ift6266: writeup/aistats2011_revised.tex annotate

annotate writeup/aistats2011_revised.tex @ 624:49933073590c

added jmlr_review1.txt and jmlr_review2.txt

author	Yoshua Bengio <bengioy@iro.umontreal.ca>
date	Sun, 13 Mar 2011 18:25:25 -0400
parents	d44c78c90669
children

rev	line source
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	1 %\documentclass[twoside,11pt]{article} % For LaTeX2e
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	2 \documentclass{article} % For LaTeX2e
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	3 \usepackage{aistats2e_2011}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	4 %\usepackage{times}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	5 \usepackage{wrapfig}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	6 \usepackage{amsthm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	7 \usepackage{amsmath}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	8 \usepackage{bbm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	9 \usepackage[utf8]{inputenc}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	10 \usepackage[psamsfonts]{amssymb}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	11 %\usepackage{algorithm,algorithmic} % not used after all
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	12 \usepackage{graphicx,subfigure}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	13 \usepackage[numbers]{natbib}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	14
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	15 \addtolength{\textwidth}{10mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	16 \addtolength{\evensidemargin}{-5mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	17 \addtolength{\oddsidemargin}{-5mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	18
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	19 %\setlength\parindent{0mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	20
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	21 \begin{document}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	22
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	23 \twocolumn[
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	24 \aistatstitle{Deep Learners Benefit More from Out-of-Distribution Examples}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	25 \runningtitle{Deep Learners for Out-of-Distribution Examples}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	26 \runningauthor{Bengio et. al.}
624 49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	27 \aistatsauthor{Anonymous Authors\\
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	28 \vspace*{5mm}}]
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	29 \iffalse
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	30 Yoshua Bengio \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	31 Frédéric Bastien \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	32 Arnaud Bergeron \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	33 Nicolas Boulanger-Lewandowski \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	34 Thomas Breuel \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	35 Youssouf Chherawala \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	36 Moustapha Cisse \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	37 Myriam Côté \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	38 Dumitru Erhan \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	39 Jeremy Eustache \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	40 Xavier Glorot \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	41 Xavier Muller \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	42 Sylvain Pannetier Lebeuf \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	43 Razvan Pascanu \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	44 Salah Rifai \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	45 Francois Savard \and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	46 Guillaume Sicard
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	47 %}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	48 \fi
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	49 %\aistatsaddress{Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	50 %\date{{\tt bengioy@iro.umontreal.ca}, Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	51 %\jmlrheading{}{2010}{}{10/2010}{XX/2011}{Yoshua Bengio et al}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	52 %\editor{}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	53
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	54 %\makeanontitle
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	55 %\maketitle
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	56
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	57 %{\bf Running title: Deep Self-Taught Learning}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	58
624 49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	59 \vspace*{5mm}
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	60 \begin{abstract}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	61 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}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	62 \end{abstract}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	63 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	64
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	65 %\begin{keywords}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	66 %Deep learning, self-taught learning, out-of-distribution examples, handwritten character recognition, multi-task learning
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	67 %\end{keywords}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	68 %\keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	69
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	70
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	71
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	72 \section{Introduction}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	73 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	74
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	75 {\bf Deep Learning} has emerged as a promising new area of research in
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	76 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.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	77 Learning algorithms for deep architectures are centered on the learning
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	78 of useful representations of data, which are better suited to the task at hand,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	79 and are organized in a hierarchy with multiple levels.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	80 This is in part inspired by observations of the mammalian visual cortex,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	81 which consists of a chain of processing elements, each of which is associated with a
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	82 different representation of the raw visual input. In fact,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	83 it was found recently that the features learnt in deep architectures resemble
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	84 those observed in the first two of these stages (in areas V1 and V2
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	85 of visual cortex) \citep{HonglakL2008}, and that they become more and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	86 more invariant to factors of variation (such as camera movement) in
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	87 higher layers~\citep{Goodfellow2009}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	88 It has been hypothesized that learning a hierarchy of features increases the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	89 ease and practicality of developing representations that are at once
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	90 tailored to specific tasks, yet are able to borrow statistical strength
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	91 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	92 feature representation can lead to higher-level (more abstract, more
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	93 general) features that are more robust to unanticipated sources of
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	94 variance extant in real data.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	95
