Mercurial > ift6266
comparison writeup/jmlr_submission.tex @ 593:18a7e7fdea4d
jmlr_submission
| author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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| date | Fri, 01 Oct 2010 15:54:34 -0400 |
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| children | 537f8b786655 |
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| 1 \documentclass{article} % For LaTeX2e | |
| 2 | |
| 3 \usepackage{times} | |
| 4 \usepackage{wrapfig} | |
| 5 %\usepackage{amsthm} % not to be used with springer tools | |
| 6 \usepackage{amsmath} | |
| 7 \usepackage{bbm} | |
| 8 \usepackage[psamsfonts]{amssymb} | |
| 9 %\usepackage{algorithm,algorithmic} % not used after all | |
| 10 \usepackage[utf8]{inputenc} | |
| 11 \usepackage{graphicx,subfigure} | |
| 12 \usepackage{natbib} % was [numbers]{natbib} | |
| 13 | |
| 14 \addtolength{\textwidth}{10mm} | |
| 15 \addtolength{\evensidemargin}{-5mm} | |
| 16 \addtolength{\oddsidemargin}{-5mm} | |
| 17 | |
| 18 %\setlength\parindent{0mm} | |
| 19 | |
| 20 \title{Deep Self-Taught Learning for Handwritten Character Recognition} | |
| 21 \author{ | |
| 22 Yoshua Bengio \and | |
| 23 Frédéric Bastien \and | |
| 24 Arnaud Bergeron \and | |
| 25 Nicolas Boulanger-Lewandowski \and | |
| 26 Thomas Breuel \and | |
| 27 Youssouf Chherawala \and | |
| 28 Moustapha Cisse \and | |
| 29 Myriam Côté \and | |
| 30 Dumitru Erhan \and | |
| 31 Jeremy Eustache \and | |
| 32 Xavier Glorot \and | |
| 33 Xavier Muller \and | |
| 34 Sylvain Pannetier Lebeuf \and | |
| 35 Razvan Pascanu \and | |
| 36 Salah Rifai \and | |
| 37 Francois Savard \and | |
| 38 Guillaume Sicard | |
| 39 } | |
| 40 \date{September 30th} | |
| 41 | |
| 42 | |
| 43 \begin{document} | |
| 44 | |
| 45 %\makeanontitle | |
| 46 \maketitle | |
| 47 | |
| 48 %\vspace*{-2mm} | |
| 49 \begin{abstract} | |
| 50 Recent theoretical and empirical work in statistical machine learning has demonstrated the potential of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple levels of representation. Self-taught learning (exploiting unlabeled examples or examples from other distributions) has already been applied to deep learners, but mostly to show the advantage of unlabeled examples. Here we explore the advantage brought by {\em out-of-distribution examples}. For this purpose we developed a powerful generator of stochastic variations and noise processes for character images, including not only affine transformations but also slant, local elastic deformations, changes in thickness, background images, grey level changes, contrast, occlusion, and various types of noise. The out-of-distribution examples are obtained from these highly distorted images or by including examples of object classes different from those in the target test set. We show that {\em deep learners benefit more from out-of-distribution examples than a corresponding shallow learner}, at least in the area of handwritten character recognition. In fact, we show that they beat previously published results and reach human-level performance on both handwritten digit classification and 62-class handwritten character recognition. | |
| 51 \end{abstract} | |
| 52 %\vspace*{-3mm} | |
| 53 | |
| 54 %\keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition} | |
| 55 | |
| 56 \section{Introduction} | |
| 57 %\vspace*{-1mm} | |
| 58 | |
| 59 {\bf Deep Learning} has emerged as a promising new area of research in | |
| 60 statistical machine learning (see \citet{Bengio-2009} for a review). | |
| 61 Learning algorithms for deep architectures are centered on the learning | |
| 62 of useful representations of data, which are better suited to the task at hand, | |
| 63 and are organized in a hierarchy with multiple levels. | |
| 64 This is in part inspired by observations of the mammalian visual cortex, | |
| 65 which consists of a chain of processing elements, each of which is associated with a | |
| 66 different representation of the raw visual input. In fact, | |
| 67 it was found recently that the features learnt in deep architectures resemble | |
| 68 those observed in the first two of these stages (in areas V1 and V2 | |
| 69 of visual cortex) \citep{HonglakL2008}, and that they become more and | |
| 70 more invariant to factors of variation (such as camera movement) in | |
| 71 higher layers~\citep{Goodfellow2009}. | |
| 72 Learning a hierarchy of features increases the | |
| 73 ease and practicality of developing representations that are at once | |
| 74 tailored to specific tasks, yet are able to borrow statistical strength | |
| 75 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the | |
| 76 feature representation can lead to higher-level (more abstract, more | |
| 77 general) features that are more robust to unanticipated sources of | |
| 78 variance extant in real data. | |
| 79 | |
| 80 {\bf Self-taught learning}~\citep{RainaR2007} is a paradigm that combines principles | |
| 81 of semi-supervised and multi-task learning: the learner can exploit examples | |
| 82 that are unlabeled and possibly come from a distribution different from the target | |
| 83 distribution, e.g., from other classes than those of interest. | |
| 84 It has already been shown that deep learners can clearly take advantage of | |
| 85 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small}, | |
| 86 but more needs to be done to explore the impact | |
| 87 of {\em out-of-distribution} examples and of the {\em multi-task} setting | |
| 88 (one exception is~\citep{CollobertR2008}, which uses a different kind | |
| 89 of learning algorithm). In particular the {\em relative | |
| 90 advantage of deep learning} for these settings has not been evaluated. | |
| 91 The hypothesis discussed in the conclusion is that in the context of | |
| 92 multi-task learning and the availability of out-of-distribution training examples, | |
| 93 a deep hierarchy of features | |
| 94 may be better able to provide sharing of statistical strength | |
| 95 between different regions in input space or different tasks, compared to | |
| 96 a shallow learner. | |
| 97 | |
| 98 Whereas a deep architecture can in principle be more powerful than a | |
| 99 shallow one in terms of representation, depth appears to render the | |
| 100 training problem more difficult in terms of optimization and local minima. | |
| 101 It is also only recently that successful algorithms were proposed to | |
| 102 overcome some of these difficulties. All are based on unsupervised | |
| 103 learning, often in an greedy layer-wise ``unsupervised pre-training'' | |
| 104 stage~\citep{Bengio-2009}. One of these layer initialization techniques, | |
| 105 applied here, is the Denoising | |
| 106 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}), | |
| 107 which | |
| 108 performed similarly or better than previously proposed Restricted Boltzmann | |
| 109 Machines in terms of unsupervised extraction of a hierarchy of features | |
| 110 useful for classification. Each layer is trained to denoise its | |
| 111 input, creating a layer of features that can be used as input for the next layer. | |
| 112 | |
| 113 %The principle is that each layer starting from | |
| 114 %the bottom is trained to encode its input (the output of the previous | |
| 115 %layer) and to reconstruct it from a corrupted version. After this | |
| 116 %unsupervised initialization, the stack of DAs can be | |
