Mercurial > ift6266

annotate writeup/aistats2011_submission.tex @ 603:eb6244c6d861

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
aistats submission
author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Sun, 31 Oct 2010 22:40:33 -0400
parents 203c6071e104
children 51213beaed8b
rev   line source
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
1 %\documentclass[twoside,11pt]{article} % For LaTeX2e
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
2 \documentclass{article} % For LaTeX2e
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
3 \usepackage{aistats2e_2011}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
4 %\usepackage{times}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
5 \usepackage{wrapfig}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
6 \usepackage{amsthm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
7 \usepackage{amsmath}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
8 \usepackage{bbm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
9 \usepackage[utf8]{inputenc}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
10 \usepackage[psamsfonts]{amssymb}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
11 %\usepackage{algorithm,algorithmic} % not used after all
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
12 \usepackage{graphicx,subfigure}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
13 \usepackage[numbers]{natbib}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
14
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
15 \addtolength{\textwidth}{10mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
16 \addtolength{\evensidemargin}{-5mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
17 \addtolength{\oddsidemargin}{-5mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
18
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
19 %\setlength\parindent{0mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
20
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
21 \begin{document}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
22
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
23 \twocolumn[
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
24 \aistatstitle{Deeper Learners Benefit More from Multi-Task and Perturbed Examples}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
25 \runningtitle{Deep Learners for Out-of-Distribution Examples}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
26 \runningauthor{Bengio et. al.}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
27 \aistatsauthor{Anonymous Authors}]
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
28 \iffalse
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
29 Yoshua Bengio \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
30 Frédéric Bastien \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
31 Arnaud Bergeron \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
32 Nicolas Boulanger-Lewandowski \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
33 Thomas Breuel \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
34 Youssouf Chherawala \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
35 Moustapha Cisse \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
36 Myriam Côté \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
37 Dumitru Erhan \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
38 Jeremy Eustache \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
39 Xavier Glorot \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
40 Xavier Muller \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
41 Sylvain Pannetier Lebeuf \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
42 Razvan Pascanu \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
43 Salah Rifai \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
44 Francois Savard \and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
45 Guillaume Sicard
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
46 %}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
47 \fi
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
48 %\aistatsaddress{Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
49 %\date{{\tt bengioy@iro.umontreal.ca}, Dept. IRO, U. Montreal, P.O. Box 6128, Centre-Ville branch, H3C 3J7, Montreal (Qc), Canada}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
50 %\jmlrheading{}{2010}{}{10/2010}{XX/2011}{Yoshua Bengio et al}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
51 %\editor{}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
52
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
53 %\makeanontitle
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
54 %\maketitle
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
55
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
56 %{\bf Running title: Deep Self-Taught Learning}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
57
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
58 %\vspace*{-2mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
59 \begin{abstract}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
60 Recent theoretical and empirical work in statistical machine learning has demonstrated the potential of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple levels of representation. The hypothesis evaluated here is that intermediate levels of representation, because
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
61 they can be shared across tasks and examples from different but related
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
62 distributions, can yield even more benefits where there are more such levels of representation. The experiments are performed on a large-scale handwritten character recognition setting with 62 classes (upper case, lower case, digits). We show that a deep learner could not only {\em beat previously published results but also reach human-level performance}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
63 \end{abstract}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
64 %\vspace*{-3mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
65
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
66 %\begin{keywords}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
