Mercurial > ift6266
comparison writeup/nipswp_submission.tex @ 597:5ab605c9a7d9
NIPS deep learning workshop submission new .tex file compressed to 8 pages
| author | boulanni <nicolas_boulanger@hotmail.com> |
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| date | Thu, 14 Oct 2010 18:04:11 -0400 |
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| 1 %\documentclass[twoside,11pt]{article} % For LaTeX2e | |
| 2 \documentclass{article} % For LaTeX2e | |
| 3 \usepackage{nips10submit_e} | |
| 4 \usepackage{times} | |
| 5 \usepackage{wrapfig} | |
| 6 \usepackage{amsthm} | |
| 7 \usepackage{amsmath} | |
| 8 \usepackage{bbm} | |
| 9 \usepackage[utf8]{inputenc} | |
| 10 \usepackage[psamsfonts]{amssymb} | |
| 11 %\usepackage{algorithm,algorithmic} % not used after all | |
| 12 \usepackage{graphicx,subfigure} | |
| 13 \usepackage[numbers]{natbib} | |
| 14 | |
| 15 \addtolength{\textwidth}{10mm} | |
| 16 \addtolength{\evensidemargin}{-5mm} | |
| 17 \addtolength{\oddsidemargin}{-5mm} | |
| 18 | |
| 19 %\setlength\parindent{0mm} | |
| 20 | |
| 21 \begin{document} | |
| 22 | |
| 23 \title{Deep Self-Taught Learning for Handwritten Character Recognition} | |
| 24 \author{ | |
| 25 Yoshua Bengio \and | |
| 26 Frédéric Bastien \and | |
| 27 Arnaud Bergeron \and | |
| 28 Nicolas Boulanger-Lewandowski \and | |
| 29 Thomas Breuel \and | |
| 30 Youssouf Chherawala \and | |
| 31 Moustapha Cisse \and | |
| 32 Myriam Côté \and | |
| 33 Dumitru Erhan \and | |
| 34 Jeremy Eustache \and | |
| 35 Xavier Glorot \and | |
| 36 Xavier Muller \and | |
| 37 Sylvain Pannetier Lebeuf \and | |
| 38 Razvan Pascanu \and | |
| 39 Salah Rifai \and | |
| 40 Francois Savard \and | |
| 41 Guillaume Sicard | |
| 42 } | |
| 43 \date{{\tt bengioy@iro.umontreal.ca}, Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada} | |
| 44 %\jmlrheading{}{2010}{}{10/2010}{XX/2011}{Yoshua Bengio et al} | |
| 45 %\editor{} | |
| 46 | |
| 47 %\makeanontitle | |
| 48 \maketitle | |
| 49 | |
| 50 %{\bf Running title: Deep Self-Taught Learning} | |
| 51 | |
| 52 \vspace*{-2mm} | |
| 53 \begin{abstract} | |
| 54 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 a large-scale handwritten character recognition setting. In fact, we show that they {\em beat previously published results and reach human-level performance}. | |
| 55 \end{abstract} | |
| 56 \vspace*{-3mm} | |
| 57 | |
| 58 %\begin{keywords} | |
| 59 %Deep learning, self-taught learning, out-of-distribution examples, handwritten character recognition, multi-task learning | |
| 60 %\end{keywords} | |
| 61 %\keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition} | |
| 62 | |
| 63 | |
| 64 | |
| 65 \section{Introduction} | |
| 66 \vspace*{-1mm} | |
| 67 | |
| 68 {\bf Deep Learning} has emerged as a promising new area of research in | |
| 69 statistical machine learning~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,VincentPLarochelleH2008,ranzato-08,TaylorHintonICML2009,Larochelle-jmlr-2009,Salakhutdinov+Hinton-2009,HonglakL2009,HonglakLNIPS2009,Jarrett-ICCV2009,Taylor-cvpr-2010}. See \citet{Bengio-2009} for a review. | |
| 70 Learning algorithms for deep architectures are centered on the learning | |
| 71 of useful representations of data, which are better suited to the task at hand, | |
| 72 and are organized in a hierarchy with multiple levels. | |
| 73 This is in part inspired by observations of the mammalian visual cortex, | |
| 74 which consists of a chain of processing elements, each of which is associated with a | |
| 75 different representation of the raw visual input. In fact, | |
| 76 it was found recently that the features learnt in deep architectures resemble | |
| 77 those observed in the first two of these stages (in areas V1 and V2 | |
| 78 of visual cortex) \citep{HonglakL2008}, and that they become more and | |
| 79 more invariant to factors of variation (such as camera movement) in | |
| 80 higher layers~\citep{Goodfellow2009}. | |
| 81 Learning a hierarchy of features increases the | |
| 82 ease and practicality of developing representations that are at once | |
| 83 tailored to specific tasks, yet are able to borrow statistical strength | |
| 84 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the | |
| 85 feature representation can lead to higher-level (more abstract, more | |
| 86 general) features that are more robust to unanticipated sources of | |
| 87 variance extant in real data. | |
| 88 | |
| 89 {\bf Self-taught learning}~\citep{RainaR2007} is a paradigm that combines principles | |
| 90 of semi-supervised and multi-task learning: the learner can exploit examples | |
| 91 that are unlabeled and possibly come from a distribution different from the target | |
| 92 distribution, e.g., from other classes than those of interest. | |
| 93 It has already been shown that deep learners can clearly take advantage of | |
| 94 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small}, | |
| 95 but more needs to be done to explore the impact | |
| 96 of {\em out-of-distribution} examples and of the {\em multi-task} setting | |
| 97 (one exception is~\citep{CollobertR2008}, which uses a different kind | |
| 98 of learning algorithm). In particular the {\em relative | |
| 99 advantage of deep learning} for these settings has not been evaluated. | |
| 100 The hypothesis discussed in the conclusion is that in the context of | |
| 101 multi-task learning and the availability of out-of-distribution training examples, | |
| 102 a deep hierarchy of features | |
| 103 may be better able to provide {\em sharing of statistical strength} | |