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	96 Whereas a deep architecture can in principle be more powerful than a
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	97 shallow one in terms of representation, depth appears to render the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	98 training problem more difficult in terms of optimization and local minima.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	99 It is also only recently that successful algorithms were proposed to
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	100 overcome some of these difficulties. All are based on unsupervised
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	101 learning, often in an greedy layer-wise ``unsupervised pre-training''
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	102 stage~\citep{Bengio-2009}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	103 The principle is that each layer starting from
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	104 the bottom is trained to represent its input (the output of the previous
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	105 layer). After this
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	106 unsupervised initialization, the stack of layers can be
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	107 converted into a deep supervised feedforward neural network and fine-tuned by
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	108 stochastic gradient descent.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	109 One of these layer initialization techniques,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	110 applied here, is the Denoising
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	111 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	112 Figure~\ref{fig:da}), which performed similarly or
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	113 better~\citep{VincentPLarochelleH2008-very-small} than previously
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	114 proposed Restricted Boltzmann Machines (RBM)~\citep{Hinton06}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	115 in terms of unsupervised extraction
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	116 of a hierarchy of features useful for classification. Each layer is trained
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	117 to denoise its input, creating a layer of features that can be used as
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	118 input for the next layer, forming a Stacked Denoising Auto-encoder (SDA).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	119 Note that training a Denoising Auto-encoder
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	120 can actually been seen as training a particular RBM by an inductive
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	121 principle different from maximum likelihood~\citep{Vincent-SM-2010},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	122 namely by Score Matching~\citep{Hyvarinen-2005,HyvarinenA2008}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	123
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	124 Previous comparative experimental results with stacking of RBMs and DAs
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	125 to build deep supervised predictors had shown that they could outperform
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	126 shallow architectures in a variety of settings, especially
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	127 when the data involves complex interactions between many factors of
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	128 variation~\citep{LarochelleH2007,Bengio-2009}. Other experiments have suggested
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	129 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	130 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	131 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	132 corresponding to better generalization.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	133
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	134 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	135 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	136 intermediate levels of representation, especially when there are
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	137 more such levels, can be exploited to {\bf share
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	138 statistical strength across different but related types of examples},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	139 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	140 (the multi-task setting), or examples coming from an overlapping
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	141 but different distribution (images with different kinds of perturbations
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	142 and noises, here). This is consistent with the hypotheses discussed
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	143 in~\citet{Bengio-2009} regarding the potential advantage
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	144 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	145 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	146
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	147 This hypothesis is related to a learning setting called
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	148 {\bf self-taught learning}~\citep{RainaR2007}, which combines principles
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	149 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	150 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	151 distribution, e.g., from other classes than those of interest.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	152 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	153 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	154 but more needed to be done to explore the impact
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	155 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	156 (one exception is~\citep{CollobertR2008}, which shares and uses unsupervised
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	157 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	158 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	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 %
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	162 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	163 {\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	164 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	165 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	166 performance and reach human-level performance
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	167 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	168 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	169 More precisely, we ask and answer the following questions:
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	170
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	171 %\begin{enumerate}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	172 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	173 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	174 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	175 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	176
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	177 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	178 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	179 noise, affine transformations, background images) make the resulting
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	180 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	181 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	182 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	183
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	184 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	185 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	186 examples, in particular do they benefit more from
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	187 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	188
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	189 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	190 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	191 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	192 a corresponding shallow and purely supervised architecture?