67 %Deep learning, self-taught learning, out-of-distribution examples, handwritten character recognition, multi-task learning
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
68 %\end{keywords}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
69 %\keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
70
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
71
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
72
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
73 \section{Introduction}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
74 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
75
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
76 {\bf Deep Learning} has emerged as a promising new area of research in
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
77 statistical machine learning~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,VincentPLarochelleH2008,ranzato-08,TaylorHintonICML2009,Larochelle-jmlr-2009,Salakhutdinov+Hinton-2009,HonglakL2009,HonglakLNIPS2009,Jarrett-ICCV2009,Taylor-cvpr-2010}. See \citet{Bengio-2009} for a review.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
78 Learning algorithms for deep architectures are centered on the learning
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
79 of useful representations of data, which are better suited to the task at hand,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
80 and are organized in a hierarchy with multiple levels.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
81 This is in part inspired by observations of the mammalian visual cortex,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
82 which consists of a chain of processing elements, each of which is associated with a
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
83 different representation of the raw visual input. In fact,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
84 it was found recently that the features learnt in deep architectures resemble
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
85 those observed in the first two of these stages (in areas V1 and V2
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
86 of visual cortex) \citep{HonglakL2008}, and that they become more and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
87 more invariant to factors of variation (such as camera movement) in
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
88 higher layers~\citep{Goodfellow2009}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
89 Learning a hierarchy of features increases the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
90 ease and practicality of developing representations that are at once
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
91 tailored to specific tasks, yet are able to borrow statistical strength
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
92 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
93 feature representation can lead to higher-level (more abstract, more
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
94 general) features that are more robust to unanticipated sources of
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
95 variance extant in real data.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
96
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
97 Whereas a deep architecture can in principle be more powerful than a
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
98 shallow one in terms of representation, depth appears to render the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
99 training problem more difficult in terms of optimization and local minima.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
100 It is also only recently that successful algorithms were proposed to
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
101 overcome some of these difficulties. All are based on unsupervised
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
102 learning, often in an greedy layer-wise ``unsupervised pre-training''
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
103 stage~\citep{Bengio-2009}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
104 The principle is that each layer starting from
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
105 the bottom is trained to represent its input (the output of the previous
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
106 layer). After this
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
107 unsupervised initialization, the stack of layers can be
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
108 converted into a deep supervised feedforward neural network and fine-tuned by
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
109 stochastic gradient descent.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
110 One of these layer initialization techniques,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
111 applied here, is the Denoising
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
112 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
113 Figure~\ref{fig:da}), which performed similarly or
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
114 better~\citep{VincentPLarochelleH2008-very-small} than previously
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
115 proposed Restricted Boltzmann Machines (RBM)~\citep{Hinton06}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
116 in terms of unsupervised extraction
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
117 of a hierarchy of features useful for classification. Each layer is trained
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
118 to denoise its input, creating a layer of features that can be used as
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
119 input for the next layer. Note that training a Denoising Auto-Encoder
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
120 can actually been seen as training a particular RBM by an inductive
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
121 principle different from maximum likelihood~\citep{ift6266-tr-anonymous}, % Vincent-SM-2010},
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
122 namely by Score Matching~\citep{Hyvarinen-2005,HyvarinenA2008}.