| 104 between different regions in input space or different tasks, compared to | |
| 105 a shallow learner. | |
| 106 | |
| 107 \iffalse | |
| 108 Whereas a deep architecture can in principle be more powerful than a | |
| 109 shallow one in terms of representation, depth appears to render the | |
| 110 training problem more difficult in terms of optimization and local minima. | |
| 111 It is also only recently that successful algorithms were proposed to | |
| 112 overcome some of these difficulties. All are based on unsupervised | |
| 113 learning, often in an greedy layer-wise ``unsupervised pre-training'' | |
| 114 stage~\citep{Bengio-2009}. One of these layer initialization techniques, | |
| 115 applied here, is the Denoising | |
| 116 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}), | |
| 117 which | |
| 118 performed similarly or better than previously proposed Restricted Boltzmann | |
| 119 Machines in terms of unsupervised extraction of a hierarchy of features | |
| 120 useful for classification. Each layer is trained to denoise its | |
| 121 input, creating a layer of features that can be used as input for the next layer. | |
| 122 \fi | |
| 123 | |
| 124 %The principle is that each layer starting from | |
| 125 %the bottom is trained to encode its input (the output of the previous | |
| 126 %layer) and to reconstruct it from a corrupted version. After this | |
| 127 %unsupervised initialization, the stack of DAs can be | |
| 128 %converted into a deep supervised feedforward neural network and fine-tuned by | |
| 129 %stochastic gradient descent. | |
| 130 | |
| 131 % | |
| 132 The {\bf main claim} of this paper is that deep learners (with several levels of representation) can | |
| 133 {\bf benefit more from self-taught learning than shallow learners} (with a single | |
| 134 level), both in the context of the multi-task setting and from {\em | |
| 135 out-of-distribution examples} in general. Because we are able to improve on state-of-the-art | |
| 136 performance and reach human-level performance | |
| 137 on a large-scale task, we consider that this paper is also a contribution | |
| 138 to advance the application of machine learning to handwritten character recognition. | |
| 139 More precisely, we ask and answer the following questions: | |
| 140 | |
| 141 %\begin{enumerate} | |
| 142 $\bullet$ %\item | |
| 143 Do the good results previously obtained with deep architectures on the | |
| 144 MNIST digit images generalize to the setting of a similar but much larger and richer | |
| 145 dataset, the NIST special database 19, with 62 classes and around 800k examples? | |
| 146 | |
| 147 $\bullet$ %\item | |
| 148 To what extent does the perturbation of input images (e.g. adding | |
| 149 noise, affine transformations, background images) make the resulting | |
| 150 classifiers better not only on similarly perturbed images but also on | |
| 151 the {\em original clean examples}? We study this question in the | |
| 152 context of the 62-class and 10-class tasks of the NIST special database 19. | |
| 153 | |
| 154 $\bullet$ %\item | |
| 155 Do deep architectures {\em benefit {\bf more} from such out-of-distribution} | |
| 156 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework? | |
| 157 We use highly perturbed examples to generate out-of-distribution examples. | |
| 158 | |
| 159 $\bullet$ %\item | |
| 160 Similarly, does the feature learning step in deep learning algorithms benefit {\bf more} | |
| 161 from training with moderately {\em different classes} (i.e. a multi-task learning scenario) than | |
| 162 a corresponding shallow and purely supervised architecture? | |
| 163 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case) | |
| 164 to answer this question. | |
| 165 %\end{enumerate} | |
| 166 | |
| 167 Our experimental results provide positive evidence towards all of these questions, | |
| 168 as well as {\em classifiers that reach human-level performance on 62-class isolated character | |
| 169 recognition and beat previously published results on the NIST dataset (special database 19)}. | |
| 170 To achieve these results, we introduce in the next section a sophisticated system | |
| 171 for stochastically transforming character images and then explain the methodology, | |
| 172 which is based on training with or without these transformed images and testing on | |
| 173 clean ones. We measure the relative advantage of out-of-distribution examples | |
| 174 (perturbed or out-of-class) | |
| 175 for a deep learner vs a supervised shallow one. | |
| 176 Code for generating these transformations as well as for the deep learning | |
| 177 algorithms are made available at {\tt http://hg.assembla.com/ift6266}. | |
| 178 We also estimate the relative advantage for deep learners of training with | |
| 179 other classes than those of interest, by comparing learners trained with | |
| 180 62 classes with learners trained with only a subset (on which they | |
| 181 are then tested). | |
| 182 The conclusion discusses | |
| 183 the more general question of why deep learners may benefit so much from | |
| 184 the self-taught learning framework. Since out-of-distribution data | |
| 185 (perturbed or from other related classes) is very common, this conclusion | |
| 186 is of practical importance. | |
| 187 | |
| 188 \vspace*{-3mm} | |
| 189 %\newpage | |
| 190 \section{Perturbed and Transformed Character Images} | |
| 191 \label{s:perturbations} | |
| 192 \vspace*{-2mm} | |
| 193 | |
| 194 Figure~\ref{fig:transform} shows the different transformations we used to stochastically | |
