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added aistats2011_revised.tex
author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Sun, 09 Jan 2011 21:47:28 -0500
parents
children d44c78c90669
rev   line source
622
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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1 %\documentclass[twoside,11pt]{article} % For LaTeX2e
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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2 \documentclass{article} % For LaTeX2e
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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3 \usepackage{aistats2e_2011}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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4 %\usepackage{times}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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5 \usepackage{wrapfig}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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6 \usepackage{amsthm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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7 \usepackage{amsmath}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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8 \usepackage{bbm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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9 \usepackage[utf8]{inputenc}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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10 \usepackage[psamsfonts]{amssymb}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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11 %\usepackage{algorithm,algorithmic} % not used after all
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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12 \usepackage{graphicx,subfigure}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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13 \usepackage[numbers]{natbib}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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14
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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15 \addtolength{\textwidth}{10mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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16 \addtolength{\evensidemargin}{-5mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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17 \addtolength{\oddsidemargin}{-5mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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18
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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19 %\setlength\parindent{0mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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20
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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21 \begin{document}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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22
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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23 \twocolumn[
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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24 \aistatstitle{Deep Learners Benefit More from Out-of-Distribution Examples}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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25 \runningtitle{Deep Learners for Out-of-Distribution Examples}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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26 \runningauthor{Bengio et. al.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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27 \aistatsauthor{Anonymous Authors}]
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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28 \iffalse
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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29 Yoshua Bengio \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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30 Frédéric Bastien \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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31 Arnaud Bergeron \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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32 Nicolas Boulanger-Lewandowski \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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33 Thomas Breuel \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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34 Youssouf Chherawala \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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35 Moustapha Cisse \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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36 Myriam Côté \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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37 Dumitru Erhan \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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38 Jeremy Eustache \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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39 Xavier Glorot \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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40 Xavier Muller \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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41 Sylvain Pannetier Lebeuf \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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42 Razvan Pascanu \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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43 Salah Rifai \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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44 Francois Savard \and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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45 Guillaume Sicard
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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46 %}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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47 \fi
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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48 %\aistatsaddress{Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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49 %\date{{\tt bengioy@iro.umontreal.ca}, Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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50 %\jmlrheading{}{2010}{}{10/2010}{XX/2011}{Yoshua Bengio et al}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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51 %\editor{}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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52
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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53 %\makeanontitle
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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54 %\maketitle
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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55
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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56 %{\bf Running title: Deep Self-Taught Learning}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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57
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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58 %\vspace*{-2mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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59 \begin{abstract}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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60 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. The hypothesis evaluated here is that intermediate levels of representation, because they can be shared across tasks and examples from different but related distributions, can yield even more benefits. Comparative experiments were performed on a large-scale handwritten character recognition setting with 62 classes (upper case, lower case, digits), using both a multi-task setting and perturbed examples in order to obtain out-of-distribution examples. The results agree with the hypothesis, and show that a deep learner did {\em beat previously published results and reached human-level performance}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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61 \end{abstract}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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62 %\vspace*{-3mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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63
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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64 %\begin{keywords}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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65 %Deep learning, self-taught learning, out-of-distribution examples, handwritten character recognition, multi-task learning
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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66 %\end{keywords}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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67 %\keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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68
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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69
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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70
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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71 \section{Introduction}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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72 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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73
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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74 {\bf Deep Learning} has emerged as a promising new area of research in
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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75 statistical machine learning~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,VincentPLarochelleH2008-very-small,ranzato-08,TaylorHintonICML2009,Larochelle-jmlr-2009,Salakhutdinov+Hinton-2009,HonglakL2009,HonglakLNIPS2009,Jarrett-ICCV2009,Taylor-cvpr-2010}. See \citet{Bengio-2009} for a review.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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76 Learning algorithms for deep architectures are centered on the learning
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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77 of useful representations of data, which are better suited to the task at hand,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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78 and are organized in a hierarchy with multiple levels.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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79 This is in part inspired by observations of the mammalian visual cortex,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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80 which consists of a chain of processing elements, each of which is associated with a
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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81 different representation of the raw visual input. In fact,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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82 it was found recently that the features learnt in deep architectures resemble
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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83 those observed in the first two of these stages (in areas V1 and V2