| 117 %converted into a deep supervised feedforward neural network and fine-tuned by | |
| 118 %stochastic gradient descent. | |
| 119 | |
| 120 % | |
| 121 In this paper we ask the following questions: | |
| 122 | |
| 123 %\begin{enumerate} | |
| 124 $\bullet$ %\item | |
| 125 Do the good results previously obtained with deep architectures on the | |
| 126 MNIST digit images generalize to the setting of a much larger and richer (but similar) | |
| 127 dataset, the NIST special database 19, with 62 classes and around 800k examples? | |
| 128 | |
| 129 $\bullet$ %\item | |
| 130 To what extent does the perturbation of input images (e.g. adding | |
| 131 noise, affine transformations, background images) make the resulting | |
| 132 classifiers better not only on similarly perturbed images but also on | |
| 133 the {\em original clean examples}? We study this question in the | |
| 134 context of the 62-class and 10-class tasks of the NIST special database 19. | |
| 135 | |
| 136 $\bullet$ %\item | |
| 137 Do deep architectures {\em benefit {\bf more} from such out-of-distribution} | |
| 138 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? | |
| 139 We use highly perturbed examples to generate out-of-distribution examples. | |
| 140 | |
| 141 $\bullet$ %\item | |
| 142 Similarly, does the feature learning step in deep learning algorithms benefit {\bf more} | |
| 143 from training with moderately {\em different classes} (i.e. a multi-task learning scenario) than | |
| 144 a corresponding shallow and purely supervised architecture? | |
| 145 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case) | |
| 146 to answer this question. | |
| 147 %\end{enumerate} | |
| 148 | |
| 149 Our experimental results provide positive evidence towards all of these questions, | |
| 150 as well as classifiers that reach human-level performance on 62-class isolated character | |
| 151 recognition and beat previously published results on the NIST dataset (special database 19). | |
| 152 To achieve these results, we introduce in the next section a sophisticated system | |
| 153 for stochastically transforming character images and then explain the methodology, | |
| 154 which is based on training with or without these transformed images and testing on | |
| 155 clean ones. We measure the relative advantage of out-of-distribution examples | |
| 156 (perturbed or out-of-class) | |
| 157 for a deep learner vs a supervised shallow one. | |
| 158 Code for generating these transformations as well as for the deep learning | |
| 159 algorithms are made available at {\tt http://hg.assembla.com/ift6266}. | |
| 160 We estimate the relative advantage for deep learners of training with | |
| 161 other classes than those of interest, by comparing learners trained with | |
| 162 62 classes with learners trained with only a subset (on which they | |
| 163 are then tested). | |
| 164 The conclusion discusses | |
| 165 the more general question of why deep learners may benefit so much from | |
| 166 the self-taught learning framework. Since out-of-distribution data | |
| 167 (perturbed or from other related classes) is very common, this conclusion | |
| 168 is of practical importance. | |
| 169 | |
| 170 %\vspace*{-3mm} | |
| 171 %\newpage | |
| 172 \section{Perturbed and Transformed Character Images} | |
| 173 \label{s:perturbations} | |
| 174 %\vspace*{-2mm} | |
| 175 | |
| 176 \begin{wrapfigure}[8]{l}{0.15\textwidth} | |
| 177 %\begin{minipage}[b]{0.14\linewidth} | |
| 178 %\vspace*{-5mm} | |
| 179 \begin{center} | |
| 180 \includegraphics[scale=.4]{images/Original.png}\\ | |
| 181 {\bf Original} | |
| 182 \end{center} | |
| 183 \end{wrapfigure} | |
| 184 %%\vspace{0.7cm} | |
| 185 %\end{minipage}% | |
| 186 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth} | |
| 187 This section describes the different transformations we used to stochastically | |
| 188 transform $32 \times 32$ source images (such as the one on the left) | |
| 189 in order to obtain data from a larger distribution which | |
| 190 covers a domain substantially larger than the clean characters distribution from | |
| 191 which we start. | |
| 192 Although character transformations have been used before to | |
| 193 improve character recognizers, this effort is on a large scale both | |
| 194 in number of classes and in the complexity of the transformations, hence | |
| 195 in the complexity of the learning task. | |
| 196 The code for these transformations (mostly python) is available at | |
| 197 {\tt http://hg.assembla.com/ift6266}. All the modules in the pipeline share | |
| 198 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the | |
| 199 amount of deformation or noise introduced. | |
| 200 There are two main parts in the pipeline. The first one, | |
| 201 from slant to pinch below, performs transformations. The second | |
| 202 part, from blur to contrast, adds different kinds of noise. | |
| 203 %\end{minipage} | |
| 204 | |
| 205 %\vspace*{1mm} | |
| 206 \subsection{Transformations} | |
| 207 %{\large\bf 2.1 Transformations} | |
| 208 %\vspace*{1mm} | |
| 209 | |
| 210 \subsubsection*{Thickness} | |
| 211 | |
| 212 %\begin{wrapfigure}[7]{l}{0.15\textwidth} | |
| 213 \begin{minipage}[b]{0.14\linewidth} | |
| 214 %\centering | |
| 215 \begin{center} | |
| 216 \vspace*{-5mm} | |
| 217 \includegraphics[scale=.4]{images/Thick_only.png}\\ | |
| 218 %{\bf Thickness} | |
| 219 \end{center} | |
| 220 \vspace{.6cm} | |
| 221 \end{minipage}% | |
| 222 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth} | |
| 223 %\end{wrapfigure} | |
| 224 To change character {\bf thickness}, morphological operators of dilation and erosion~\citep{Haralick87,Serra82} | |
| 225 are applied. The neighborhood of each pixel is multiplied | |
| 226 element-wise with a {\em structuring element} matrix. | |
| 227 The pixel value is replaced by the maximum or the minimum of the resulting | |
| 228 matrix, respectively for dilation or erosion. Ten different structural elements with | |
| 229 increasing dimensions (largest is $5\times5$) were used. For each image, | |
| 230 randomly sample the operator type (dilation or erosion) with equal probability and one structural | |
| 231 element from a subset of the $n=round(m \times complexity)$ smallest structuring elements | |
| 232 where $m=10$ for dilation and $m=6$ for erosion (to avoid completely erasing thin characters). | |
| 233 A neutral element (no transformation) | |
| 234 is always present in the set. | |
| 235 %%\vspace{.4cm} | |
| 236 \end{minipage} | |
| 237 | |
| 238 \vspace{2mm} | |
| 239 | |
| 240 \subsubsection*{Slant} | |
| 241 \vspace*{2mm} | |
| 242 | |
| 243 \begin{minipage}[b]{0.14\linewidth} | |
| 244 \centering | |
| 245 \includegraphics[scale=.4]{images/Slant_only.png}\\ | |
| 246 %{\bf Slant} | |
| 247 \end{minipage}% | |
| 248 \hspace{0.3cm} | |
| 249 \begin{minipage}[b]{0.83\linewidth} | |
| 250 %\centering | |
| 251 To produce {\bf slant}, each row of the image is shifted | |
| 252 proportionally to its height: $shift = round(slant \times height)$. | |
| 253 $slant \sim U[-complexity,complexity]$. | |
| 254 The shift is randomly chosen to be either to the left or to the right. | |
| 255 \vspace{5mm} | |
| 256 \end{minipage} | |
| 257 %\vspace*{-4mm} | |
| 258 | |
| 259 %\newpage | |
| 260 | |
| 261 \subsubsection*{Affine Transformations} | |
| 262 | |
| 263 \begin{minipage}[b]{0.14\linewidth} | |
| 264 %\centering | |