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
123
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
124 Previous comparative experimental results with stacking of RBMs and DAs
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
125 to build deep supervised predictors had shown that they could outperform
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
126 shallow architectures in a variety of settings (see~\citet{Bengio-2009}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
127 for a review), especially
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
128 when the data involves complex interactions between many factors of
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
129 variation~\citep{LarochelleH2007}. Other experiments have suggested
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
130 that the unsupervised layer-wise pre-training acted as a useful
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
131 prior~\citep{Erhan+al-2010} that allows one to initialize a deep
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
132 neural network in a relatively much smaller region of parameter space,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
133 corresponding to better generalization.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
134
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
135 To further the understanding of the reasons for the good performance
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
136 observed with deep learners, we focus here on the following {\em hypothesis}:
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
137 intermediate levels of representation, especially when there are
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
138 more such levels, can be exploited to {\bf share
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
139 statistical strength across different but related types of examples},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
140 such as examples coming from other tasks than the task of interest
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
141 (the multi-task setting), or examples coming from an overlapping
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
142 but different distribution (images with different kinds of perturbations
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
143 and noises, here). This is consistent with the hypotheses discussed
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
144 at length in~\citet{Bengio-2009} regarding the potential advantage
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
145 of deep learning and the idea that more levels of representation can
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
146 give rise to more abstract, more general features of the raw input.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
147
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
148 This hypothesis is related to a learning setting called
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
149 {\bf self-taught learning}~\citep{RainaR2007}, which combines principles
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
150 of semi-supervised and multi-task learning: the learner can exploit examples
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
151 that are unlabeled and possibly come from a distribution different from the target
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
152 distribution, e.g., from other classes than those of interest.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
153 It has already been shown that deep learners can clearly take advantage of
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
154 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
155 but more needed to be done to explore the impact
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
156 of {\em out-of-distribution} examples and of the {\em multi-task} setting
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
157 (one exception is~\citep{CollobertR2008}, which shares and uses unsupervised
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
158 pre-training only with the first layer). In particular the {\em relative
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
159 advantage of deep learning} for these settings has not been evaluated.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
160
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
161
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
162 %
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
163 The {\bf main claim} of this paper is that deep learners (with several levels of representation) can
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
164 {\bf benefit more from out-of-distribution examples than shallow learners} (with a single
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
165 level), both in the context of the multi-task setting and from
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
166 perturbed examples. Because we are able to improve on state-of-the-art
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
167 performance and reach human-level performance
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
168 on a large-scale task, we consider that this paper is also a contribution
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
169 to advance the application of machine learning to handwritten character recognition.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
170 More precisely, we ask and answer the following questions:
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
171
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
172 %\begin{enumerate}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
173 $\bullet$ %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
174 Do the good results previously obtained with deep architectures on the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
175 MNIST digit images generalize to the setting of a similar but much larger and richer
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
176 dataset, the NIST special database 19, with 62 classes and around 800k examples?
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
177
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
178 $\bullet$ %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
179 To what extent does the perturbation of input images (e.g. adding
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
180 noise, affine transformations, background images) make the resulting
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
181 classifiers better not only on similarly perturbed images but also on
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
182 the {\em original clean examples}? We study this question in the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
183 context of the 62-class and 10-class tasks of the NIST special database 19.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
184
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
185 $\bullet$ %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
186 Do deep architectures {\em benefit {\bf more} from such out-of-distribution}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
187 examples, in particular do they benefit more from
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
188 examples that are perturbed versions of the examples from the task of interest?
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
189
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
190 $\bullet$ %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
191 Similarly, does the feature learning step in deep learning algorithms benefit {\bf more}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
192 from training with moderately {\em different classes} (i.e. a multi-task learning scenario) than
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
193 a corresponding shallow and purely supervised architecture?
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
194 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
195 to answer this question.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
196 %\end{enumerate}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
197
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
198 Our experimental results provide positive evidence towards all of these questions,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