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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84 of visual cortex) \citep{HonglakL2008}, and that they become more and
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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85 more invariant to factors of variation (such as camera movement) in
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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86 higher layers~\citep{Goodfellow2009}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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87 It has been hypothesized that learning a hierarchy of features increases the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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88 ease and practicality of developing representations that are at once
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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89 tailored to specific tasks, yet are able to borrow statistical strength
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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90 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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91 feature representation can lead to higher-level (more abstract, more
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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92 general) features that are more robust to unanticipated sources of
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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93 variance extant in real data.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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94
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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95 Whereas a deep architecture can in principle be more powerful than a
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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96 shallow one in terms of representation, depth appears to render the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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97 training problem more difficult in terms of optimization and local minima.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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98 It is also only recently that successful algorithms were proposed to
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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99 overcome some of these difficulties. All are based on unsupervised
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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100 learning, often in an greedy layer-wise ``unsupervised pre-training''
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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101 stage~\citep{Bengio-2009}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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102 The principle is that each layer starting from
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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103 the bottom is trained to represent its input (the output of the previous
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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104 layer). After this
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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105 unsupervised initialization, the stack of layers can be
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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106 converted into a deep supervised feedforward neural network and fine-tuned by
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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107 stochastic gradient descent.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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108 One of these layer initialization techniques,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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109 applied here, is the Denoising
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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110 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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111 Figure~\ref{fig:da}), which performed similarly or
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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112 better~\citep{VincentPLarochelleH2008-very-small} than previously
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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113 proposed Restricted Boltzmann Machines (RBM)~\citep{Hinton06}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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114 in terms of unsupervised extraction
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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115 of a hierarchy of features useful for classification. Each layer is trained
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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116 to denoise its input, creating a layer of features that can be used as
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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117 input for the next layer, forming a Stacked Denoising Auto-encoder (SDA).
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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118 Note that training a Denoising Auto-encoder
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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119 can actually been seen as training a particular RBM by an inductive
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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120 principle different from maximum likelihood~\citep{Vincent-SM-2010},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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121 namely by Score Matching~\citep{Hyvarinen-2005,HyvarinenA2008}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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122
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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123 Previous comparative experimental results with stacking of RBMs and DAs
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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124 to build deep supervised predictors had shown that they could outperform
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Yoshua Bengio <bengioy@iro.umontreal.ca>
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125 shallow architectures in a variety of settings, especially
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
126 when the data involves complex interactions between many factors of
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
127 variation~\citep{LarochelleH2007,Bengio-2009}. Other experiments have suggested
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
128 that the unsupervised layer-wise pre-training acted as a useful
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
129 prior~\citep{Erhan+al-2010} that allows one to initialize a deep
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
130 neural network in a relatively much smaller region of parameter space,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
131 corresponding to better generalization.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
132
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
133 To further the understanding of the reasons for the good performance
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
134 observed with deep learners, we focus here on the following {\em hypothesis}:
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
135 intermediate levels of representation, especially when there are
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
136 more such levels, can be exploited to {\bf share
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
137 statistical strength across different but related types of examples},
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
138 such as examples coming from other tasks than the task of interest
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
139 (the multi-task setting), or examples coming from an overlapping
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
140 but different distribution (images with different kinds of perturbations
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
141 and noises, here). This is consistent with the hypotheses discussed
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
142 in~\citet{Bengio-2009} regarding the potential advantage
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
143 of deep learning and the idea that more levels of representation can
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
144 give rise to more abstract, more general features of the raw input.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
145
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
146 This hypothesis is related to a learning setting called
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
147 {\bf self-taught learning}~\citep{RainaR2007}, which combines principles
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
148 of semi-supervised and multi-task learning: the learner can exploit examples
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
149 that are unlabeled and possibly come from a distribution different from the target
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
150 distribution, e.g., from other classes than those of interest.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
151 It has already been shown that deep learners can clearly take advantage of
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
152 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
153 but more needed to be done to explore the impact
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
154 of {\em out-of-distribution} examples and of the {\em multi-task} setting
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
155 (one exception is~\citep{CollobertR2008}, which shares and uses unsupervised
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
156 pre-training only with the first layer). In particular the {\em relative
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
157 advantage of deep learning} for these settings has not been evaluated.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
158
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
159
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
160 %
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
161 The {\bf main claim} of this paper is that deep learners (with several levels of representation) can
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
162 {\bf benefit more from out-of-distribution examples than shallow learners} (with a single
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
163 level), both in the context of the multi-task setting and from
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
164 perturbed examples. Because we are able to improve on state-of-the-art
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
165 performance and reach human-level performance
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
166 on a large-scale task, we consider that this paper is also a contribution
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
167 to advance the application of machine learning to handwritten character recognition.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
168 More precisely, we ask and answer the following questions:
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
169
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
170 %\begin{enumerate}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
171 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
172 Do the good results previously obtained with deep architectures on the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
173 MNIST digit images generalize to the setting of a similar but much larger and richer
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