| 195 transform $32 \times 32$ source images (such as the one in Fig.\ref{fig:torig}) | |
| 196 in order to obtain data from a larger distribution which | |
| 197 covers a domain substantially larger than the clean characters distribution from | |
| 198 which we start. | |
| 199 Although character transformations have been used before to | |
| 200 improve character recognizers, this effort is on a large scale both | |
| 201 in number of classes and in the complexity of the transformations, hence | |
| 202 in the complexity of the learning task. | |
| 203 The code for these transformations (mostly python) is available at | |
| 204 {\tt http://anonymous.url.net}. All the modules in the pipeline share | |
| 205 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the | |
| 206 amount of deformation or noise introduced. | |
| 207 There are two main parts in the pipeline. The first one, | |
| 208 from slant to pinch below, performs transformations. The second | |
| 209 part, from blur to contrast, adds different kinds of noise. | |
| 210 More details can be found in~\citep{ift6266-tr-anonymous}. | |
| 211 | |
| 212 \begin{figure}[ht] | |
| 213 \centering | |
| 214 \subfigure[Original]{\includegraphics[scale=0.6]{images/Original.png}\label{fig:torig}} | |
| 215 \subfigure[Thickness]{\includegraphics[scale=0.6]{images/Thick_only.png}} | |
| 216 \subfigure[Slant]{\includegraphics[scale=0.6]{images/Slant_only.png}} | |
| 217 \subfigure[Affine Transformation]{\includegraphics[scale=0.6]{images/Affine_only.png}} | |
| 218 \subfigure[Local Elastic Deformation]{\includegraphics[scale=0.6]{images/Localelasticdistorsions_only.png}} | |
| 219 \subfigure[Pinch]{\includegraphics[scale=0.6]{images/Pinch_only.png}} | |
| 220 %Noise | |
| 221 \subfigure[Motion Blur]{\includegraphics[scale=0.6]{images/Motionblur_only.png}} | |
| 222 \subfigure[Occlusion]{\includegraphics[scale=0.6]{images/occlusion_only.png}} | |
| 223 \subfigure[Gaussian Smoothing]{\includegraphics[scale=0.6]{images/Bruitgauss_only.png}} | |
| 224 \subfigure[Pixels Permutation]{\includegraphics[scale=0.6]{images/Permutpixel_only.png}} | |
| 225 \subfigure[Gaussian Noise]{\includegraphics[scale=0.6]{images/Distorsiongauss_only.png}} | |
| 226 \subfigure[Background Image Addition]{\includegraphics[scale=0.6]{images/background_other_only.png}} | |
| 227 \subfigure[Salt \& Pepper]{\includegraphics[scale=0.6]{images/Poivresel_only.png}} | |
| 228 \subfigure[Scratches]{\includegraphics[scale=0.6]{images/Rature_only.png}} | |
| 229 \subfigure[Grey Level \& Contrast]{\includegraphics[scale=0.6]{images/Contrast_only.png}} | |
| 230 \caption{Transformation modules} | |
| 231 \label{fig:transform} | |
| 232 \vspace*{-2mm} | |
| 233 \end{figure} | |
| 234 | |
| 235 \vspace*{-3mm} | |
| 236 \section{Experimental Setup} | |
| 237 \vspace*{-1mm} | |
| 238 | |
| 239 Much previous work on deep learning had been performed on | |
| 240 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009}, | |
| 241 with 60~000 examples, and variants involving 10~000 | |
| 242 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}. | |
| 243 The focus here is on much larger training sets, from 10 times to | |
| 244 to 1000 times larger, and 62 classes. | |
| 245 | |
| 246 The first step in constructing the larger datasets (called NISTP and P07) is to sample from | |
| 247 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas}, | |
| 248 and {\bf OCR data} (scanned machine printed characters). Once a character | |
| 249 is sampled from one of these sources (chosen randomly), the second step is to | |
| 250 apply a pipeline of transformations and/or noise processes described in section \ref{s:perturbations}. | |
| 251 | |
| 252 To provide a baseline of error rate comparison we also estimate human performance | |
| 253 on both the 62-class task and the 10-class digits task. | |
| 254 We compare the best Multi-Layer Perceptrons (MLP) against | |
| 255 the best Stacked Denoising Auto-encoders (SDA), when | |
| 256 both models' hyper-parameters are selected to minimize the validation set error. | |
| 257 We also provide a comparison against a precise estimate | |
| 258 of human performance obtained via Amazon's Mechanical Turk (AMT) | |
| 259 service (http://mturk.com). | |
| 260 AMT users are paid small amounts | |
| 261 of money to perform tasks for which human intelligence is required. | |
| 262 Mechanical Turk has been used extensively in natural language processing and vision. | |
| 263 %processing \citep{SnowEtAl2008} and vision | |
| 264 %\citep{SorokinAndForsyth2008,whitehill09}. | |
| 265 AMT users were presented | |
| 266 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII | |
| 267 characters. They were forced to choose a single character class (either among the | |
| 268 62 or 10 character classes) for each image. | |
| 269 80 subjects classified 2500 images per (dataset,task) pair. | |
| 270 Different humans labelers sometimes provided a different label for the same | |
| 271 example, and we were able to estimate the error variance due to this effect | |
| 272 because each image was classified by 3 different persons. | |
| 273 The average error of humans on the 62-class task NIST test set | |
| 274 is 18.2\%, with a standard error of 0.1\%. | |
| 275 | |
| 276 \vspace*{-3mm} | |
| 277 \subsection{Data Sources} | |
| 278 \vspace*{-2mm} | |
| 279 | |
| 280 %\begin{itemize} | |
| 281 %\item | |
| 282 {\bf NIST.} | |
| 283 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995}, | |
| 284 widely used for training and testing character | |
| 285 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}. | |