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	193 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	194 to answer this question.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	195 %\end{enumerate}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	196
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	197 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	198 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	199 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	200 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	201 for stochastically transforming character images and then explain the methodology,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	202 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	203 clean ones.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	204 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	205 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	206
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	207 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	208 %\newpage
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	209 \section{Perturbed and Transformed Character Images}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	210 \label{s:perturbations}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	211 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	212
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	213 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	214 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	215 in order to obtain data from a larger distribution which
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	216 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	217 which we start.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	218 Although character transformations have been used before to
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	219 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	220 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	221 in the complexity of the learning task.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	222 The code for these transformations (mostly Python) is available at
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	223 {\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	224 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	225 amount of deformation or noise introduced.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	226 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	227 from thickness to pinch, performs transformations. The second
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	228 part, from blur to contrast, adds different kinds of noise.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	229 More details can be found in~\citep{ift6266-tr-anonymous}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	230
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	231 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	232 \centering
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	233 \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	234 \subfigure[Thickness]{\includegraphics[scale=0.6]{images/Thick_only.png}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	235 \subfigure[Slant]{\includegraphics[scale=0.6]{images/Slant_only.png}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	236 \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	237 \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	238 \subfigure[Pinch]{\includegraphics[scale=0.6]{images/Pinch_only.png}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	239 %Noise
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	240 \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	241 \subfigure[Occlusion]{\includegraphics[scale=0.6]{images/occlusion_only.png}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	242 \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	243 \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	244 \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	245 \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	246 \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	247 \subfigure[Scratches]{\includegraphics[scale=0.6]{images/Rature_only.png}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	248 \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	249 \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	250 of each transformation module taken separately. Actual perturbed examples are obtained by
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	251 a pipeline of these, with random choices about which module to apply and how much perturbation
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	252 to apply.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	253 \label{fig:transform}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	254 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	255 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	256
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	257 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	258 \section{Experimental Setup}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	259 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	260
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	261 Much previous work on deep learning had been performed on
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	262 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	263 with 60,000 examples, and variants involving 10,000
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	264 examples~\citep{Larochelle-jmlr-2009,VincentPLarochelleH2008-very-small}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	265 The focus here is on much larger training sets, from 10 times to
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	266 to 1000 times larger, and 62 classes.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	267
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	268 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	269 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	270 and {\bf OCR data} (scanned machine printed characters). See more in
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	271 Section~\ref{sec:sources} below. Once a character
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	272 is sampled from one of these sources (chosen randomly), the second step is to
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	273 apply a pipeline of transformations and/or noise processes outlined in section \ref{s:perturbations}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	274
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	275 To provide a baseline of error rate comparison we also estimate human performance
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	276 on both the 62-class task and the 10-class digits task.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	277 We compare the best Multi-Layer Perceptrons (MLP) against
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	278 the best Stacked Denoising Auto-encoders (SDA), when
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	279 both models' hyper-parameters are selected to minimize the validation set error.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	280 We also provide a comparison against a precise estimate
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	281 of human performance obtained via Amazon's Mechanical Turk (AMT)
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	282 service ({\tt http://mturk.com}).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	283 AMT users are paid small amounts
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	284 of money to perform tasks for which human intelligence is required.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	285 Mechanical Turk has been used extensively in natural language processing and vision.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	286 %processing \citep{SnowEtAl2008} and vision
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	287 %\citep{SorokinAndForsyth2008,whitehill09}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	288 AMT users were presented
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	289 with 10 character images (from a test set) on a screen
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	290 and asked to label them.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	291 They were forced to choose a single character class (either among the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	292 62 or 10 character classes) for each image.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	293 80 subjects classified 2500 images per (dataset,task) pair.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	294 Different humans labelers sometimes provided a different label for the same
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	295 example, and we were able to estimate the error variance due to this effect
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	296 because each image was classified by 3 different persons.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	297 The average error of humans on the 62-class task NIST test set
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	298 is 18.2\%, with a standard error of 0.1\%.