174 dataset, the NIST special database 19, with 62 classes and around 800k examples?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
175
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
176 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
177 To what extent does the perturbation of input images (e.g. adding
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
178 noise, affine transformations, background images) make the resulting
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
179 classifiers better not only on similarly perturbed images but also on
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
180 the {\em original clean examples}? We study this question in the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
181 context of the 62-class and 10-class tasks of the NIST special database 19.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
182
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
183 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
184 Do deep architectures {\em benefit {\bf more} from such out-of-distribution}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
185 examples, in particular do they benefit more from
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
186 examples that are perturbed versions of the examples from the task of interest?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
187
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
188 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
189 Similarly, does the feature learning step in deep learning algorithms benefit {\bf more}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
190 from training with moderately {\em different classes} (i.e. a multi-task learning scenario) than
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
191 a corresponding shallow and purely supervised architecture?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
192 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
193 to answer this question.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
194 %\end{enumerate}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
195
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
196 Our experimental results provide positive evidence towards all of these questions,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
197 as well as {\bf classifiers that reach human-level performance on 62-class isolated character
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
198 recognition and beat previously published results on the NIST dataset (special database 19)}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
199 To achieve these results, we introduce in the next section a sophisticated system
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
200 for stochastically transforming character images and then explain the methodology,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
201 which is based on training with or without these transformed images and testing on
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
202 clean ones.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
203 Code for generating these transformations as well as for the deep learning
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
204 algorithms are made available at {\tt http://anonymous.url.net}.%{\tt http://hg.assembla.com/ift6266}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
205
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
206 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
207 %\newpage
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
208 \section{Perturbed and Transformed Character Images}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
209 \label{s:perturbations}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
210 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
211
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
212 Figure~\ref{fig:transform} shows the different transformations we used to stochastically
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
213 transform $32 \times 32$ source images (such as the one in Fig.\ref{fig:torig})
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
214 in order to obtain data from a larger distribution which
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
215 covers a domain substantially larger than the clean characters distribution from
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
216 which we start.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
217 Although character transformations have been used before to
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
218 improve character recognizers, this effort is on a large scale both
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
219 in number of classes and in the complexity of the transformations, hence
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
220 in the complexity of the learning task.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
221 The code for these transformations (mostly Python) is available at
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
222 {\tt http://anonymous.url.net}. All the modules in the pipeline (Figure~\ref{fig:transform}) share
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
223 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
224 amount of deformation or noise introduced.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
225 There are two main parts in the pipeline. The first one,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
226 from thickness to pinch, performs transformations. The second
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
227 part, from blur to contrast, adds different kinds of noise.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
228 More details can be found in~\citep{ift6266-tr-anonymous}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
229
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
230 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
231 \centering
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
232 \subfigure[Original]{\includegraphics[scale=0.6]{images/Original.png}\label{fig:torig}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
233 \subfigure[Thickness]{\includegraphics[scale=0.6]{images/Thick_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
234 \subfigure[Slant]{\includegraphics[scale=0.6]{images/Slant_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
235 \subfigure[Affine Transformation]{\includegraphics[scale=0.6]{images/Affine_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
236 \subfigure[Local Elastic Deformation]{\includegraphics[scale=0.6]{images/Localelasticdistorsions_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
237 \subfigure[Pinch]{\includegraphics[scale=0.6]{images/Pinch_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
238 %Noise
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
239 \subfigure[Motion Blur]{\includegraphics[scale=0.6]{images/Motionblur_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
240 \subfigure[Occlusion]{\includegraphics[scale=0.6]{images/occlusion_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
241 \subfigure[Gaussian Smoothing]{\includegraphics[scale=0.6]{images/Bruitgauss_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
242 \subfigure[Pixels Permutation]{\includegraphics[scale=0.6]{images/Permutpixel_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
243 \subfigure[Gaussian Noise]{\includegraphics[scale=0.6]{images/Distorsiongauss_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
244 \subfigure[Background Image Addition]{\includegraphics[scale=0.6]{images/background_other_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
245 \subfigure[Salt \& Pepper]{\includegraphics[scale=0.6]{images/Poivresel_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
246 \subfigure[Scratches]{\includegraphics[scale=0.6]{images/Rature_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
247 \subfigure[Grey Level \& Contrast]{\includegraphics[scale=0.6]{images/Contrast_only.png}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
248 \caption{Top left (a): example original image. Others (b-o): examples of the effect
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
249 of each transformation module taken separately. Actual perturbed examples are obtained by
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
250 a pipeline of these, with random choices about which module to apply and how much perturbation
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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251 to apply.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
252 \label{fig:transform}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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253 %\vspace*{-2mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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254 \end{figure*}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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255
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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256 %\vspace*{-3mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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257 \section{Experimental Setup}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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258 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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259
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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260 Much previous work on deep learning had been performed on
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
261 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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262 with 60,000 examples, and variants involving 10,000
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
263 examples~\citep{Larochelle-jmlr-2009,VincentPLarochelleH2008-very-small}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
264 The focus here is on much larger training sets, from 10 times to
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
265 to 1000 times larger, and 62 classes.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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266
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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267 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
268 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
269 and {\bf OCR data} (scanned machine printed characters). See more in
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
270 Section~\ref{sec:sources} below. Once a character
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
271 is sampled from one of these sources (chosen randomly), the second step is to
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
272 apply a pipeline of transformations and/or noise processes outlined in section \ref{s:perturbations}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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273
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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274 To provide a baseline of error rate comparison we also estimate human performance
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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275 on both the 62-class task and the 10-class digits task.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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276 We compare the best Multi-Layer Perceptrons (MLP) against
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
277 the best Stacked Denoising Auto-encoders (SDA), when
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
278 both models' hyper-parameters are selected to minimize the validation set error.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
279 We also provide a comparison against a precise estimate
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
280 of human performance obtained via Amazon's Mechanical Turk (AMT)
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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281 service ({\tt http://mturk.com}).