| 286 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications, | |
| 287 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes | |
| 288 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity. | |
| 289 The fourth partition (called $hsf_4$, 82587 examples), | |
| 290 experimentally recognized to be the most difficult one, is the one recommended | |
| 291 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} | |
| 292 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for | |
| 293 model selection. | |
| 294 The performances reported by previous work on that dataset mostly use only the digits. | |
| 295 Here we use all the classes both in the training and testing phase. This is especially | |
| 296 useful to estimate the effect of a multi-task setting. | |
| 297 The distribution of the classes in the NIST training and test sets differs | |
| 298 substantially, with relatively many more digits in the test set, and a more uniform distribution | |
| 299 of letters in the test set (whereas in the training set they are distributed | |
| 300 more like in natural text). | |
| 301 %\vspace*{-1mm} | |
| 302 | |
| 303 %\item | |
| 304 {\bf Fonts.} | |
| 305 In order to have a good variety of sources we downloaded an important number of free fonts from: | |
| 306 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}. | |
| 307 % TODO: pointless to anonymize, it's not pointing to our work | |
| 308 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from. | |
| 309 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image, | |
| 310 directly as input to our models. | |
| 311 \vspace*{-1mm} | |
| 312 | |
| 313 %\item | |
| 314 {\bf Captchas.} | |
| 315 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for | |
| 316 generating characters of the same format as the NIST dataset. This software is based on | |
| 317 a random character class generator and various kinds of transformations similar to those described in the previous sections. | |
| 318 In order to increase the variability of the data generated, many different fonts are used for generating the characters. | |
| 319 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity | |
| 320 depending on the value of the complexity parameter provided by the user of the data source. | |
| 321 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class? | |
| 322 \vspace*{-1mm} | |
| 323 | |
| 324 %\item | |
| 325 {\bf OCR data.} | |
| 326 A large set (2 million) of scanned, OCRed and manually verified machine-printed | |
| 327 characters where included as an | |
| 328 additional source. This set is part of a larger corpus being collected by the Image Understanding | |
| 329 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern | |
| 330 ({\tt http://www.iupr.com}), and which will be publicly released. | |
| 331 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this | |
| 332 %\end{itemize} | |
| 333 | |
| 334 \vspace*{-3mm} | |
| 335 \subsection{Data Sets} | |
| 336 \vspace*{-2mm} | |
| 337 | |
| 338 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label | |
| 339 from one of the 62 character classes. | |
| 340 %\begin{itemize} | |
| 341 \vspace*{-1mm} | |
| 342 | |
| 343 %\item | |
| 344 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has | |
| 345 \{651668 / 80000 / 82587\} \{training / validation / test\} examples. | |
| 346 \vspace*{-1mm} | |
| 347 | |
| 348 %\item | |
| 349 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources | |
| 350 and sending them through the transformation pipeline described in section \ref{s:perturbations}. | |
| 351 For each new example to generate, a data source is selected with probability $10\%$ from the fonts, | |
| 352 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the | |
| 353 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$. | |
| 354 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples. | |
| 355 \vspace*{-1mm} | |
| 356 | |
| 357 %\item | |
| 358 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources) | |
| 359 except that we only apply | |
| 360 transformations from slant to pinch. Therefore, the character is | |
| 361 transformed but no additional noise is added to the image, giving images | |
| 362 closer to the NIST dataset. | |
| 363 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples. | |
| 364 %\end{itemize} | |
| 365 | |
| 366 \vspace*{-3mm} | |
| 367 \subsection{Models and their Hyperparameters} | |
| 368 \vspace*{-2mm} | |
| 369 | |
| 370 The experiments are performed using MLPs (with a single | |
| 371 hidden layer) and SDAs. | |
| 372 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.} | |
| 373 | |
| 374 {\bf Multi-Layer Perceptrons (MLP).} | |
| 375 Whereas previous work had compared deep architectures to both shallow MLPs and | |
| 376 SVMs, we only compared to MLPs here because of the very large datasets used | |
| 377 (making the use of SVMs computationally challenging because of their quadratic | |
| 378 scaling behavior). Preliminary experiments on training SVMs (libSVM) with subsets of the training | |
| 379 set allowing the program to fit in memory yielded substantially worse results | |
| 380 than those obtained with MLPs. For training on nearly a billion examples | |
| 381 (with the perturbed data), the MLPs and SDA are much more convenient than | |
| 382 classifiers based on kernel methods. | |
| 383 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized | |
| 384 exponentials) on the output layer for estimating $P(class | image)$. | |
| 385 The number of hidden units is taken in $\{300,500,800,1000,1500\}$. | |