623 d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	299 We controlled noise in the labelling process by (1)
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	300 requiring AMT workers with a higher than normal average of accepted
624 49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	301 responses ($>$95\%) on other tasks (2) discarding responses that were not
623 d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	302 complete (10 predictions) (3) discarding responses for which for which the
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	303 time to predict was smaller than 3 seconds for NIST (the mean response time
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	304 was 20 seconds) and 6 seconds seconds for NISTP (average response time of
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	305 45 seconds) (4) discarding responses which were obviously wrong (10
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	306 identical ones, or "12345..."). Overall, after such filtering, we kept
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	307 approximately 95\% of the AMT workers' responses.
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	308
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	309 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	310 \subsection{Data Sources}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	311 \label{sec:sources}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	312 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	313
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	314 %\begin{itemize}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	315 %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	316 {\bf NIST.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	317 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	318 widely used for training and testing character
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	319 recognition systems~\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	320 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	321 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	322 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	323 The fourth partition (called $hsf_4$, 82,587 examples),
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	324 experimentally recognized to be the most difficult one, is the one recommended
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	325 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}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	326 for that purpose. We randomly split the remainder (731,668 examples) into a training set and a validation set for
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	327 model selection.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	328 The performances reported by previous work on that dataset mostly use only the digits.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	329 Here we use all the classes both in the training and testing phase. This is especially
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	330 useful to estimate the effect of a multi-task setting.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	331 The distribution of the classes in the NIST training and test sets differs
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	332 substantially, with relatively many more digits in the test set, and a more uniform distribution
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	333 of letters in the test set (whereas in the training set they are distributed
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	334 more like in natural text).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	335 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	336
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	337 %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	338 {\bf Fonts.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	339 In order to have a good variety of sources we downloaded an important number of free fonts from:
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	340 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	341 % TODO: pointless to anonymize, it's not pointing to our work
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	342 Including an operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	343 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	344 directly as input to our models.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	345 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	346
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	347 %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	348 {\bf Captchas.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	349 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a Python-based captcha generator library) for
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	350 generating characters of the same format as the NIST dataset. This software is based on
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	351 a random character class generator and various kinds of transformations similar to those described in the previous sections.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	352 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	353 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	354 depending on the value of the complexity parameter provided by the user of the data source.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	355 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	356 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	357
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	358 %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	359 {\bf OCR data.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	360 A large set (2 million) of scanned, OCRed and manually verified machine-printed
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	361 characters where included as an
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	362 additional source. This set is part of a larger corpus being collected by the Image Understanding
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	363 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	364 ({\tt http://www.iupr.com}), and which will be publicly released.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	365 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	366 %\end{itemize}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	367
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	368 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	369 \subsection{Data Sets}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	370 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	371
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	372 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	373 from one of the 62 character classes.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	374 %\begin{itemize}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	375 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	376
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	377 %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	378 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	379 \{651,668 / 80,000 / 82,587\} \{training / validation / test\} examples.
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 P07.} This dataset is obtained by taking raw characters from all four of the above sources
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	384 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	385 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	386 $25\%$ 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	387 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	388 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	389 obtained from the corresponding NIST sets plus other sources.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	390 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	391
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	392 %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	393 {\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	394 except that we only apply
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	395 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	396 Therefore, the character is
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	397 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	398 closer to the NIST dataset.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	399 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	400 obtained from the corresponding NIST sets plus other sources.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	401 %\end{itemize}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	402
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	403 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	404 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	405 \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	406 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	407 \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	408 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	409 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	410 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	411 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	412 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	413 $L_H(x,z)$, whose expected value is approximately minimized during training