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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282 AMT users are paid small amounts
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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283 of money to perform tasks for which human intelligence is required.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
284 Mechanical Turk has been used extensively in natural language processing and vision.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
285 %processing \citep{SnowEtAl2008} and vision
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
286 %\citep{SorokinAndForsyth2008,whitehill09}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
287 AMT users were presented
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
288 with 10 character images (from a test set) on a screen
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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289 and asked to label them.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
290 They were forced to choose a single character class (either among the
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
291 62 or 10 character classes) for each image.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
292 80 subjects classified 2500 images per (dataset,task) pair.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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293 Different humans labelers sometimes provided a different label for the same
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
294 example, and we were able to estimate the error variance due to this effect
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
295 because each image was classified by 3 different persons.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
296 The average error of humans on the 62-class task NIST test set
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
297 is 18.2\%, with a standard error of 0.1\%.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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298
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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299 %\vspace*{-3mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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300 \subsection{Data Sources}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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301 \label{sec:sources}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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302 %\vspace*{-2mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
303
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
304 %\begin{itemize}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
305 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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306 {\bf NIST.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
307 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
308 widely used for training and testing character
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
309 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
310 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
311 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
312 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
313 The fourth partition (called $hsf_4$, 82,587 examples),
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
314 experimentally recognized to be the most difficult one, is the one recommended
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
315 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}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
316 for that purpose. We randomly split the remainder (731,668 examples) into a training set and a validation set for
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
317 model selection.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
318 The performances reported by previous work on that dataset mostly use only the digits.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
319 Here we use all the classes both in the training and testing phase. This is especially
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
320 useful to estimate the effect of a multi-task setting.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
321 The distribution of the classes in the NIST training and test sets differs
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
322 substantially, with relatively many more digits in the test set, and a more uniform distribution
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
323 of letters in the test set (whereas in the training set they are distributed
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
324 more like in natural text).
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
325 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
326
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
327 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
328 {\bf Fonts.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
329 In order to have a good variety of sources we downloaded an important number of free fonts from:
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
330 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
331 % TODO: pointless to anonymize, it's not pointing to our work
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
332 Including an operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
333 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
334 directly as input to our models.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
335 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
336
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
337 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
338 {\bf Captchas.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
339 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a Python-based captcha generator library) for
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
340 generating characters of the same format as the NIST dataset. This software is based on
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
341 a random character class generator and various kinds of transformations similar to those described in the previous sections.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
342 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
343 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
344 depending on the value of the complexity parameter provided by the user of the data source.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
345 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
346 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
347
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
348 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
349 {\bf OCR data.}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
350 A large set (2 million) of scanned, OCRed and manually verified machine-printed
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
351 characters where included as an
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
352 additional source. This set is part of a larger corpus being collected by the Image Understanding
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
353 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
354 ({\tt http://www.iupr.com}), and which will be publicly released.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
355 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
356 %\end{itemize}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
357
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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358 %\vspace*{-3mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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359 \subsection{Data Sets}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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360 %\vspace*{-2mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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361
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
362 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
363 from one of the 62 character classes.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
364 %\begin{itemize}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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365 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
366
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
367 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
368 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
369 \{651,668 / 80,000 / 82,587\} \{training / validation / test\} examples.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
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370 %\vspace*{-1mm}
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
371
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
372 %\item
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
373 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
374 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
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Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
375 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
376 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
377 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
378 It has \{81,920,000 / 80,000 / 20,000\} \{training / validation / test\} examples
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
379 obtained from the corresponding NIST sets plus other sources.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
380 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
381
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
382 %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
383 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
384 except that we only apply
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
385 transformations from slant to pinch (see Fig.\ref{fig:transform}(b-f)).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
386 Therefore, the character is
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
387 transformed but no additional noise is added to the image, giving images