| 386 Training examples are presented in minibatches of size 20. A constant learning | |
| 387 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$. | |
| 388 %through preliminary experiments (measuring performance on a validation set), | |
| 389 %and $0.1$ (which was found to work best) was then selected for optimizing on | |
| 390 %the whole training sets. | |
| 391 \vspace*{-1mm} | |
| 392 | |
| 393 | |
| 394 {\bf Stacked Denoising Auto-Encoders (SDA).} | |
| 395 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs) | |
| 396 can be used to initialize the weights of each layer of a deep MLP (with many hidden | |
| 397 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006}, | |
| 398 apparently setting parameters in the | |
| 399 basin of attraction of supervised gradient descent yielding better | |
| 400 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised | |
| 401 pre-training phase} uses all of the training images but not the training labels. | |
| 402 Each layer is trained in turn to produce a new representation of its input | |
| 403 (starting from the raw pixels). | |
| 404 It is hypothesized that the | |
| 405 advantage brought by this procedure stems from a better prior, | |
| 406 on the one hand taking advantage of the link between the input | |
| 407 distribution $P(x)$ and the conditional distribution of interest | |
| 408 $P(y|x)$ (like in semi-supervised learning), and on the other hand | |
| 409 taking advantage of the expressive power and bias implicit in the | |
| 410 deep architecture (whereby complex concepts are expressed as | |
| 411 compositions of simpler ones through a deep hierarchy). | |
| 412 | |
| 413 \begin{figure}[ht] | |
| 414 \vspace*{-2mm} | |
| 415 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}} | |
| 416 \vspace*{-2mm} | |
| 417 \caption{Illustration of the computations and training criterion for the denoising | |
| 418 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of | |
| 419 the layer (i.e. raw input or output of previous layer) | |
| 420 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$. | |
| 421 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which | |
| 422 is compared to the uncorrupted input $x$ through the loss function | |
| 423 $L_H(x,z)$, whose expected value is approximately minimized during training | |
| 424 by tuning $\theta$ and $\theta'$.} | |
| 425 \label{fig:da} | |
| 426 \vspace*{-2mm} | |
| 427 \end{figure} | |
| 428 | |
| 429 Here we chose to use the Denoising | |
| 430 Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for | |
| 431 these deep hierarchies of features, as it is simple to train and | |
| 432 explain (see Figure~\ref{fig:da}, as well as | |
| 433 tutorial and code there: {\tt http://deeplearning.net/tutorial}), | |
| 434 provides efficient inference, and yielded results | |
| 435 comparable or better than RBMs in series of experiments | |
| 436 \citep{VincentPLarochelleH2008}. During training, a Denoising | |
| 437 Auto-encoder is presented with a stochastically corrupted version | |
| 438 of the input and trained to reconstruct the uncorrupted input, | |
| 439 forcing the hidden units to represent the leading regularities in | |
| 440 the data. Here we use the random binary masking corruption | |
| 441 (which sets to 0 a random subset of the inputs). | |
| 442 Once it is trained, in a purely unsupervised way, | |
| 443 its hidden units' activations can | |
| 444 be used as inputs for training a second one, etc. | |
| 445 After this unsupervised pre-training stage, the parameters | |
| 446 are used to initialize a deep MLP, which is fine-tuned by | |
| 447 the same standard procedure used to train them (see previous section). | |
| 448 The SDA hyper-parameters are the same as for the MLP, with the addition of the | |
| 449 amount of corruption noise (we used the masking noise process, whereby a | |
| 450 fixed proportion of the input values, randomly selected, are zeroed), and a | |
| 451 separate learning rate for the unsupervised pre-training stage (selected | |
| 452 from the same above set). The fraction of inputs corrupted was selected | |
| 453 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number | |
| 454 of hidden layers but it was fixed to 3 based on previous work with | |
| 455 SDAs on MNIST~\citep{VincentPLarochelleH2008}. The size of the hidden | |
| 456 layers was kept constant across hidden layers, and the best results | |
| 457 were obtained with the largest values that we could experiment | |
| 458 with given our patience, with 1000 hidden units. | |
| 459 | |
| 460 \vspace*{-1mm} | |
| 461 | |
| 462 \begin{figure}[ht] | |
| 463 %\vspace*{-2mm} | |
| 464 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}} | |
| 465 %\vspace*{-3mm} | |
| 466 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained | |
| 467 on NIST, 1 on NISTP, and 2 on P07. Left: overall results | |
| 468 of all models, on NIST and NISTP test sets. | |
| 469 Right: error rates on NIST test digits only, along with the previous results from | |
| 470 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005} | |
| 471 respectively based on ART, nearest neighbors, MLPs, and SVMs.} | |
| 472 \label{fig:error-rates-charts} | |
| 473 \vspace*{-2mm} | |
| 474 \end{figure} | |
| 475 | |
| 476 | |
| 477 \begin{figure}[ht] | |
| 478 \vspace*{-3mm} | |
| 479 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}} | |
| 480 \vspace*{-3mm} | |
| 481 \caption{Relative improvement in error rate due to self-taught learning. | |
| 482 Left: Improvement (or loss, when negative) | |
| 483 induced by out-of-distribution examples (perturbed data). | |