199 as well as {\em classifiers that reach human-level performance on 62-class isolated character
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
200 recognition and beat previously published results on the NIST dataset (special database 19)}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
201 To achieve these results, we introduce in the next section a sophisticated system
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
202 for stochastically transforming character images and then explain the methodology,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
203 which is based on training with or without these transformed images and testing on
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
204 clean ones. We measure the relative advantage of out-of-distribution examples
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
205 (perturbed or out-of-class)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
206 for a deep learner vs a supervised shallow one.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
207 Code for generating these transformations as well as for the deep learning
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
208 algorithms are made available at {\tt http://anonymous.url.net}.%{\tt http://hg.assembla.com/ift6266}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
209 We also estimate the relative advantage for deep learners of training with
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
210 other classes than those of interest, by comparing learners trained with
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
211 62 classes with learners trained with only a subset (on which they
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
212 are then tested).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
213 The conclusion discusses
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
214 the more general question of why deep learners may benefit so much from
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
215 out-of-distribution examples. Since out-of-distribution data
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
216 (perturbed or from other related classes) is very common, this conclusion
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
217 is of practical importance.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
218
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
219 %\vspace*{-3mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
220 %\newpage
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
221 \section{Perturbed and Transformed Character Images}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
222 \label{s:perturbations}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
223 %\vspace*{-2mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
224
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
225 Figure~\ref{fig:transform} shows the different transformations we used to stochastically
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
226 transform $32 \times 32$ source images (such as the one in Fig.\ref{fig:torig})
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
227 in order to obtain data from a larger distribution which
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
228 covers a domain substantially larger than the clean characters distribution from
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
229 which we start.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
230 Although character transformations have been used before to
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
231 improve character recognizers, this effort is on a large scale both
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
232 in number of classes and in the complexity of the transformations, hence
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
233 in the complexity of the learning task.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
234 The code for these transformations (mostly python) is available at
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
235 {\tt http://anonymous.url.net}. All the modules in the pipeline share
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
236 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
237 amount of deformation or noise introduced.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
238 There are two main parts in the pipeline. The first one,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
239 from slant to pinch below, performs transformations. The second
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
240 part, from blur to contrast, adds different kinds of noise.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
241 More details can be found in~\citep{ift6266-tr-anonymous}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
242
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
243 \begin{figure*}[ht]
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
244 \centering
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
245 \subfigure[Original]{\includegraphics[scale=0.6]{images/Original.png}\label{fig:torig}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
246 \subfigure[Thickness]{\includegraphics[scale=0.6]{images/Thick_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
247 \subfigure[Slant]{\includegraphics[scale=0.6]{images/Slant_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
248 \subfigure[Affine Transformation]{\includegraphics[scale=0.6]{images/Affine_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
249 \subfigure[Local Elastic Deformation]{\includegraphics[scale=0.6]{images/Localelasticdistorsions_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
250 \subfigure[Pinch]{\includegraphics[scale=0.6]{images/Pinch_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
251 %Noise
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
252 \subfigure[Motion Blur]{\includegraphics[scale=0.6]{images/Motionblur_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
253 \subfigure[Occlusion]{\includegraphics[scale=0.6]{images/occlusion_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
254 \subfigure[Gaussian Smoothing]{\includegraphics[scale=0.6]{images/Bruitgauss_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
255 \subfigure[Pixels Permutation]{\includegraphics[scale=0.6]{images/Permutpixel_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
256 \subfigure[Gaussian Noise]{\includegraphics[scale=0.6]{images/Distorsiongauss_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
257 \subfigure[Background Image Addition]{\includegraphics[scale=0.6]{images/background_other_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
258 \subfigure[Salt \& Pepper]{\includegraphics[scale=0.6]{images/Poivresel_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
259 \subfigure[Scratches]{\includegraphics[scale=0.6]{images/Rature_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
260 \subfigure[Grey Level \& Contrast]{\includegraphics[scale=0.6]{images/Contrast_only.png}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
261 \caption{Top left (a): example original image. Others (b-o): examples of the effect
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
262 of each transformation module taken separately. Actual perturbed examples are obtained by
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
263 a pipeline of these, with random choices about which module to apply and how much perturbation
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
264 to apply.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
265 \label{fig:transform}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
266 %\vspace*{-2mm}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
267 \end{figure*}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
268
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
269 %\vspace*{-3mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
270 \section{Experimental Setup}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
271 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
272
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
273 Much previous work on deep learning had been performed on
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
274 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
275 with 60~000 examples, and variants involving 10~000
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
276 examples~\citep{Larochelle-jmlr-2009,VincentPLarochelleH2008}.