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
388 closer to the NIST dataset.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
389 It has \{81,920,000 / 80,000 / 20,000\} \{training / validation / test\} examples
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
390 obtained from the corresponding NIST sets plus other sources.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
391 %\end{itemize}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
392
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
393 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
394 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
395 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
396 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
397 \caption{Illustration of the computations and training criterion for the denoising
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
398 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
399 the layer (i.e. raw input or output of previous layer)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
400 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
401 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
402 is compared to the uncorrupted input $x$ through the loss function
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
403 $L_H(x,z)$, whose expected value is approximately minimized during training
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
404 by tuning $\theta$ and $\theta'$.}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
405 \label{fig:da}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
406 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
407 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
408
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
409 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
410 \subsection{Models and their Hyper-parameters}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
411 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
412
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
413 The experiments are performed using MLPs (with a single
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
414 hidden layer) and deep SDAs.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
415 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
416
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
417 {\bf Multi-Layer Perceptrons (MLP).}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
418 Whereas previous work had compared deep architectures to both shallow MLPs and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
419 SVMs, we only compared to MLPs here because of the very large datasets used
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
420 (making the use of SVMs computationally challenging because of their quadratic
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
421 scaling behavior). Preliminary experiments on training SVMs (libSVM) with subsets of the training
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
422 set allowing the program to fit in memory yielded substantially worse results
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
423 than those obtained with MLPs. For training on nearly a hundred million examples
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
424 (with the perturbed data), the MLPs and SDA are much more convenient than
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
425 classifiers based on kernel methods.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
426 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
427 exponentials) on the output layer for estimating $P(class | image)$.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
428 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
429 Training examples are presented in minibatches of size 20. A constant learning
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
430 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
431 %through preliminary experiments (measuring performance on a validation set),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
432 %and $0.1$ (which was found to work best) was then selected for optimizing on
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
433 %the whole training sets.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
434 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
435
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
436
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
437 {\bf Stacked Denoising Auto-encoders (SDA).}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
438 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
439 can be used to initialize the weights of each layer of a deep MLP (with many hidden
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
440 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
441 apparently setting parameters in the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
442 basin of attraction of supervised gradient descent yielding better
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
443 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
444 pre-training phase} uses all of the training images but not the training labels.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
445 Each layer is trained in turn to produce a new representation of its input
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
446 (starting from the raw pixels).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
447 It is hypothesized that the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
448 advantage brought by this procedure stems from a better prior,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
449 on the one hand taking advantage of the link between the input
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
450 distribution $P(x)$ and the conditional distribution of interest
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
451 $P(y|x)$ (like in semi-supervised learning), and on the other hand
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
452 taking advantage of the expressive power and bias implicit in the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
453 deep architecture (whereby complex concepts are expressed as
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
454 compositions of simpler ones through a deep hierarchy).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
455
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
456 Here we chose to use the Denoising
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
457 Auto-encoder~\citep{VincentPLarochelleH2008-very-small} as the building block for
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
458 these deep hierarchies of features, as it is simple to train and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
459 explain (see Figure~\ref{fig:da}, as well as
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
460 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
461 provides efficient inference, and yielded results
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
462 comparable or better than RBMs in series of experiments
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
463 \citep{VincentPLarochelleH2008-very-small}. It really corresponds to a Gaussian
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
464 RBM trained by a Score Matching criterion~\cite{Vincent-SM-2010}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
465 During training, a Denoising
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
466 Auto-encoder is presented with a stochastically corrupted version
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
467 of the input and trained to reconstruct the uncorrupted input,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
468 forcing the hidden units to represent the leading regularities in
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
469 the data. Here we use the random binary masking corruption
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
470 (which sets to 0 a random subset of the inputs).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
471 Once it is trained, in a purely unsupervised way,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
472 its hidden units' activations can
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
473 be used as inputs for training a second one, etc.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
474 After this unsupervised pre-training stage, the parameters
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
475 are used to initialize a deep MLP, which is fine-tuned by
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
476 the same standard procedure used to train them (see above).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
477 The SDA hyper-parameters are the same as for the MLP, with the addition of the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
478 amount of corruption noise (we used the masking noise process, whereby a
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
479 fixed proportion of the input values, randomly selected, are zeroed), and a
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
480 separate learning rate for the unsupervised pre-training stage (selected
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
481 from the same above set). The fraction of inputs corrupted was selected
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
482 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
483 of hidden layers but it was fixed to 3 based on previous work with
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
484 SDAs on MNIST~\citep{VincentPLarochelleH2008-very-small}. The size of the hidden
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
485 layers was kept constant across hidden layers, and the best results
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
486 were obtained with the largest values that we could experiment
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
487 with given our patience, with 1000 hidden units.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
488
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
489 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
490
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
491 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