| 265 %\begin{wrapfigure}[8]{l}{0.15\textwidth} | |
| 266 \begin{center} | |
| 267 \includegraphics[scale=.4]{images/Affine_only.png} | |
| 268 \vspace*{6mm} | |
| 269 %{\small {\bf Affine \mbox{Transformation}}} | |
| 270 \end{center} | |
| 271 %\end{wrapfigure} | |
| 272 \end{minipage}% | |
| 273 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth} | |
| 274 \noindent A $2 \times 3$ {\bf affine transform} matrix (with | |
| 275 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$. | |
| 276 Output pixel $(x,y)$ takes the value of input pixel | |
| 277 nearest to $(ax+by+c,dx+ey+f)$, | |
| 278 producing scaling, translation, rotation and shearing. | |
| 279 Marginal distributions of $(a,b,c,d,e,f)$ have been tuned to | |
| 280 forbid large rotations (to avoid confusing classes) but to give good | |
| 281 variability of the transformation: $a$ and $d$ $\sim U[1-3 | |
| 282 complexity,1+3\,complexity]$, $b$ and $e$ $\sim U[-3 \,complexity,3\, | |
| 283 complexity]$, and $c$ and $f \sim U[-4 \,complexity, 4 \, | |
| 284 complexity]$.\\ | |
| 285 \end{minipage} | |
| 286 | |
| 287 %\vspace*{-4.5mm} | |
| 288 \subsubsection*{Local Elastic Deformations} | |
| 289 | |
| 290 %\begin{minipage}[t]{\linewidth} | |
| 291 %\begin{wrapfigure}[7]{l}{0.15\textwidth} | |
| 292 %\hspace*{-8mm} | |
| 293 \begin{minipage}[b]{0.14\linewidth} | |
| 294 %\centering | |
| 295 \begin{center} | |
| 296 \vspace*{5mm} | |
| 297 \includegraphics[scale=.4]{images/Localelasticdistorsions_only.png} | |
| 298 %{\bf Local Elastic Deformation} | |
| 299 \end{center} | |
| 300 %\end{wrapfigure} | |
| 301 \end{minipage}% | |
| 302 \hspace{3mm} | |
| 303 \begin{minipage}[b]{0.85\linewidth} | |
| 304 %%\vspace*{-20mm} | |
| 305 The {\bf local elastic deformation} | |
| 306 module induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short}, | |
| 307 which provides more details. | |
| 308 The intensity of the displacement fields is given by | |
| 309 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are | |
| 310 convolved with a Gaussian 2D kernel (resulting in a blur) of | |
| 311 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$. | |
| 312 \vspace{2mm} | |
| 313 \end{minipage} | |
| 314 | |
| 315 \vspace*{4mm} | |
| 316 | |
| 317 \subsubsection*{Pinch} | |
| 318 | |
| 319 \begin{minipage}[b]{0.14\linewidth} | |
| 320 %\centering | |
| 321 %\begin{wrapfigure}[7]{l}{0.15\textwidth} | |
| 322 %\vspace*{-5mm} | |
| 323 \begin{center} | |
| 324 \includegraphics[scale=.4]{images/Pinch_only.png}\\ | |
| 325 \vspace*{15mm} | |
| 326 %{\bf Pinch} | |
| 327 \end{center} | |
| 328 %\end{wrapfigure} | |
| 329 %%\vspace{.6cm} | |
| 330 \end{minipage}% | |
| 331 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth} | |
| 332 The {\bf pinch} module applies the ``Whirl and pinch'' GIMP filter with whirl set to 0. | |
| 333 A pinch is ``similar to projecting the image onto an elastic | |
| 334 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual). | |
| 335 For a square input image, draw a radius-$r$ disk | |
| 336 around its center $C$. Any pixel $P$ belonging to | |
| 337 that disk has its value replaced by | |
| 338 the value of a ``source'' pixel in the original image, | |
| 339 on the line that goes through $C$ and $P$, but | |
| 340 at some other distance $d_2$. Define $d_1=distance(P,C)$ | |
| 341 and $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times | |
| 342 d_1$, where $pinch$ is a parameter of the filter. | |
| 343 The actual value is given by bilinear interpolation considering the pixels | |
| 344 around the (non-integer) source position thus found. | |
| 345 Here $pinch \sim U[-complexity, 0.7 \times complexity]$. | |
| 346 %%\vspace{1.5cm} | |
| 347 \end{minipage} | |
| 348 | |
| 349 %\vspace{1mm} | |
| 350 | |
| 351 %{\large\bf 2.2 Injecting Noise} | |
| 352 \subsection{Injecting Noise} | |
| 353 %\vspace{2mm} | |
| 354 | |
| 355 \subsubsection*{Motion Blur} | |
| 356 | |
| 357 %%\vspace*{-.2cm} | |
| 358 \begin{minipage}[t]{0.14\linewidth} | |
| 359 \centering | |
| 360 \vspace*{0mm} | |
| 361 \includegraphics[scale=.4]{images/Motionblur_only.png} | |
| 362 %{\bf Motion Blur} | |
| 363 \end{minipage}% | |
| 364 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth} | |
| 365 %%\vspace*{.5mm} | |
| 366 \vspace*{2mm} | |
| 367 The {\bf motion blur} module is GIMP's ``linear motion blur'', which | |
| 368 has parameters $length$ and $angle$. The value of | |
| 369 a pixel in the final image is approximately the mean of the first $length$ pixels | |
| 370 found by moving in the $angle$ direction, | |
| 371 $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$. | |
| 372 %\vspace{5mm} | |
| 373 \end{minipage} | |
| 374 | |
| 375 %\vspace*{1mm} | |
| 376 | |
| 377 \subsubsection*{Occlusion} | |
| 378 | |
| 379 \begin{minipage}[t]{0.14\linewidth} | |
| 380 \centering | |
| 381 \vspace*{3mm} | |
| 382 \includegraphics[scale=.4]{images/occlusion_only.png}\\ | |
| 383 %{\bf Occlusion} | |
| 384 %%\vspace{.5cm} | |
| 385 \end{minipage}% | |
| 386 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth} | |
| 387 %\vspace*{-18mm} | |
| 388 The {\bf occlusion} module selects a random rectangle from an {\em occluder} character | |
| 389 image and places it over the original {\em occluded} | |
| 390 image. Pixels are combined by taking the max(occluder, occluded), | |
| 391 i.e. keeping the lighter ones. | |
| 392 The rectangle corners | |
| 393 are sampled so that larger complexity gives larger rectangles. | |
| 394 The destination position in the occluded image are also sampled | |
| 395 according to a normal distribution. | |
| 396 This module is skipped with probability 60\%. | |
| 397 %%\vspace{7mm} | |
| 398 \end{minipage} | |
| 399 | |
| 400 %\vspace*{1mm} | |
| 401 \subsubsection*{Gaussian Smoothing} | |
| 402 | |
| 403 %\begin{wrapfigure}[8]{l}{0.15\textwidth} | |
| 404 %\vspace*{-6mm} | |
| 405 \begin{minipage}[t]{0.14\linewidth} | |
| 406 \begin{center} | |
| 407 %\centering | |
| 408 \vspace*{6mm} | |
| 409 \includegraphics[scale=.4]{images/Bruitgauss_only.png} | |
| 410 %{\bf Gaussian Smoothing} | |
| 411 \end{center} | |
| 412 %\end{wrapfigure} | |
| 413 %%\vspace{.5cm} | |
| 414 \end{minipage}% | |
| 415 \hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth} | |
| 416 With the {\bf Gaussian smoothing} module, | |
| 417 different regions of the image are spatially smoothed. | |
| 418 This is achieved by first convolving | |
| 419 the image with an isotropic Gaussian kernel of | |
| 420 size and variance chosen uniformly in the ranges $[12,12 + 20 \times | |
| 421 complexity]$ and $[2,2 + 6 \times complexity]$. This filtered image is normalized | |
| 422 between $0$ and $1$. We also create an isotropic weighted averaging window, of the | |
| 423 kernel size, with maximum value at the center. For each image we sample | |
| 424 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be | |
| 425 averaging centers between the original image and the filtered one. We | |
| 426 initialize to zero a mask matrix of the image size. For each selected pixel | |
| 427 we add to the mask the averaging window centered on it. The final image is | |
| 428 computed from the following element-wise operation: $\frac{image + filtered\_image | |
| 429 \times mask}{mask+1}$. | |
| 430 This module is skipped with probability 75\%. | |
| 431 \end{minipage} | |
| 432 | |
| 433 %\newpage | |
| 434 | |
| 435 %\vspace*{-9mm} | |