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
277 The focus here is on much larger training sets, from 10 times to
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
278 to 1000 times larger, and 62 classes.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
279
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
280 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
281 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
282 and {\bf OCR data} (scanned machine printed characters). Once a character
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
283 is sampled from one of these sources (chosen randomly), the second step is to
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
284 apply a pipeline of transformations and/or noise processes outlined in section \ref{s:perturbations}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
285
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
286 To provide a baseline of error rate comparison we also estimate human performance
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
287 on both the 62-class task and the 10-class digits task.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
288 We compare the best Multi-Layer Perceptrons (MLP) against
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
289 the best Stacked Denoising Auto-encoders (SDA), when
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
290 both models' hyper-parameters are selected to minimize the validation set error.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
291 We also provide a comparison against a precise estimate
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
292 of human performance obtained via Amazon's Mechanical Turk (AMT)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
293 service ({\tt http://mturk.com}).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
294 AMT users are paid small amounts
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
295 of money to perform tasks for which human intelligence is required.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
296 Mechanical Turk has been used extensively in natural language processing and vision.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
297 %processing \citep{SnowEtAl2008} and vision
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
298 %\citep{SorokinAndForsyth2008,whitehill09}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
299 AMT users were presented
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
300 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
301 characters. They were forced to choose a single character class (either among the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
302 62 or 10 character classes) for each image.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
303 80 subjects classified 2500 images per (dataset,task) pair.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
304 Different humans labelers sometimes provided a different label for the same
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
305 example, and we were able to estimate the error variance due to this effect
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
306 because each image was classified by 3 different persons.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
307 The average error of humans on the 62-class task NIST test set
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
308 is 18.2\%, with a standard error of 0.1\%.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
309
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
310 %\vspace*{-3mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
311 \subsection{Data Sources}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
312 %\vspace*{-2mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
313
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
314 %\begin{itemize}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
315 %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
316 {\bf NIST.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
317 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
318 widely used for training and testing character
1f5d2d01b84d draft submission to AISTATS 2011
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}.
1f5d2d01b84d draft submission to AISTATS 2011
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,
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
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.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
323 The fourth partition (called $hsf_4$, 82587 examples),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
324 experimentally recognized to be the most difficult one, is the one recommended
1f5d2d01b84d draft submission to AISTATS 2011
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}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
326 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
327 model selection.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
328 The performances reported by previous work on that dataset mostly use only the digits.
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
330 useful to estimate the effect of a multi-task setting.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
331 The distribution of the classes in the NIST training and test sets differs
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
333 of letters in the test set (whereas in the training set they are distributed
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
334 more like in natural text).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
335 %\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
336
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
337 %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
338 {\bf Fonts.}
1f5d2d01b84d draft submission to AISTATS 2011
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:
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
340 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
341 % TODO: pointless to anonymize, it's not pointing to our work
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
342 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
1f5d2d01b84d draft submission to AISTATS 2011
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,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
344 directly as input to our models.
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
345 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
346
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
347 %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
348 {\bf Captchas.}
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
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.
1f5d2d01b84d draft submission to AISTATS 2011
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.
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
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.
1f5d2d01b84d draft submission to AISTATS 2011
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?
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
356 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
357
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
358 %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
359 {\bf OCR data.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
360 A large set (2 million) of scanned, OCRed and manually verified machine-printed
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
361 characters where included as an
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
363 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
364 ({\tt http://www.iupr.com}), and which will be publicly released.