492 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
493 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
494 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
495 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
496 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
497 of all models, on NIST and NISTP test sets.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
498 Right: error rates on NIST test digits only, along with the previous results from
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
499 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
500 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
501 \label{fig:error-rates-charts}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
502 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
503 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
504
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
505
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
506 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
507 \vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
508 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
509 \vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
510 \caption{Relative improvement in error rate due to out-of-distribution examples.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
511 Left: Improvement (or loss, when negative)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
512 induced by out-of-distribution examples (perturbed data).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
513 Right: Improvement (or loss, when negative) induced by multi-task
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
514 learning (training on all classes and testing only on either digits,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
515 upper case, or lower-case). The deep learner (SDA) benefits more from
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
516 out-of-distribution examples, compared to the shallow MLP.}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
517 \label{fig:improvements-charts}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
518 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
519 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
520
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
521 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
522 \section{Experimental Results}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
523 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
524
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
525 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
526 %\subsection{SDA vs MLP vs Humans}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
527 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
528 The models are either trained on NIST (MLP0 and SDA0),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
529 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
530 on either NIST, NISTP or P07 (regardless of the data set used for training),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
531 either on the 62-class task
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
532 or on the 10-digits task. Training time (including about half
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
533 for unsupervised pre-training, for DAs) on the larger
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
534 datasets is around one day on a GPU (GTX 285).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
535 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
536 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
537 SDA2), along with the previous results on the digits NIST special database
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
538 19 test set from the literature, respectively based on ARTMAP neural
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
539 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
540 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
541 ~\citep{Milgram+al-2005}.% More detailed and complete numerical results
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
542 %(figures and tables, including standard errors on the error rates) can be
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
543 %found in Appendix.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
544 The deep learner not only outperformed the shallow ones and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
545 previously published performance (in a statistically and qualitatively
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
546 significant way) but when trained with perturbed data
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
547 reaches human performance on both the 62-class task
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
548 and the 10-class (digits) task.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
549 17\% error (SDA1) or 18\% error (humans) may seem large but a large
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
550 majority of the errors from humans and from SDA1 are from out-of-context
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
551 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
552 ``c'' and a ``C'' are often indistinguishible).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
553
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
554 In addition, as shown in the left of
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
555 Figure~\ref{fig:improvements-charts}, the relative improvement in error
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
556 rate brought by out-of-distribution examples is greater for the deep
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
557 SDA, and these
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
558 differences with the shallow MLP are statistically and qualitatively
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
559 significant.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
560 The left side of the figure shows the improvement to the clean
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
561 NIST test set error brought by the use of out-of-distribution examples
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
562 (i.e. the perturbed examples examples from NISTP or P07),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
563 over the models trained exclusively on NIST (respectively SDA0 and MLP0).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
564 Relative percent change is measured by taking
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
565 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
566 The right side of
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
567 Figure~\ref{fig:improvements-charts} shows the relative improvement
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
568 brought by the use of a multi-task setting, in which the same model is
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
569 trained for more classes than the target classes of interest (i.e. training
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
570 with all 62 classes when the target classes are respectively the digits,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
571 lower-case, or upper-case characters). Again, whereas the gain from the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
572 multi-task setting is marginal or negative for the MLP, it is substantial
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
573 for the SDA. Note that to simplify these multi-task experiments, only the original
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
574 NIST dataset is used. For example, the MLP-digits bar shows the relative
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
575 percent improvement in MLP error rate on the NIST digits test set
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
576 as $100\% \times$ (single-task
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
577 model's error / multi-task model's error - 1). The single-task model is
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
578 trained with only 10 outputs (one per digit), seeing only digit examples,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
579 whereas the multi-task model is trained with 62 outputs, with all 62
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
580 character classes as examples. Hence the hidden units are shared across
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
581 all tasks. For the multi-task model, the digit error rate is measured by
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
582 comparing the correct digit class with the output class associated with the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
583 maximum conditional probability among only the digit classes outputs. The
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
584 setting is similar for the other two target classes (lower case characters
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
585 and upper case characters). Note however that some types of perturbations
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
586 (NISTP) help more than others (P07) when testing on the clean images.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
587 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
588 %\subsection{Perturbed Training Data More Helpful for SDA}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
589 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
590
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
591 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
592 %\subsection{Multi-Task Learning Effects}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
593 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
594
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
595 \iffalse
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
596 As previously seen, the SDA is better able to benefit from the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
597 transformations applied to the data than the MLP. In this experiment we
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
598 define three tasks: recognizing digits (knowing that the input is a digit),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
599 recognizing upper case characters (knowing that the input is one), and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