| 484 Right: Improvement (or loss, when negative) induced by multi-task | |
| 485 learning (training on all classes and testing only on either digits, | |
| 486 upper case, or lower-case). The deep learner (SDA) benefits more from | |
| 487 both self-taught learning scenarios, compared to the shallow MLP.} | |
| 488 \label{fig:improvements-charts} | |
| 489 \vspace*{-2mm} | |
| 490 \end{figure} | |
| 491 | |
| 492 \section{Experimental Results} | |
| 493 \vspace*{-2mm} | |
| 494 | |
| 495 %%\vspace*{-1mm} | |
| 496 %\subsection{SDA vs MLP vs Humans} | |
| 497 %%\vspace*{-1mm} | |
| 498 The models are either trained on NIST (MLP0 and SDA0), | |
| 499 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested | |
| 500 on either NIST, NISTP or P07, either on the 62-class task | |
| 501 or on the 10-digits task. Training (including about half | |
| 502 for unsupervised pre-training, for DAs) on the larger | |
| 503 datasets takes around one day on a GPU-285. | |
| 504 Figure~\ref{fig:error-rates-charts} summarizes the results obtained, | |
| 505 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1, | |
| 506 SDA2), along with the previous results on the digits NIST special database | |
| 507 19 test set from the literature, respectively based on ARTMAP neural | |
| 508 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search | |
| 509 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs | |
| 510 ~\citep{Milgram+al-2005}.% More detailed and complete numerical results | |
| 511 %(figures and tables, including standard errors on the error rates) can be | |
| 512 %found in Appendix. | |
| 513 The deep learner not only outperformed the shallow ones and | |
| 514 previously published performance (in a statistically and qualitatively | |
| 515 significant way) but when trained with perturbed data | |
| 516 reaches human performance on both the 62-class task | |
| 517 and the 10-class (digits) task. | |
| 518 17\% error (SDA1) or 18\% error (humans) may seem large but a large | |
| 519 majority of the errors from humans and from SDA1 are from out-of-context | |
| 520 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a | |
| 521 ``c'' and a ``C'' are often indistinguishible). | |
| 522 | |
| 523 In addition, as shown in the left of | |
| 524 Figure~\ref{fig:improvements-charts}, the relative improvement in error | |
| 525 rate brought by self-taught learning is greater for the SDA, and these | |
| 526 differences with the MLP are statistically and qualitatively | |
| 527 significant. | |
| 528 The left side of the figure shows the improvement to the clean | |
| 529 NIST test set error brought by the use of out-of-distribution examples | |
| 530 (i.e. the perturbed examples examples from NISTP or P07). | |
| 531 Relative percent change is measured by taking | |
| 532 $100 \% \times$ (original model's error / perturbed-data model's error - 1). | |
| 533 The right side of | |
| 534 Figure~\ref{fig:improvements-charts} shows the relative improvement | |
| 535 brought by the use of a multi-task setting, in which the same model is | |
| 536 trained for more classes than the target classes of interest (i.e. training | |
| 537 with all 62 classes when the target classes are respectively the digits, | |
| 538 lower-case, or upper-case characters). Again, whereas the gain from the | |
| 539 multi-task setting is marginal or negative for the MLP, it is substantial | |
| 540 for the SDA. Note that to simplify these multi-task experiments, only the original | |
| 541 NIST dataset is used. For example, the MLP-digits bar shows the relative | |
| 542 percent improvement in MLP error rate on the NIST digits test set | |
| 543 is $100\% \times$ (single-task | |
| 544 model's error / multi-task model's error - 1). The single-task model is | |
| 545 trained with only 10 outputs (one per digit), seeing only digit examples, | |
| 546 whereas the multi-task model is trained with 62 outputs, with all 62 | |
| 547 character classes as examples. Hence the hidden units are shared across | |
| 548 all tasks. For the multi-task model, the digit error rate is measured by | |
| 549 comparing the correct digit class with the output class associated with the | |
| 550 maximum conditional probability among only the digit classes outputs. The | |
| 551 setting is similar for the other two target classes (lower case characters | |
| 552 and upper case characters). | |
| 553 %%\vspace*{-1mm} | |
| 554 %\subsection{Perturbed Training Data More Helpful for SDA} | |
| 555 %%\vspace*{-1mm} | |
| 556 | |
| 557 %%\vspace*{-1mm} | |
| 558 %\subsection{Multi-Task Learning Effects} | |
| 559 %%\vspace*{-1mm} | |
| 560 | |
| 561 \iffalse | |
| 562 As previously seen, the SDA is better able to benefit from the | |
| 563 transformations applied to the data than the MLP. In this experiment we | |
| 564 define three tasks: recognizing digits (knowing that the input is a digit), | |
| 565 recognizing upper case characters (knowing that the input is one), and | |
| 566 recognizing lower case characters (knowing that the input is one). We | |
| 567 consider the digit classification task as the target task and we want to | |
| 568 evaluate whether training with the other tasks can help or hurt, and | |
| 569 whether the effect is different for MLPs versus SDAs. The goal is to find | |
| 570 out if deep learning can benefit more (or less) from multiple related tasks | |
| 571 (i.e. the multi-task setting) compared to a corresponding purely supervised | |
| 572 shallow learner. | |
| 573 | |
| 574 We use a single hidden layer MLP with 1000 hidden units, and a SDA | |