| 436 \subsubsection*{Permute Pixels} | |
| 437 | |
| 438 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth} | |
| 439 %\centering | |
| 440 \begin{minipage}[t]{0.14\textwidth} | |
| 441 %\begin{wrapfigure}[7]{l}{ | |
| 442 %\vspace*{-5mm} | |
| 443 \begin{center} | |
| 444 \vspace*{1mm} | |
| 445 \includegraphics[scale=.4]{images/Permutpixel_only.png} | |
| 446 %{\small\bf Permute Pixels} | |
| 447 \end{center} | |
| 448 %\end{wrapfigure} | |
| 449 \end{minipage}% | |
| 450 \hspace{3mm}\begin{minipage}[t]{0.86\linewidth} | |
| 451 \vspace*{1mm} | |
| 452 %%\vspace*{-20mm} | |
| 453 This module {\bf permutes neighbouring pixels}. It first selects a | |
| 454 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each | |
| 455 of these pixels is then sequentially exchanged with a random pixel | |
| 456 among its four nearest neighbors (on its left, right, top or bottom). | |
| 457 This module is skipped with probability 80\%.\\ | |
| 458 %\vspace*{1mm} | |
| 459 \end{minipage} | |
| 460 | |
| 461 %\vspace{-3mm} | |
| 462 | |
| 463 \subsubsection*{Gaussian Noise} | |
| 464 | |
| 465 \begin{minipage}[t]{0.14\textwidth} | |
| 466 %\begin{wrapfigure}[7]{l}{ | |
| 467 %%\vspace*{-3mm} | |
| 468 \begin{center} | |
| 469 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth} | |
| 470 %\centering | |
| 471 \vspace*{0mm} | |
| 472 \includegraphics[scale=.4]{images/Distorsiongauss_only.png} | |
| 473 %{\small \bf Gauss. Noise} | |
| 474 \end{center} | |
| 475 %\end{wrapfigure} | |
| 476 \end{minipage}% | |
| 477 \hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth} | |
| 478 \vspace*{1mm} | |
| 479 %\vspace*{12mm} | |
| 480 The {\bf Gaussian noise} module simply adds, to each pixel of the image independently, a | |
| 481 noise $\sim Normal(0,(\frac{complexity}{10})^2)$. | |
| 482 This module is skipped with probability 70\%. | |
| 483 %%\vspace{1.1cm} | |
| 484 \end{minipage} | |
| 485 | |
| 486 %\vspace*{1.2cm} | |
| 487 | |
| 488 \subsubsection*{Background Image Addition} | |
| 489 | |
| 490 \begin{minipage}[t]{\linewidth} | |
| 491 \begin{minipage}[t]{0.14\linewidth} | |
| 492 \centering | |
| 493 \vspace*{0mm} | |
| 494 \includegraphics[scale=.4]{images/background_other_only.png} | |
| 495 %{\small \bf Bg Image} | |
| 496 \end{minipage}% | |
| 497 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth} | |
| 498 \vspace*{1mm} | |
| 499 Following~\citet{Larochelle-jmlr-2009}, the {\bf background image} module adds a random | |
| 500 background image behind the letter, from a randomly chosen natural image, | |
| 501 with contrast adjustments depending on $complexity$, to preserve | |
| 502 more or less of the original character image. | |
| 503 %%\vspace{.8cm} | |
| 504 \end{minipage} | |
| 505 \end{minipage} | |
| 506 %%\vspace{-.7cm} | |
| 507 | |
| 508 \subsubsection*{Salt and Pepper Noise} | |
| 509 | |
| 510 \begin{minipage}[t]{0.14\linewidth} | |
| 511 \centering | |
| 512 \vspace*{0mm} | |
| 513 \includegraphics[scale=.4]{images/Poivresel_only.png} | |
| 514 %{\small \bf Salt \& Pepper} | |
| 515 \end{minipage}% | |
| 516 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth} | |
| 517 \vspace*{1mm} | |
| 518 The {\bf salt and pepper noise} module adds noise $\sim U[0,1]$ to random subsets of pixels. | |
| 519 The number of selected pixels is $0.2 \times complexity$. | |
| 520 This module is skipped with probability 75\%. | |
| 521 %%\vspace{.9cm} | |
| 522 \end{minipage} | |
| 523 %%\vspace{-.7cm} | |
| 524 | |
| 525 %\vspace{1mm} | |
| 526 \subsubsection*{Scratches} | |
| 527 | |
| 528 \begin{minipage}[t]{0.14\textwidth} | |
| 529 %\begin{wrapfigure}[7]{l}{ | |
| 530 %\begin{minipage}[t]{0.14\linewidth} | |
| 531 %\centering | |
| 532 \begin{center} | |
| 533 \vspace*{4mm} | |
| 534 %\hspace*{-1mm} | |
| 535 \includegraphics[scale=.4]{images/Rature_only.png}\\ | |
| 536 %{\bf Scratches} | |
| 537 \end{center} | |
| 538 \end{minipage}% | |
| 539 %\end{wrapfigure} | |
| 540 \hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth} | |
| 541 %%\vspace{.4cm} | |
| 542 The {\bf scratches} module places line-like white patches on the image. The | |
| 543 lines are heavily transformed images of the digit ``1'' (one), chosen | |
| 544 at random among 500 such 1 images, | |
| 545 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times | |
| 546 complexity)^2$ (in degrees), using bi-cubic interpolation. | |
| 547 Two passes of a grey-scale morphological erosion filter | |
| 548 are applied, reducing the width of the line | |
| 549 by an amount controlled by $complexity$. | |
| 550 This module is skipped with probability 85\%. The probabilities | |
| 551 of applying 1, 2, or 3 patches are (50\%,30\%,20\%). | |
| 552 \end{minipage} | |
| 553 | |
| 554 %\vspace*{1mm} | |
| 555 | |
| 556 \subsubsection*{Grey Level and Contrast Changes} | |
| 557 | |
| 558 \begin{minipage}[t]{0.15\linewidth} | |
| 559 \centering | |
| 560 \vspace*{0mm} | |
| 561 \includegraphics[scale=.4]{images/Contrast_only.png} | |
| 562 %{\bf Grey Level \& Contrast} | |
| 563 \end{minipage}% | |
| 564 \hspace{3mm}\begin{minipage}[t]{0.85\linewidth} | |
| 565 \vspace*{1mm} | |
| 566 The {\bf grey level and contrast} module changes the contrast by changing grey levels, and may invert the image polarity (white | |
| 567 to black and black to white). The contrast is $C \sim U[1-0.85 \times complexity,1]$ | |
| 568 so the image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The | |
| 569 polarity is inverted with probability 50\%. | |
| 570 %%\vspace{.7cm} | |
| 571 \end{minipage} | |
| 572 %\vspace{2mm} | |
| 573 | |
| 574 | |
| 575 \iffalse | |
| 576 \begin{figure}[ht] | |
| 577 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/example_t.png}}}\\ | |
| 578 \caption{Illustration of the pipeline of stochastic | |
| 579 transformations applied to the image of a lower-case \emph{t} | |
| 580 (the upper left image). Each image in the pipeline (going from | |
| 581 left to right, first top line, then bottom line) shows the result | |
| 582 of applying one of the modules in the pipeline. The last image | |
| 583 (bottom right) is used as training example.} | |
| 584 \label{fig:pipeline} | |
| 585 \end{figure} | |
| 586 \fi | |
| 587 | |
| 588 %\vspace*{-3mm} | |
| 589 \section{Experimental Setup} | |
| 590 %\vspace*{-1mm} | |
| 591 | |
| 592 Much previous work on deep learning had been performed on | |
| 593 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009}, | |
| 594 with 60~000 examples, and variants involving 10~000 | |
| 595 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}. | |
| 596 The focus here is on much larger training sets, from 10 times to | |
| 597 to 1000 times larger, and 62 classes. | |
| 598 | |
| 599 The first step in constructing the larger datasets (called NISTP and P07) is to sample from | |
| 600 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas}, | |
| 601 and {\bf OCR data} (scanned machine printed characters). Once a character | |
| 602 is sampled from one of these sources (chosen randomly), the second step is to | |
| 603 apply a pipeline of transformations and/or noise processes described in section \ref{s:perturbations}. | |
| 604 | |
| 605 To provide a baseline of error rate comparison we also estimate human performance | |
| 606 on both the 62-class task and the 10-class digits task. | |
| 607 We compare the best Multi-Layer Perceptrons (MLP) against | |