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
366 %\end{itemize}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
367
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
368 %\vspace*{-3mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
369 \subsection{Data Sets}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
370 %\vspace*{-2mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
371
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
373 from one of the 62 character classes.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
374 %\begin{itemize}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
375 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
376
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
377 %\item
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
379 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
380 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
381
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
382 %\item
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
384 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
1f5d2d01b84d draft submission to AISTATS 2011
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,
1f5d2d01b84d draft submission to AISTATS 2011
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
1f5d2d01b84d draft submission to AISTATS 2011
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 $[0,0.7]$.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
388 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
389 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
390
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
391 %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
392 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
393 except that we only apply
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
394 transformations from slant to pinch. Therefore, the character is
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
395 transformed but no additional noise is added to the image, giving images
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
396 closer to the NIST dataset.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
397 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
398 %\end{itemize}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
399
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
400 \begin{figure*}[ht]
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
401 %\vspace*{-2mm}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
402 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
403 %\vspace*{-2mm}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
404 \caption{Illustration of the computations and training criterion for the denoising
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
405 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
406 the layer (i.e. raw input or output of previous layer)
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
407 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
408 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
409 is compared to the uncorrupted input $x$ through the loss function
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
410 $L_H(x,z)$, whose expected value is approximately minimized during training
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
411 by tuning $\theta$ and $\theta'$.}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
412 \label{fig:da}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
413 %\vspace*{-2mm}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
414 \end{figure*}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
415
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
416 %\vspace*{-3mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
417 \subsection{Models and their Hyperparameters}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
418 %\vspace*{-2mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
419
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
420 The experiments are performed using MLPs (with a single
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
421 hidden layer) and SDAs.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
422 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
423
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
424 {\bf Multi-Layer Perceptrons (MLP).}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
425 Whereas previous work had compared deep architectures to both shallow MLPs and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
426 SVMs, we only compared to MLPs here because of the very large datasets used
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
427 (making the use of SVMs computationally challenging because of their quadratic
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
428 scaling behavior). Preliminary experiments on training SVMs (libSVM) with subsets of the training
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
429 set allowing the program to fit in memory yielded substantially worse results
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
430 than those obtained with MLPs. For training on nearly a billion examples
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
431 (with the perturbed data), the MLPs and SDA are much more convenient than
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
432 classifiers based on kernel methods.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
433 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
434 exponentials) on the output layer for estimating $P(class | image)$.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
435 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
436 Training examples are presented in minibatches of size 20. A constant learning
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
437 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
438 %through preliminary experiments (measuring performance on a validation set),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
439 %and $0.1$ (which was found to work best) was then selected for optimizing on
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
440 %the whole training sets.
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
441 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
442
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
443
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
444 {\bf Stacked Denoising Auto-Encoders (SDA).}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
445 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
446 can be used to initialize the weights of each layer of a deep MLP (with many hidden
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
447 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
448 apparently setting parameters in the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
449 basin of attraction of supervised gradient descent yielding better
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
450 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
451 pre-training phase} uses all of the training images but not the training labels.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
452 Each layer is trained in turn to produce a new representation of its input
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
453 (starting from the raw pixels).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
454 It is hypothesized that the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
455 advantage brought by this procedure stems from a better prior,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
456 on the one hand taking advantage of the link between the input
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
457 distribution $P(x)$ and the conditional distribution of interest
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
458 $P(y|x)$ (like in semi-supervised learning), and on the other hand
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
459 taking advantage of the expressive power and bias implicit in the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
460 deep architecture (whereby complex concepts are expressed as
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
461 compositions of simpler ones through a deep hierarchy).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
462
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
463 Here we chose to use the Denoising
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
464 Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
465 these deep hierarchies of features, as it is simple to train and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
466 explain (see Figure~\ref{fig:da}, as well as
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
467 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
468 provides efficient inference, and yielded results
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
469 comparable or better than RBMs in series of experiments
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