600 recognizing lower case characters (knowing that the input is one). We
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
601 consider the digit classification task as the target task and we want to
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
602 evaluate whether training with the other tasks can help or hurt, and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
603 whether the effect is different for MLPs versus SDAs. The goal is to find
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
604 out if deep learning can benefit more (or less) from multiple related tasks
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
605 (i.e. the multi-task setting) compared to a corresponding purely supervised
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
606 shallow learner.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
607
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
608 We use a single hidden layer MLP with 1000 hidden units, and a SDA
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
609 with 3 hidden layers (1000 hidden units per layer), pre-trained and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
610 fine-tuned on NIST.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
611
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
612 Our results show that the MLP benefits marginally from the multi-task setting
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
613 in the case of digits (5\% relative improvement) but is actually hurt in the case
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
614 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
615 On the other hand the SDA benefited from the multi-task setting, with relative
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
616 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
617 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
618 \fi
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
619
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
620
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
621 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
622 \section{Conclusions and Discussion}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
623 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
624
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
625 We have found that out-of-distribution examples (multi-task learning
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
626 and perturbed examples) are more beneficial
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
627 to a deep learner than to a traditional shallow and purely
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
628 supervised learner. More precisely,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
629 the answers are positive for all the questions asked in the introduction.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
630 %\begin{itemize}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
631
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
632 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
633 {\bf Do the good results previously obtained with deep architectures on the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
634 MNIST digits generalize to a much larger and richer (but similar)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
635 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
636 Yes, the SDA {\em systematically outperformed the MLP and all the previously
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
637 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
638 performance} at around 17\% error on the 62-class task and 1.4\% on the digits,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
639 and beating previously published results on the same data.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
640
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
641 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
642 {\bf To what extent do out-of-distribution examples help deep learners,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
643 and do they help them more than shallow supervised ones}?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
644 We found that distorted training examples not only made the resulting
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
645 classifier better on similarly perturbed images but also on
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
646 the {\em original clean examples}, and more importantly and more novel,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
647 that deep architectures benefit more from such {\em out-of-distribution}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
648 examples. Shallow MLPs were helped by perturbed training examples when tested on perturbed input
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
649 images (65\% relative improvement on NISTP)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
650 but only marginally helped (5\% relative improvement on all classes)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
651 or even hurt (10\% relative loss on digits)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
652 with respect to clean examples. On the other hand, the deep SDAs
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
653 were significantly boosted by these out-of-distribution examples.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
654 Similarly, whereas the improvement due to the multi-task setting was marginal or
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
655 negative for the MLP (from +5.6\% to -3.6\% relative change),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
656 it was quite significant for the SDA (from +13\% to +27\% relative change),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
657 which may be explained by the arguments below.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
658 Since out-of-distribution data
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
659 (perturbed or from other related classes) is very common, this conclusion
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
660 is of practical importance.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
661 %\end{itemize}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
662
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
663 In the original self-taught learning framework~\citep{RainaR2007}, the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
664 out-of-sample examples were used as a source of unsupervised data, and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
665 experiments showed its positive effects in a \emph{limited labeled data}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
666 scenario. However, many of the results by \citet{RainaR2007} (who used a
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
667 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
668 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
669 We note instead that, for deep
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
670 architectures, our experiments show that such a positive effect is accomplished
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
671 even in a scenario with a \emph{large number of labeled examples},
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
672 i.e., here, the relative gain of self-taught learning and
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
673 out-of-distribution examples is probably preserved
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
674 in the asymptotic regime. However, note that in our perturbation experiments
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
675 (but not in our multi-task experiments),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
676 even the out-of-distribution examples are labeled, unlike in the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
677 earlier self-taught learning experiments~\citep{RainaR2007}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
678
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
679 {\bf Why would deep learners benefit more from the self-taught learning
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
680 framework and out-of-distribution examples}?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
681 The key idea is that the lower layers of the predictor compute a hierarchy
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
682 of features that can be shared across tasks or across variants of the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
683 input distribution. A theoretical analysis of generalization improvements
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
684 due to sharing of intermediate features across tasks already points
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
685 towards that explanation~\cite{baxter95a}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
686 Intermediate features that can be used in different
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
687 contexts can be estimated in a way that allows to share statistical
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
688 strength. Features extracted through many levels are more likely to
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
689 be more abstract and more invariant to some of the factors of variation
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
690 in the underlying distribution (as the experiments in~\citet{Goodfellow2009} suggest),
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
691 increasing the likelihood that they would be useful for a larger array
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
692 of tasks and input conditions.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
693 Therefore, we hypothesize that both depth and unsupervised
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
694 pre-training play a part in explaining the advantages observed here, and future
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
695 experiments could attempt at teasing apart these factors.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
696 And why would deep learners benefit from the self-taught learning
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
697 scenarios even when the number of labeled examples is very large?
