 \end{tabular} |
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682 \end{center} |
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683 \end{table} |
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684 |
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686 \end{document} |