470 \citep{VincentPLarochelleH2008}. During training, a Denoising
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
471 Auto-encoder is presented with a stochastically corrupted version
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
472 of the input and trained to reconstruct the uncorrupted input,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
473 forcing the hidden units to represent the leading regularities in
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
474 the data. Here we use the random binary masking corruption
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
475 (which sets to 0 a random subset of the inputs).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
476 Once it is trained, in a purely unsupervised way,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
477 its hidden units' activations can
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
478 be used as inputs for training a second one, etc.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
479 After this unsupervised pre-training stage, the parameters
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
480 are used to initialize a deep MLP, which is fine-tuned by
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
481 the same standard procedure used to train them (see previous section).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
482 The SDA hyper-parameters are the same as for the MLP, with the addition of the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
483 amount of corruption noise (we used the masking noise process, whereby a
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
484 fixed proportion of the input values, randomly selected, are zeroed), and a
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
485 separate learning rate for the unsupervised pre-training stage (selected
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
486 from the same above set). The fraction of inputs corrupted was selected
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
487 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
488 of hidden layers but it was fixed to 3 based on previous work with
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
489 SDAs on MNIST~\citep{VincentPLarochelleH2008}. The size of the hidden
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
490 layers was kept constant across hidden layers, and the best results
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
491 were obtained with the largest values that we could experiment
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
492 with given our patience, with 1000 hidden units.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
493
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
494 %\vspace*{-1mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
495
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
496 \begin{figure*}[ht]
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
497 %\vspace*{-2mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
498 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
499 %\vspace*{-3mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
500 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
501 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
502 of all models, on NIST and NISTP test sets.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
503 Right: error rates on NIST test digits only, along with the previous results from
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
504 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
505 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
506 \label{fig:error-rates-charts}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
507 %\vspace*{-2mm}
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
508 \end{figure*}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
509
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
510
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
511 \begin{figure*}[ht]
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
512 \vspace*{-3mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
513 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
514 \vspace*{-3mm}
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
515 \caption{Relative improvement in error rate due to out-of-distribution examples.
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
516 Left: Improvement (or loss, when negative)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
517 induced by out-of-distribution examples (perturbed data).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
518 Right: Improvement (or loss, when negative) induced by multi-task
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
519 learning (training on all classes and testing only on either digits,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
520 upper case, or lower-case). The deep learner (SDA) benefits more from
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
521 out-of-distribution examples, compared to the shallow MLP.}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
522 \label{fig:improvements-charts}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
523 \vspace*{-2mm}
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
524 \end{figure*}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
525
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
526 \vspace*{-2mm}
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
527 \section{Experimental Results}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
528 \vspace*{-2mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
529
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
530 %%\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
531 %\subsection{SDA vs MLP vs Humans}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
532 %%\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
533 The models are either trained on NIST (MLP0 and SDA0),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
534 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
535 on either NIST, NISTP or P07, either on the 62-class task
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
536 or on the 10-digits task. Training (including about half
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
537 for unsupervised pre-training, for DAs) on the larger
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
538 datasets takes around one day on a GPU-285.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
539 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
540 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
541 SDA2), along with the previous results on the digits NIST special database
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
542 19 test set from the literature, respectively based on ARTMAP neural
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
543 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
544 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
545 ~\citep{Milgram+al-2005}.% More detailed and complete numerical results
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
546 %(figures and tables, including standard errors on the error rates) can be
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
547 %found in Appendix.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
548 The deep learner not only outperformed the shallow ones and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
549 previously published performance (in a statistically and qualitatively
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
550 significant way) but when trained with perturbed data
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
551 reaches human performance on both the 62-class task
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
552 and the 10-class (digits) task.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
553 17\% error (SDA1) or 18\% error (humans) may seem large but a large
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
554 majority of the errors from humans and from SDA1 are from out-of-context
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
555 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
556 ``c'' and a ``C'' are often indistinguishible).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
557
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
558 In addition, as shown in the left of
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
559 Figure~\ref{fig:improvements-charts}, the relative improvement in error
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
560 rate brought by out-of-distribution examples is greater for the deep
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
561 stacked SDA, and these
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
562 differences with the shallow MLP are statistically and qualitatively
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
563 significant.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
564 The left side of the figure shows the improvement to the clean