| 608 the best Stacked Denoising Auto-encoders (SDA), when | |
| 609 both models' hyper-parameters are selected to minimize the validation set error. | |
| 610 We also provide a comparison against a precise estimate | |
| 611 of human performance obtained via Amazon's Mechanical Turk (AMT) | |
| 612 service (http://mturk.com). | |
| 613 AMT users are paid small amounts | |
| 614 of money to perform tasks for which human intelligence is required. | |
| 615 Mechanical Turk has been used extensively in natural language processing and vision. | |
| 616 %processing \citep{SnowEtAl2008} and vision | |
| 617 %\citep{SorokinAndForsyth2008,whitehill09}. | |
| 618 AMT users were presented | |
| 619 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII | |
| 620 characters. They were forced to choose a single character class (either among the | |
| 621 62 or 10 character classes) for each image. | |
| 622 80 subjects classified 2500 images per (dataset,task) pair. | |
| 623 Different humans labelers sometimes provided a different label for the same | |
| 624 example, and we were able to estimate the error variance due to this effect | |
| 625 because each image was classified by 3 different persons. | |
| 626 The average error of humans on the 62-class task NIST test set | |
| 627 is 18.2\%, with a standard error of 0.1\%. | |
| 628 | |
| 629 %\vspace*{-3mm} | |
| 630 \subsection{Data Sources} | |
| 631 %\vspace*{-2mm} | |
| 632 | |
| 633 %\begin{itemize} | |
| 634 %\item | |
| 635 {\bf NIST.} | |
| 636 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995}, | |
| 637 widely used for training and testing character | |
| 638 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}. | |
| 639 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications, | |
| 640 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes | |
| 641 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity. | |
| 642 The fourth partition (called $hsf_4$, 82587 examples), | |
| 643 experimentally recognized to be the most difficult one, is the one recommended | |
| 644 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} | |
| 645 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for | |
| 646 model selection. | |
| 647 The performances reported by previous work on that dataset mostly use only the digits. | |
| 648 Here we use all the classes both in the training and testing phase. This is especially | |
| 649 useful to estimate the effect of a multi-task setting. | |
| 650 The distribution of the classes in the NIST training and test sets differs | |
| 651 substantially, with relatively many more digits in the test set, and a more uniform distribution | |
| 652 of letters in the test set (whereas in the training set they are distributed | |
| 653 more like in natural text). | |
| 654 %\vspace*{-1mm} | |
| 655 | |
| 656 %\item | |
| 657 {\bf Fonts.} | |
| 658 In order to have a good variety of sources we downloaded an important number of free fonts from: | |
| 659 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}. | |
| 660 % TODO: pointless to anonymize, it's not pointing to our work | |
| 661 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from. | |
| 662 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image, | |
| 663 directly as input to our models. | |
| 664 %\vspace*{-1mm} | |
| 665 | |
| 666 %\item | |
| 667 {\bf Captchas.} | |
| 668 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for | |
| 669 generating characters of the same format as the NIST dataset. This software is based on | |
| 670 a random character class generator and various kinds of transformations similar to those described in the previous sections. | |
| 671 In order to increase the variability of the data generated, many different fonts are used for generating the characters. | |
| 672 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity | |
| 673 depending on the value of the complexity parameter provided by the user of the data source. | |
| 674 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class? | |
| 675 %\vspace*{-1mm} | |
| 676 | |
| 677 %\item | |
| 678 {\bf OCR data.} | |
| 679 A large set (2 million) of scanned, OCRed and manually verified machine-printed | |
| 680 characters where included as an | |
| 681 additional source. This set is part of a larger corpus being collected by the Image Understanding | |
| 682 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern | |
| 683 ({\tt http://www.iupr.com}), and which will be publicly released. | |
| 684 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this | |
| 685 %\end{itemize} | |
| 686 | |
| 687 %\vspace*{-3mm} | |
| 688 \subsection{Data Sets} | |
| 689 %\vspace*{-2mm} | |
| 690 | |
| 691 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label | |
| 692 from one of the 62 character classes. | |
| 693 %\begin{itemize} | |
| 694 %\vspace*{-1mm} | |
| 695 | |
| 696 %\item | |
| 697 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has | |
| 698 \{651668 / 80000 / 82587\} \{training / validation / test\} examples. | |
| 699 %\vspace*{-1mm} | |
| 700 | |
| 701 %\item | |
| 702 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources | |
| 703 and sending them through the transformation pipeline described in section \ref{s:perturbations}. | |
| 704 For each new example to generate, a data source is selected with probability $10\%$ from the fonts, | |
| 705 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the | |
| 706 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$. | |
| 707 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples. | |
| 708 %\vspace*{-1mm} | |
| 709 | |
| 710 %\item | |
| 711 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources) | |
| 712 except that we only apply | |
| 713 transformations from slant to pinch. Therefore, the character is | |
| 714 transformed but no additional noise is added to the image, giving images | |
| 715 closer to the NIST dataset. | |
| 716 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples. | |
| 717 %\end{itemize} | |
| 718 | |
| 719 %\vspace*{-3mm} | |
| 720 \subsection{Models and their Hyperparameters} | |
| 721 %\vspace*{-2mm} | |
| 722 | |
| 723 The experiments are performed using MLPs (with a single | |
| 724 hidden layer) and SDAs. | |
| 725 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.} | |
| 726 | |
| 727 {\bf Multi-Layer Perceptrons (MLP).} | |
| 728 Whereas previous work had compared deep architectures to both shallow MLPs and | |
| 729 SVMs, we only compared to MLPs here because of the very large datasets used | |
| 730 (making the use of SVMs computationally challenging because of their quadratic | |
| 731 scaling behavior). Preliminary experiments on training SVMs (libSVM) with subsets of the training | |
| 732 set allowing the program to fit in memory yielded substantially worse results | |
| 733 than those obtained with MLPs. For training on nearly a billion examples | |
| 734 (with the perturbed data), the MLPs and SDA are much more convenient than | |
| 735 classifiers based on kernel methods. | |
| 736 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized | |
| 737 exponentials) on the output layer for estimating $P(class | image)$. | |
| 738 The number of hidden units is taken in $\{300,500,800,1000,1500\}$. | |
| 739 Training examples are presented in minibatches of size 20. A constant learning | |
| 740 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$. | |