| 575 with 3 hidden layers (1000 hidden units per layer), pre-trained and | |
| 576 fine-tuned on NIST. | |
| 577 | |
| 578 Our results show that the MLP benefits marginally from the multi-task setting | |
| 579 in the case of digits (5\% relative improvement) but is actually hurt in the case | |
| 580 of characters (respectively 3\% and 4\% worse for lower and upper class characters). | |
| 581 On the other hand the SDA benefited from the multi-task setting, with relative | |
| 582 error rate improvements of 27\%, 15\% and 13\% respectively for digits, | |
| 583 lower and upper case characters, as shown in Table~\ref{tab:multi-task}. | |
| 584 \fi | |
| 585 | |
| 586 | |
| 587 \vspace*{-2mm} | |
| 588 \section{Conclusions and Discussion} | |
| 589 \vspace*{-2mm} | |
| 590 | |
| 591 We have found that the self-taught learning framework is more beneficial | |
| 592 to a deep learner than to a traditional shallow and purely | |
| 593 supervised learner. More precisely, | |
| 594 the answers are positive for all the questions asked in the introduction. | |
| 595 %\begin{itemize} | |
| 596 | |
| 597 $\bullet$ %\item | |
| 598 {\bf Do the good results previously obtained with deep architectures on the | |
| 599 MNIST digits generalize to a much larger and richer (but similar) | |
| 600 dataset, the NIST special database 19, with 62 classes and around 800k examples}? | |
| 601 Yes, the SDA {\em systematically outperformed the MLP and all the previously | |
| 602 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level | |
| 603 performance} at around 17\% error on the 62-class task and 1.4\% on the digits, | |
| 604 and beating previously published results on the same data. | |
| 605 | |
| 606 $\bullet$ %\item | |
| 607 {\bf To what extent do self-taught learning scenarios help deep learners, | |
| 608 and do they help them more than shallow supervised ones}? | |
| 609 We found that distorted training examples not only made the resulting | |
| 610 classifier better on similarly perturbed images but also on | |
| 611 the {\em original clean examples}, and more importantly and more novel, | |
| 612 that deep architectures benefit more from such {\em out-of-distribution} | |
| 613 examples. MLPs were helped by perturbed training examples when tested on perturbed input | |
| 614 images (65\% relative improvement on NISTP) | |
| 615 but only marginally helped (5\% relative improvement on all classes) | |
| 616 or even hurt (10\% relative loss on digits) | |
| 617 with respect to clean examples . On the other hand, the deep SDAs | |
| 618 were significantly boosted by these out-of-distribution examples. | |
| 619 Similarly, whereas the improvement due to the multi-task setting was marginal or | |
| 620 negative for the MLP (from +5.6\% to -3.6\% relative change), | |
| 621 it was quite significant for the SDA (from +13\% to +27\% relative change), | |
| 622 which may be explained by the arguments below. | |
| 623 %\end{itemize} | |
| 624 | |
| 625 In the original self-taught learning framework~\citep{RainaR2007}, the | |
| 626 out-of-sample examples were used as a source of unsupervised data, and | |
| 627 experiments showed its positive effects in a \emph{limited labeled data} | |
| 628 scenario. However, many of the results by \citet{RainaR2007} (who used a | |
| 629 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught | |
| 630 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases. | |
| 631 We note instead that, for deep | |
| 632 architectures, our experiments show that such a positive effect is accomplished | |
| 633 even in a scenario with a \emph{large number of labeled examples}, | |
| 634 i.e., here, the relative gain of self-taught learning is probably preserved | |
| 635 in the asymptotic regime. | |
| 636 | |
| 637 {\bf Why would deep learners benefit more from the self-taught learning framework}? | |
| 638 The key idea is that the lower layers of the predictor compute a hierarchy | |
| 639 of features that can be shared across tasks or across variants of the | |
| 640 input distribution. A theoretical analysis of generalization improvements | |
| 641 due to sharing of intermediate features across tasks already points | |
| 642 towards that explanation~\cite{baxter95a}. | |
| 643 Intermediate features that can be used in different | |
| 644 contexts can be estimated in a way that allows to share statistical | |
| 645 strength. Features extracted through many levels are more likely to | |
| 646 be more abstract and more invariant to some of the factors of variation | |
| 647 in the underlying distribution (as the experiments in~\citet{Goodfellow2009} suggest), | |
| 648 increasing the likelihood that they would be useful for a larger array | |
| 649 of tasks and input conditions. | |
| 650 Therefore, we hypothesize that both depth and unsupervised | |
| 651 pre-training play a part in explaining the advantages observed here, and future | |
| 652 experiments could attempt at teasing apart these factors. | |
| 653 And why would deep learners benefit from the self-taught learning | |
| 654 scenarios even when the number of labeled examples is very large? | |
| 655 We hypothesize that this is related to the hypotheses studied | |
| 656 in~\citet{Erhan+al-2010}. In~\citet{Erhan+al-2010} | |
| 657 it was found that online learning on a huge dataset did not make the | |
| 658 advantage of the deep learning bias vanish, and a similar phenomenon | |
| 659 may be happening here. We hypothesize that unsupervised pre-training | |
| 660 of a deep hierarchy with self-taught learning initializes the | |