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	414 by tuning $\theta$ and $\theta'$.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	415 \label{fig:da}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	416 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	417 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	418
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	419 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	420 \subsection{Models and their Hyper-parameters}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	421 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	422
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	423 The experiments are performed using MLPs (with a single
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	424 hidden layer) and deep SDAs.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	425 \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	426
623 d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	427 {\bf Multi-Layer Perceptrons (MLP).} Whereas previous work had compared
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	428 deep architectures to both shallow MLPs and SVMs, we only compared to MLPs
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	429 here because of the very large datasets used (making the use of SVMs
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	430 computationally challenging because of their quadratic scaling
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	431 behavior). Preliminary experiments on training SVMs (libSVM) with subsets
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	432 of the training set allowing the program to fit in memory yielded
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	433 substantially worse results than those obtained with MLPs\footnote{RBF SVMs
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	434 trained with a subset of NISTP or NIST, 100k examples, to fit in memory,
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	435 yielded 64\% test error or worse; online linear SVMs trained on the whole
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	436 of NIST or 800k from NISTP yielded no better than 42\% error; slightly
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	437 better results were obtained by sparsifying the pixel intensities and
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	438 projecting to a second-order polynomial (a very sparse vector), still
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	439 41\% error. We expect that better results could be obtained with a
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	440 better implementation allowing for training with more examples and
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	441 a higher-order non-linear projection.} For training on nearly a hundred million examples (with the
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	442 perturbed data), the MLPs and SDA are much more convenient than classifiers
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	443 based on kernel methods. The MLP has a single hidden layer with $\tanh$
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	444 activation functions, and softmax (normalized exponentials) on the output
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	445 layer for estimating $P(class \| image)$. The number of hidden units is
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	446 taken in $\{300,500,800,1000,1500\}$. Training examples are presented in
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	447 minibatches of size 20. A constant learning rate was chosen among $\{0.001,
d44c78c90669 entered revisions for AMT and SVMs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 622 diff changeset	448 0.01, 0.025, 0.075, 0.1, 0.5\}$.
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	449 %through preliminary experiments (measuring performance on a validation set),
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	450 %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	451 %the whole training sets.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	452 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	453
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	454
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	455 {\bf Stacked Denoising Auto-encoders (SDA).}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	456 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	457 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	458 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	459 apparently setting parameters in the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	460 basin of attraction of supervised gradient descent yielding better
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	461 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	462 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	463 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	464 (starting from the raw pixels).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	465 It is hypothesized that the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	466 advantage brought by this procedure stems from a better prior,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	467 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	468 distribution $P(x)$ and the conditional distribution of interest
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	469 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	470 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	471 deep architecture (whereby complex concepts are expressed as
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	472 compositions of simpler ones through a deep hierarchy).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	473
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	474 Here we chose to use the Denoising
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	475 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	476 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	477 explain (see Figure~\ref{fig:da}, as well as
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	478 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	479 provides efficient inference, and yielded results
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	480 comparable or better than RBMs in series of experiments
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	481 \citep{VincentPLarochelleH2008-very-small}. It really corresponds to a Gaussian
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	482 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	483 During training, a Denoising
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	484 Auto-encoder is presented with a stochastically corrupted version
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	485 of the input and trained to reconstruct the uncorrupted input,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	486 forcing the hidden units to represent the leading regularities in
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	487 the data. Here we use the random binary masking corruption
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	488 (which sets to 0 a random subset of the inputs).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	489 Once it is trained, in a purely unsupervised way,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	490 its hidden units' activations can
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	491 be used as inputs for training a second one, etc.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	492 After this unsupervised pre-training stage, the parameters
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	493 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	494 the same standard procedure used to train them (see above).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	495 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	496 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	497 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	498 separate learning rate for the unsupervised pre-training stage (selected
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	499 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	500 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
624 49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	501 of hidden layers but it was fixed to 3 for most experiments,
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	502 based on previous work with
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	503 SDAs on MNIST~\citep{VincentPLarochelleH2008-very-small}.
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	504 We also compared against 1 and against 2 hidden layers, in order
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	505 to disantangle the effect of depth from the effect of unsupervised
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	506 pre-training.