| 741 %through preliminary experiments (measuring performance on a validation set), | |
| 742 %and $0.1$ (which was found to work best) was then selected for optimizing on | |
| 743 %the whole training sets. | |
| 744 %\vspace*{-1mm} | |
| 745 | |
| 746 | |
| 747 {\bf Stacked Denoising Auto-Encoders (SDA).} | |
| 748 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs) | |
| 749 can be used to initialize the weights of each layer of a deep MLP (with many hidden | |
| 750 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006}, | |
| 751 apparently setting parameters in the | |
| 752 basin of attraction of supervised gradient descent yielding better | |
| 753 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised | |
| 754 pre-training phase} uses all of the training images but not the training labels. | |
| 755 Each layer is trained in turn to produce a new representation of its input | |
| 756 (starting from the raw pixels). | |
| 757 It is hypothesized that the | |
| 758 advantage brought by this procedure stems from a better prior, | |
| 759 on the one hand taking advantage of the link between the input | |
| 760 distribution $P(x)$ and the conditional distribution of interest | |
| 761 $P(y|x)$ (like in semi-supervised learning), and on the other hand | |
| 762 taking advantage of the expressive power and bias implicit in the | |
| 763 deep architecture (whereby complex concepts are expressed as | |
| 764 compositions of simpler ones through a deep hierarchy). | |
| 765 | |
| 766 \begin{figure}[ht] | |
| 767 %\vspace*{-2mm} | |
| 768 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}} | |
| 769 %\vspace*{-2mm} | |
| 770 \caption{Illustration of the computations and training criterion for the denoising | |
| 771 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of | |
| 772 the layer (i.e. raw input or output of previous layer) | |
| 773 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$. | |
| 774 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which | |
| 775 is compared to the uncorrupted input $x$ through the loss function | |
| 776 $L_H(x,z)$, whose expected value is approximately minimized during training | |
| 777 by tuning $\theta$ and $\theta'$.} | |
| 778 \label{fig:da} | |
| 779 %\vspace*{-2mm} | |
| 780 \end{figure} | |
| 781 | |
| 782 Here we chose to use the Denoising | |
| 783 Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for | |
| 784 these deep hierarchies of features, as it is simple to train and | |
| 785 explain (see Figure~\ref{fig:da}, as well as | |
| 786 tutorial and code there: {\tt http://deeplearning.net/tutorial}), | |
| 787 provides efficient inference, and yielded results | |
| 788 comparable or better than RBMs in series of experiments | |
| 789 \citep{VincentPLarochelleH2008}. During training, a Denoising | |
| 790 Auto-encoder is presented with a stochastically corrupted version | |
| 791 of the input and trained to reconstruct the uncorrupted input, | |
| 792 forcing the hidden units to represent the leading regularities in | |
| 793 the data. Here we use the random binary masking corruption | |
| 794 (which sets to 0 a random subset of the inputs). | |
| 795 Once it is trained, in a purely unsupervised way, | |
| 796 its hidden units' activations can | |
| 797 be used as inputs for training a second one, etc. | |
| 798 After this unsupervised pre-training stage, the parameters | |
| 799 are used to initialize a deep MLP, which is fine-tuned by | |
| 800 the same standard procedure used to train them (see previous section). | |
| 801 The SDA hyper-parameters are the same as for the MLP, with the addition of the | |
| 802 amount of corruption noise (we used the masking noise process, whereby a | |
| 803 fixed proportion of the input values, randomly selected, are zeroed), and a | |
| 804 separate learning rate for the unsupervised pre-training stage (selected | |
| 805 from the same above set). The fraction of inputs corrupted was selected | |
| 806 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number | |
| 807 of hidden layers but it was fixed to 3 based on previous work with | |
| 808 SDAs on MNIST~\citep{VincentPLarochelleH2008}. The size of the hidden | |
| 809 layers was kept constant across hidden layers, and the best results | |
| 810 were obtained with the largest values that we could experiment | |
| 811 with given our patience, with 1000 hidden units. | |
| 812 | |
| 813 %\vspace*{-1mm} | |
| 814 | |
| 815 \begin{figure}[ht] | |
| 816 %\vspace*{-2mm} | |
| 817 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}} | |
| 818 %\vspace*{-3mm} | |
| 819 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained | |
| 820 on NIST, 1 on NISTP, and 2 on P07. Left: overall results | |
| 821 of all models, on NIST and NISTP test sets. | |
| 822 Right: error rates on NIST test digits only, along with the previous results from | |
| 823 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005} | |
| 824 respectively based on ART, nearest neighbors, MLPs, and SVMs.} | |
| 825 \label{fig:error-rates-charts} | |
| 826 %\vspace*{-2mm} | |
| 827 \end{figure} | |
| 828 | |
| 829 | |
| 830 \begin{figure}[ht] | |
| 831 %\vspace*{-3mm} | |
| 832 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}} | |
| 833 %\vspace*{-3mm} | |
| 834 \caption{Relative improvement in error rate due to self-taught learning. | |
| 835 Left: Improvement (or loss, when negative) | |
| 836 induced by out-of-distribution examples (perturbed data). | |
| 837 Right: Improvement (or loss, when negative) induced by multi-task | |
| 838 learning (training on all classes and testing only on either digits, | |
| 839 upper case, or lower-case). The deep learner (SDA) benefits more from | |
| 840 both self-taught learning scenarios, compared to the shallow MLP.} | |
| 841 \label{fig:improvements-charts} | |
| 842 %\vspace*{-2mm} | |
| 843 \end{figure} | |
| 844 | |
| 845 \section{Experimental Results} | |
| 846 %\vspace*{-2mm} | |
| 847 | |
| 848 %%\vspace*{-1mm} | |
| 849 %\subsection{SDA vs MLP vs Humans} | |
| 850 %%\vspace*{-1mm} | |
| 851 The models are either trained on NIST (MLP0 and SDA0), | |
| 852 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested | |
| 853 on either NIST, NISTP or P07, either on the 62-class task | |
| 854 or on the 10-digits task. Training (including about half | |
| 855 for unsupervised pre-training, for DAs) on the larger | |
| 856 datasets takes around one day on a GPU-285. | |
| 857 Figure~\ref{fig:error-rates-charts} summarizes the results obtained, | |
| 858 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1, | |
| 859 SDA2), along with the previous results on the digits NIST special database | |
| 860 19 test set from the literature, respectively based on ARTMAP neural | |
| 861 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search | |
| 862 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs | |
| 863 ~\citep{Milgram+al-2005}. More detailed and complete numerical results | |
| 864 (figures and tables, including standard errors on the error rates) can be | |
| 865 found in Appendix. | |
| 866 The deep learner not only outperformed the shallow ones and | |
| 867 previously published performance (in a statistically and qualitatively | |
| 868 significant way) but when trained with perturbed data | |
| 869 reaches human performance on both the 62-class task | |
| 870 and the 10-class (digits) task. | |