| 661 model in the basin of attraction of supervised gradient descent | |
| 662 that corresponds to better generalization. Furthermore, such good | |
| 663 basins of attraction are not discovered by pure supervised learning | |
| 664 (with or without self-taught settings) from random initialization, and more labeled examples | |
| 665 does not allow the shallow or purely supervised models to discover | |
| 666 the kind of better basins associated | |
| 667 with deep learning and self-taught learning. | |
| 668 | |
| 669 A Flash demo of the recognizer (where both the MLP and the SDA can be compared) | |
| 670 can be executed on-line at {\tt http://deep.host22.com}. | |
| 671 | |
| 672 \iffalse | |
| 673 \section*{Appendix I: Detailed Numerical Results} | |
| 674 | |
| 675 These tables correspond to Figures 2 and 3 and contain the raw error rates for each model and dataset considered. | |
| 676 They also contain additional data such as test errors on P07 and standard errors. | |
| 677 | |
| 678 \begin{table}[ht] | |
| 679 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits + | |
| 680 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training | |
| 681 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture | |
| 682 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07) | |
| 683 and using a validation set to select hyper-parameters and other training choices. | |
| 684 \{SDA,MLP\}0 are trained on NIST, | |
| 685 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07. | |
| 686 The human error rate on digits is a lower bound because it does not count digits that were | |
| 687 recognized as letters. For comparison, the results found in the literature | |
| 688 on NIST digits classification using the same test set are included.} | |
| 689 \label{tab:sda-vs-mlp-vs-humans} | |
| 690 \begin{center} | |
| 691 \begin{tabular}{|l|r|r|r|r|} \hline | |
| 692 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 693 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline | |
| 694 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline | |
| 695 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline | |
| 696 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline | |
| 697 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline | |
| 698 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline | |
| 699 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline | |
| 700 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline | |
| 701 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline | |
| 702 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline | |
| 703 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline | |
| 704 \end{tabular} | |
| 705 \end{center} | |
| 706 \end{table} | |
| 707 | |
| 708 \begin{table}[ht] | |
| 709 \caption{Relative change in error rates due to the use of perturbed training data, | |
| 710 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models. | |
| 711 A positive value indicates that training on the perturbed data helped for the | |
| 712 given test set (the first 3 columns on the 62-class tasks and the last one is | |
| 713 on the clean 10-class digits). Clearly, the deep learning models did benefit more | |
| 714 from perturbed training data, even when testing on clean data, whereas the MLP | |
| 715 trained on perturbed data performed worse on the clean digits and about the same | |
| 716 on the clean characters. } | |
| 717 \label{tab:perturbation-effect} | |
| 718 \begin{center} | |
| 719 \begin{tabular}{|l|r|r|r|r|} \hline | |
| 720 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 721 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline | |
| 722 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline | |
| 723 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline | |
| 724 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline | |
| 725 \end{tabular} | |
| 726 \end{center} | |
| 727 \end{table} | |
| 728 | |
| 729 \begin{table}[ht] | |
| 730 \caption{Test error rates and relative change in error rates due to the use of | |
| 731 a multi-task setting, i.e., training on each task in isolation vs training | |
| 732 for all three tasks together, for MLPs vs SDAs. The SDA benefits much | |
| 733 more from the multi-task setting. All experiments on only on the | |
| 734 unperturbed NIST data, using validation error for model selection. | |
| 735 Relative improvement is 1 - single-task error / multi-task error.} | |
| 736 \label{tab:multi-task} | |
| 737 \begin{center} | |
| 738 \begin{tabular}{|l|r|r|r|} \hline | |
| 739 & single-task & multi-task & relative \\ | |
| 740 & setting & setting & improvement \\ \hline | |
| 741 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline | |
| 742 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline | |
| 743 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline | |
| 744 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline | |
| 745 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline | |
| 746 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline | |
| 747 \end{tabular} | |
| 748 \end{center} | |
| 749 \end{table} | |
| 750 | |
| 751 \fi | |
| 752 | |
| 753 %\afterpage{\clearpage} | |
| 754 %\clearpage | |
| 755 { | |
| 756 %\bibliographystyle{spbasic} % basic style, author-year citations | |
| 757 \bibliographystyle{plainnat} | |
| 758 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,specials,aigaion-shorter} | |
| 759 %\bibliographystyle{unsrtnat} | |
| 760 %\bibliographystyle{apalike} | |
| 761 } | |
| 762 | |
| 763 | |
| 764 \end{document} |