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	507 The size of the hidden
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	508 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	509 were obtained with the largest values that we could experiment
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	510 with given our patience, with 1000 hidden units.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	511
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	512 %\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	513
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	514 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	515 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	516 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	517 %\vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	518 \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	519 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	520 of all models, on NIST and NISTP test sets.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	521 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	522 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	523 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	524 \label{fig:error-rates-charts}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	525 %\vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	526 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	527
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	528
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	529 \begin{figure*}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	530 \vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	531 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	532 \vspace*{-3mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	533 \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	534 Left: Improvement (or loss, when negative)
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	535 induced by out-of-distribution examples (perturbed data).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	536 Right: Improvement (or loss, when negative) induced by multi-task
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	537 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	538 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	539 out-of-distribution examples, compared to the shallow MLP.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	540 \label{fig:improvements-charts}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	541 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	542 \end{figure*}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	543
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	544 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	545 \section{Experimental Results}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	546 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	547
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	548 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	549 %\subsection{SDA vs MLP vs Humans}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	550 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	551 The models are either trained on NIST (MLP0 and SDA0),
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	552 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	553 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	554 either on the 62-class task
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	555 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	556 for unsupervised pre-training, for DAs) on the larger
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	557 datasets is around one day on a GPU (GTX 285).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	558 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	559 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	560 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	561 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	562 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	563 ~\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	564 ~\citep{Milgram+al-2005}.% More detailed and complete numerical results
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	565 %(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	566 %found in Appendix.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	567 The deep learner not only outperformed the shallow ones and
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	568 previously published performance (in a statistically and qualitatively
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	569 significant way) but when trained with perturbed data
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	570 reaches human performance on both the 62-class task
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	571 and the 10-class (digits) task.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	572 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	573 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	574 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	575 ``c'' and a ``C'' are often indistinguishible).
624 49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	576 Regarding shallower networks pre-trained with unsupervised denoising
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	577 auto-encders, we find that the NIST test error is 21\% with one hidden
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	578 layer and 20\% with two hidden layers (vs 17\% in the same conditions
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	579 with 3 hidden layers). Compare this with the 23\% error achieved
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	580 by the MLP, i.e. a single hidden layer and no unsupervised pre-training.
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	581 As found in previous work~\cite{Erhan+al-2010,Larochelle-jmlr-2009},
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	582 these results show that both depth and
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	583 unsupervised pre-training need to be combined in order to achieve
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	584 the best results.
49933073590c added jmlr_review1.txt and jmlr_review2.txt Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 623 diff changeset	585
622 09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	586
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	587 In addition, as shown in the left of
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	588 Figure~\ref{fig:improvements-charts}, the relative improvement in error
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	589 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	590 SDA, and these
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	591 differences with the shallow MLP are statistically and qualitatively
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	592 significant.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	593 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	594 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	595 (i.e. the perturbed examples examples from NISTP or P07),
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	596 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	597 Relative percent change is measured by taking
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	598 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	599 The right side of
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	600 Figure~\ref{fig:improvements-charts} shows the relative improvement
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	601 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	602 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	603 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	604 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	605 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	606 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	607 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	608 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	609 as $100\% \times$ (single-task
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	610 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	611 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	612 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	613 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	614 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	615 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	616 maximum conditional probability among only the digit classes outputs. The
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	617 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	618 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	619 (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	620 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	621 %\subsection{Perturbed Training Data More Helpful for SDA}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	622 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	623
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	624 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	625 %\subsection{Multi-Task Learning Effects}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	626 %%\vspace*{-1mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	627
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	628 \iffalse
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	629 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	630 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	631 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	632 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	633 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	634 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	635 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	636 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	637 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	638 (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	639 shallow learner.
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 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	642 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	643 fine-tuned on NIST.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	644
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	645 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	646 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	647 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	648 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	649 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	650 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	651 \fi
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	652
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	653
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	654 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	655 \section{Conclusions and Discussion}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	656 \vspace*{-2mm}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	657
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	658 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	659 and perturbed examples) are more beneficial
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	660 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	661 supervised learner. More precisely,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	662 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	663 %\begin{itemize}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	664
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	665 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	666 {\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	667 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	668 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	669 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	670 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	671 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	672 and beating previously published results on the same data.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	673
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	674 $\bullet$ %\item
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	675 {\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	676 and do they help them more than shallow supervised ones}?