| 871 17\% error (SDA1) or 18\% error (humans) may seem large but a large | |
| 872 majority of the errors from humans and from SDA1 are from out-of-context | |
| 873 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a | |
| 874 ``c'' and a ``C'' are often indistinguishible). | |
| 875 | |
| 876 In addition, as shown in the left of | |
| 877 Figure~\ref{fig:improvements-charts}, the relative improvement in error | |
| 878 rate brought by self-taught learning is greater for the SDA, and these | |
| 879 differences with the MLP are statistically and qualitatively | |
| 880 significant. | |
| 881 The left side of the figure shows the improvement to the clean | |
| 882 NIST test set error brought by the use of out-of-distribution examples | |
| 883 (i.e. the perturbed examples examples from NISTP or P07). | |
| 884 Relative percent change is measured by taking | |
| 885 $100 \% \times$ (original model's error / perturbed-data model's error - 1). | |
| 886 The right side of | |
| 887 Figure~\ref{fig:improvements-charts} shows the relative improvement | |
| 888 brought by the use of a multi-task setting, in which the same model is | |
| 889 trained for more classes than the target classes of interest (i.e. training | |
| 890 with all 62 classes when the target classes are respectively the digits, | |
| 891 lower-case, or upper-case characters). Again, whereas the gain from the | |
| 892 multi-task setting is marginal or negative for the MLP, it is substantial | |
| 893 for the SDA. Note that to simplify these multi-task experiments, only the original | |
| 894 NIST dataset is used. For example, the MLP-digits bar shows the relative | |
| 895 percent improvement in MLP error rate on the NIST digits test set | |
| 896 is $100\% \times$ (single-task | |
| 897 model's error / multi-task model's error - 1). The single-task model is | |
| 898 trained with only 10 outputs (one per digit), seeing only digit examples, | |
| 899 whereas the multi-task model is trained with 62 outputs, with all 62 | |
| 900 character classes as examples. Hence the hidden units are shared across | |
| 901 all tasks. For the multi-task model, the digit error rate is measured by | |
| 902 comparing the correct digit class with the output class associated with the | |
| 903 maximum conditional probability among only the digit classes outputs. The | |
| 904 setting is similar for the other two target classes (lower case characters | |
| 905 and upper case characters). | |
| 906 %%\vspace*{-1mm} | |
| 907 %\subsection{Perturbed Training Data More Helpful for SDA} | |
| 908 %%\vspace*{-1mm} | |
| 909 | |
| 910 %%\vspace*{-1mm} | |
| 911 %\subsection{Multi-Task Learning Effects} | |
| 912 %%\vspace*{-1mm} | |
| 913 | |
| 914 \iffalse | |
| 915 As previously seen, the SDA is better able to benefit from the | |
| 916 transformations applied to the data than the MLP. In this experiment we | |
| 917 define three tasks: recognizing digits (knowing that the input is a digit), | |
| 918 recognizing upper case characters (knowing that the input is one), and | |
| 919 recognizing lower case characters (knowing that the input is one). We | |
| 920 consider the digit classification task as the target task and we want to | |
| 921 evaluate whether training with the other tasks can help or hurt, and | |
| 922 whether the effect is different for MLPs versus SDAs. The goal is to find | |
| 923 out if deep learning can benefit more (or less) from multiple related tasks | |
| 924 (i.e. the multi-task setting) compared to a corresponding purely supervised | |
| 925 shallow learner. | |
| 926 | |
| 927 We use a single hidden layer MLP with 1000 hidden units, and a SDA | |
| 928 with 3 hidden layers (1000 hidden units per layer), pre-trained and | |
| 929 fine-tuned on NIST. | |
| 930 | |
| 931 Our results show that the MLP benefits marginally from the multi-task setting | |
| 932 in the case of digits (5\% relative improvement) but is actually hurt in the case | |
| 933 of characters (respectively 3\% and 4\% worse for lower and upper class characters). | |
| 934 On the other hand the SDA benefited from the multi-task setting, with relative | |
| 935 error rate improvements of 27\%, 15\% and 13\% respectively for digits, | |
| 936 lower and upper case characters, as shown in Table~\ref{tab:multi-task}. | |
| 937 \fi | |
| 938 | |
| 939 | |
| 940 %\vspace*{-2mm} | |
| 941 \section{Conclusions and Discussion} | |
| 942 %\vspace*{-2mm} | |
| 943 | |
| 944 We have found that the self-taught learning framework is more beneficial | |
| 945 to a deep learner than to a traditional shallow and purely | |
| 946 supervised learner. More precisely, | |
| 947 the answers are positive for all the questions asked in the introduction. | |
| 948 %\begin{itemize} | |
| 949 | |
| 950 $\bullet$ %\item | |
| 951 {\bf Do the good results previously obtained with deep architectures on the | |
| 952 MNIST digits generalize to a much larger and richer (but similar) | |
| 953 dataset, the NIST special database 19, with 62 classes and around 800k examples}? | |
| 954 Yes, the SDA {\em systematically outperformed the MLP and all the previously | |
| 955 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level | |
| 956 performance} at around 17\% error on the 62-class task and 1.4\% on the digits, | |
| 957 and beating previously published results on the same data. | |
| 958 | |
| 959 $\bullet$ %\item | |
| 960 {\bf To what extent do self-taught learning scenarios help deep learners, | |
| 961 and do they help them more than shallow supervised ones}? | |
| 962 We found that distorted training examples not only made the resulting | |
| 963 classifier better on similarly perturbed images but also on | |
| 964 the {\em original clean examples}, and more importantly and more novel, | |
| 965 that deep architectures benefit more from such {\em out-of-distribution} | |
| 966 examples. MLPs were helped by perturbed training examples when tested on perturbed input | |
| 967 images (65\% relative improvement on NISTP) | |
| 968 but only marginally helped (5\% relative improvement on all classes) | |
| 969 or even hurt (10\% relative loss on digits) | |
| 970 with respect to clean examples . On the other hand, the deep SDAs | |
| 971 were significantly boosted by these out-of-distribution examples. | |
| 972 Similarly, whereas the improvement due to the multi-task setting was marginal or | |
| 973 negative for the MLP (from +5.6\% to -3.6\% relative change), | |
| 974 it was quite significant for the SDA (from +13\% to +27\% relative change), | |
| 975 which may be explained by the arguments below. | |
| 976 %\end{itemize} | |
| 977 | |
| 978 In the original self-taught learning framework~\citep{RainaR2007}, the | |
| 979 out-of-sample examples were used as a source of unsupervised data, and | |
| 980 experiments showed its positive effects in a \emph{limited labeled data} | |
| 981 scenario. However, many of the results by \citet{RainaR2007} (who used a | |
| 982 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught | |
| 983 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases. | |
| 984 We note instead that, for deep | |
| 985 architectures, our experiments show that such a positive effect is accomplished | |
| 986 even in a scenario with a \emph{large number of labeled examples}, | |
| 987 i.e., here, the relative gain of self-taught learning is probably preserved | |
| 988 in the asymptotic regime. | |