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
698 We hypothesize that this is related to the hypotheses studied
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
699 in~\citet{Erhan+al-2010}. In~\citet{Erhan+al-2010}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
700 it was found that online learning on a huge dataset did not make the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
701 advantage of the deep learning bias vanish, and a similar phenomenon
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
702 may be happening here. We hypothesize that unsupervised pre-training
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
703 of a deep hierarchy with out-of-distribution examples initializes the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
704 model in the basin of attraction of supervised gradient descent
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
705 that corresponds to better generalization. Furthermore, such good
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
706 basins of attraction are not discovered by pure supervised learning
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
707 (with or without out-of-distribution examples) from random initialization, and more labeled examples
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
708 does not allow the shallow or purely supervised models to discover
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
709 the kind of better basins associated
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
710 with deep learning and out-of-distribution examples.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
711
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
712 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
713 can be executed on-line at the anonymous site {\tt http://deep.host22.com}.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
714
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
715 \iffalse
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
716 \section*{Appendix I: Detailed Numerical Results}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
717
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
718 These tables correspond to Figures 2 and 3 and contain the raw error rates for each model and dataset considered.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
719 They also contain additional data such as test errors on P07 and standard errors.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
720
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
721 \begin{table}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
722 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
723 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
724 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
725 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
726 and using a validation set to select hyper-parameters and other training choices.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
727 \{SDA,MLP\}0 are trained on NIST,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
728 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
729 The human error rate on digits is a lower bound because it does not count digits that were
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
730 recognized as letters. For comparison, the results found in the literature
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
731 on NIST digits classification using the same test set are included.}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
732 \label{tab:sda-vs-mlp-vs-humans}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
733 \begin{center}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
734 \begin{tabular}{|l|r|r|r|r|} \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
735 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
736 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
737 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
738 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
739 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
740 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
741 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
742 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
743 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
744 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
745 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
746 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
747 \end{tabular}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
748 \end{center}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
749 \end{table}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
750
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
751 \begin{table}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
752 \caption{Relative change in error rates due to the use of perturbed training data,
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
753 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
754 A positive value indicates that training on the perturbed data helped for the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
755 given test set (the first 3 columns on the 62-class tasks and the last one is
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
756 on the clean 10-class digits). Clearly, the deep learning models did benefit more
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
757 from perturbed training data, even when testing on clean data, whereas the MLP
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
758 trained on perturbed data performed worse on the clean digits and about the same
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
759 on the clean characters. }
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
760 \label{tab:perturbation-effect}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
761 \begin{center}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
762 \begin{tabular}{|l|r|r|r|r|} \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
763 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
764 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
765 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
766 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
767 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
768 \end{tabular}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
769 \end{center}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
770 \end{table}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
771
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
772 \begin{table}[ht]
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
773 \caption{Test error rates and relative change in error rates due to the use of
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
774 a multi-task setting, i.e., training on each task in isolation vs training
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
775 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
776 more from the multi-task setting. All experiments on only on the
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
777 unperturbed NIST data, using validation error for model selection.
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
778 Relative improvement is 1 - single-task error / multi-task error.}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
779 \label{tab:multi-task}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
780 \begin{center}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
781 \begin{tabular}{|l|r|r|r|} \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
782 & single-task & multi-task & relative \\
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
783 & setting & setting & improvement \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
784 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
785 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
786 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
787 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
788 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
789 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
790 \end{tabular}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
791 \end{center}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
792 \end{table}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
793
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
794 \fi
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
795
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
796 %\afterpage{\clearpage}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
797 %\clearpage
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
798 {
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
799 %\bibliographystyle{spbasic} % basic style, author-year citations
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
800 \bibliographystyle{plainnat}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
801 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,specials,aigaion-shorter}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
802 %\bibliographystyle{unsrtnat}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
803 %\bibliographystyle{apalike}
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
804 }
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
805
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
806
09b7dee216f4 added aistats2011_revised.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
807 \end{document}