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	677 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	678 classifier better on similarly perturbed images but also on
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	679 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	680 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	681 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	682 images (65\% relative improvement on NISTP)
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	683 but only marginally helped (5\% relative improvement on all classes)
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	684 or even hurt (10\% relative loss on digits)
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	685 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	686 were significantly boosted by these out-of-distribution examples.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	687 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	688 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	689 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	690 which may be explained by the arguments below.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	691 Since out-of-distribution data
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	692 (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	693 is of practical importance.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	694 %\end{itemize}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	695
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	696 In the original self-taught learning framework~\citep{RainaR2007}, the
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	697 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	698 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	699 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	700 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	701 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	702 We note instead that, for deep
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	703 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	704 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	705 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	706 out-of-distribution examples is probably preserved
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	707 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	708 (but not in our multi-task experiments),
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	709 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	710 earlier self-taught learning experiments~\citep{RainaR2007}.
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 {\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	713 framework and out-of-distribution examples}?
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	714 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	715 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	716 input distribution. A theoretical analysis of generalization improvements
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	717 due to sharing of intermediate features across tasks already points
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	718 towards that explanation~\cite{baxter95a}.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	719 Intermediate features that can be used in different
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	720 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	721 strength. Features extracted through many levels are more likely to
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	722 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	723 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	724 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	725 of tasks and input conditions.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	726 Therefore, we hypothesize that both depth and unsupervised
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	727 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	728 experiments could attempt at teasing apart these factors.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	729 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	730 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	731 We hypothesize that this is related to the hypotheses studied
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	732 in~\citet{Erhan+al-2010}. In~\citet{Erhan+al-2010}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	733 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	734 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	735 may be happening here. We hypothesize that unsupervised pre-training
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	736 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	737 model in the basin of attraction of supervised gradient descent
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	738 that corresponds to better generalization. Furthermore, such good
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	739 basins of attraction are not discovered by pure supervised learning
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	740 (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	741 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	742 the kind of better basins associated
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	743 with deep learning and out-of-distribution examples.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	744
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	745 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	746 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	747
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	748 \iffalse
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	749 \section*{Appendix I: Detailed Numerical Results}
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 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	752 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	753
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	754 \begin{table}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	755 \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	756 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	757 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	758 (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	759 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	760 \{SDA,MLP\}0 are trained on NIST,
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	761 \{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	762 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	763 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	764 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	765 \label{tab:sda-vs-mlp-vs-humans}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	766 \begin{center}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	767 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	768 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	769 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	770 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	771 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	772 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	773 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	774 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	775 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	776 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	777 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	778 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	779 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	780 \end{tabular}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	781 \end{center}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	782 \end{table}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	783
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	784 \begin{table}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	785 \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	786 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	787 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	788 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	789 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	790 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	791 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	792 on the clean characters. }
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	793 \label{tab:perturbation-effect}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	794 \begin{center}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	795 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	796 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	797 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	798 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	799 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	800 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	801 \end{tabular}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	802 \end{center}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	803 \end{table}
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 \begin{table}[ht]
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	806 \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	807 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	808 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	809 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	810 unperturbed NIST data, using validation error for model selection.
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	811 Relative improvement is 1 - single-task error / multi-task error.}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	812 \label{tab:multi-task}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	813 \begin{center}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	814 \begin{tabular}{\|l\|r\|r\|r\|} \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	815 & single-task & multi-task & relative \\
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	816 & setting & setting & improvement \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	817 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	818 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	819 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	820 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	821 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	822 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	823 \end{tabular}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	824 \end{center}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	825 \end{table}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	826
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	827 \fi
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	828
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	829 %\afterpage{\clearpage}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	830 %\clearpage
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	831 {
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	832 %\bibliographystyle{spbasic} % basic style, author-year citations
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	833 \bibliographystyle{plainnat}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	834 \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	835 %\bibliographystyle{unsrtnat}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	836 %\bibliographystyle{apalike}
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	837 }
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	838
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	839
09b7dee216f4 added aistats2011_revised.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	840 \end{document}

Mercurial > ift6266

annotate writeup/aistats2011_revised.tex @ 624:49933073590c