| 989 | |
| 990 {\bf Why would deep learners benefit more from the self-taught learning framework}? | |
| 991 The key idea is that the lower layers of the predictor compute a hierarchy | |
| 992 of features that can be shared across tasks or across variants of the | |
| 993 input distribution. A theoretical analysis of generalization improvements | |
| 994 due to sharing of intermediate features across tasks already points | |
| 995 towards that explanation~\cite{baxter95a}. | |
| 996 Intermediate features that can be used in different | |
| 997 contexts can be estimated in a way that allows to share statistical | |
| 998 strength. Features extracted through many levels are more likely to | |
| 999 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest), | |
| 1000 increasing the likelihood that they would be useful for a larger array | |
| 1001 of tasks and input conditions. | |
| 1002 Therefore, we hypothesize that both depth and unsupervised | |
| 1003 pre-training play a part in explaining the advantages observed here, and future | |
| 1004 experiments could attempt at teasing apart these factors. | |
| 1005 And why would deep learners benefit from the self-taught learning | |
| 1006 scenarios even when the number of labeled examples is very large? | |
| 1007 We hypothesize that this is related to the hypotheses studied | |
| 1008 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010} | |
| 1009 it was found that online learning on a huge dataset did not make the | |
| 1010 advantage of the deep learning bias vanish, a similar phenomenon | |
| 1011 may be happening here. We hypothesize that unsupervised pre-training | |
| 1012 of a deep hierarchy with self-taught learning initializes the | |
| 1013 model in the basin of attraction of supervised gradient descent | |
| 1014 that corresponds to better generalization. Furthermore, such good | |
| 1015 basins of attraction are not discovered by pure supervised learning | |
| 1016 (with or without self-taught settings), and more labeled examples | |
| 1017 does not allow the model to go from the poorer basins of attraction discovered | |
| 1018 by the purely supervised shallow models to the kind of better basins associated | |
| 1019 with deep learning and self-taught learning. | |
| 1020 | |
| 1021 A Flash demo of the recognizer (where both the MLP and the SDA can be compared) | |
| 1022 can be executed on-line at {\tt http://deep.host22.com}. | |
| 1023 | |
| 1024 | |
| 1025 \section*{Appendix I: Detailed Numerical Results} | |
| 1026 | |
| 1027 These tables correspond to Figures 2 and 3 and contain the raw error rates for each model and dataset considered. | |
| 1028 They also contain additional data such as test errors on P07 and standard errors. | |
| 1029 | |
| 1030 \begin{table}[ht] | |
| 1031 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits + | |
| 1032 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training | |
| 1033 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture | |
| 1034 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07) | |
| 1035 and using a validation set to select hyper-parameters and other training choices. | |
| 1036 \{SDA,MLP\}0 are trained on NIST, | |
| 1037 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07. | |
| 1038 The human error rate on digits is a lower bound because it does not count digits that were | |
| 1039 recognized as letters. For comparison, the results found in the literature | |
| 1040 on NIST digits classification using the same test set are included.} | |
| 1041 \label{tab:sda-vs-mlp-vs-humans} | |
| 1042 \begin{center} | |
| 1043 \begin{tabular}{|l|r|r|r|r|} \hline | |
| 1044 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 1045 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline | |
| 1046 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline | |
| 1047 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline | |
| 1048 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline | |
| 1049 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline | |
| 1050 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline | |
| 1051 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline | |
| 1052 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline | |
| 1053 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline | |
| 1054 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline | |
| 1055 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline | |
| 1056 \end{tabular} | |
| 1057 \end{center} | |
| 1058 \end{table} | |
| 1059 | |
| 1060 \begin{table}[ht] | |
| 1061 \caption{Relative change in error rates due to the use of perturbed training data, | |
| 1062 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models. | |
| 1063 A positive value indicates that training on the perturbed data helped for the | |
| 1064 given test set (the first 3 columns on the 62-class tasks and the last one is | |
| 1065 on the clean 10-class digits). Clearly, the deep learning models did benefit more | |
| 1066 from perturbed training data, even when testing on clean data, whereas the MLP | |
| 1067 trained on perturbed data performed worse on the clean digits and about the same | |
| 1068 on the clean characters. } | |
| 1069 \label{tab:perturbation-effect} | |
| 1070 \begin{center} | |
| 1071 \begin{tabular}{|l|r|r|r|r|} \hline | |
| 1072 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 1073 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline | |
| 1074 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline | |
| 1075 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline | |
| 1076 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline | |
| 1077 \end{tabular} | |
| 1078 \end{center} | |
| 1079 \end{table} | |
| 1080 | |
| 1081 \begin{table}[ht] | |
| 1082 \caption{Test error rates and relative change in error rates due to the use of | |
| 1083 a multi-task setting, i.e., training on each task in isolation vs training | |
| 1084 for all three tasks together, for MLPs vs SDAs. The SDA benefits much | |
| 1085 more from the multi-task setting. All experiments on only on the | |
| 1086 unperturbed NIST data, using validation error for model selection. | |
| 1087 Relative improvement is 1 - single-task error / multi-task error.} | |
| 1088 \label{tab:multi-task} | |
| 1089 \begin{center} | |
| 1090 \begin{tabular}{|l|r|r|r|} \hline | |
| 1091 & single-task & multi-task & relative \\ | |
| 1092 & setting & setting & improvement \\ \hline | |
| 1093 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline | |
| 1094 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline | |
| 1095 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline | |
| 1096 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline | |
| 1097 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline | |
| 1098 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline | |
| 1099 \end{tabular} | |
| 1100 \end{center} | |
| 1101 \end{table} | |
| 1102 | |
| 1103 %\afterpage{\clearpage} | |
| 1104 \clearpage | |
| 1105 { | |
| 1106 %\bibliographystyle{spbasic} % basic style, author-year citations | |
| 1107 \bibliographystyle{plainnat} | |
| 1108 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,specials,aigaion-shorter} | |
| 1109 %\bibliographystyle{unsrtnat} | |
| 1110 %\bibliographystyle{apalike} | |
| 1111 } | |
| 1112 | |
| 1113 | |
| 1114 \end{document} |