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
565 NIST test set error brought by the use of out-of-distribution examples
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
566 (i.e. the perturbed examples examples from NISTP or P07).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
567 Relative percent change is measured by taking
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
568 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
569 The right side of
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
570 Figure~\ref{fig:improvements-charts} shows the relative improvement
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
571 brought by the use of a multi-task setting, in which the same model is
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
572 trained for more classes than the target classes of interest (i.e. training
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
573 with all 62 classes when the target classes are respectively the digits,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
574 lower-case, or upper-case characters). Again, whereas the gain from the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
575 multi-task setting is marginal or negative for the MLP, it is substantial
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
576 for the SDA. Note that to simplify these multi-task experiments, only the original
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
577 NIST dataset is used. For example, the MLP-digits bar shows the relative
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
578 percent improvement in MLP error rate on the NIST digits test set
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
579 is $100\% \times$ (single-task
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
580 model's error / multi-task model's error - 1). The single-task model is
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
581 trained with only 10 outputs (one per digit), seeing only digit examples,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
582 whereas the multi-task model is trained with 62 outputs, with all 62
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
583 character classes as examples. Hence the hidden units are shared across
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
584 all tasks. For the multi-task model, the digit error rate is measured by
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
585 comparing the correct digit class with the output class associated with the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
586 maximum conditional probability among only the digit classes outputs. The
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
587 setting is similar for the other two target classes (lower case characters
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
588 and upper case characters).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
589 %%\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
590 %\subsection{Perturbed Training Data More Helpful for SDA}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
591 %%\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
592
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
593 %%\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
594 %\subsection{Multi-Task Learning Effects}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
595 %%\vspace*{-1mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
596
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
597 \iffalse
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
598 As previously seen, the SDA is better able to benefit from the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
599 transformations applied to the data than the MLP. In this experiment we
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
600 define three tasks: recognizing digits (knowing that the input is a digit),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
601 recognizing upper case characters (knowing that the input is one), and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
602 recognizing lower case characters (knowing that the input is one). We
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
603 consider the digit classification task as the target task and we want to
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
604 evaluate whether training with the other tasks can help or hurt, and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
605 whether the effect is different for MLPs versus SDAs. The goal is to find
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
606 out if deep learning can benefit more (or less) from multiple related tasks
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
607 (i.e. the multi-task setting) compared to a corresponding purely supervised
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
608 shallow learner.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
609
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
610 We use a single hidden layer MLP with 1000 hidden units, and a SDA
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
611 with 3 hidden layers (1000 hidden units per layer), pre-trained and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
612 fine-tuned on NIST.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
613
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
614 Our results show that the MLP benefits marginally from the multi-task setting
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
615 in the case of digits (5\% relative improvement) but is actually hurt in the case
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
616 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
617 On the other hand the SDA benefited from the multi-task setting, with relative
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
618 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
619 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
620 \fi
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
621
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
622
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
623 \vspace*{-2mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
624 \section{Conclusions and Discussion}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
625 \vspace*{-2mm}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
626
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
627 We have found that out-of-distribution examples (multi-task learning
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
628 and perturbed examples) are more beneficial
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
629 to a deep learner than to a traditional shallow and purely
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
630 supervised learner. More precisely,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
631 the answers are positive for all the questions asked in the introduction.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
632 %\begin{itemize}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
633
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
634 $\bullet$ %\item
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
635 {\bf Do the good results previously obtained with deep architectures on the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
636 MNIST digits generalize to a much larger and richer (but similar)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
637 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
638 Yes, the SDA {\em systematically outperformed the MLP and all the previously
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
639 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
640 performance} at around 17\% error on the 62-class task and 1.4\% on the digits,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
641 and beating previously published results on the same data.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
642
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
643 $\bullet$ %\item
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
644 {\bf To what extent do out-of-distribution examples help deep learners,
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
645 and do they help them more than shallow supervised ones}?
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
646 We found that distorted training examples not only made the resulting
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
647 classifier better on similarly perturbed images but also on
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
648 the {\em original clean examples}, and more importantly and more novel,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
649 that deep architectures benefit more from such {\em out-of-distribution}
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
650 examples. Shallow MLPs were helped by perturbed training examples when tested on perturbed input
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
651 images (65\% relative improvement on NISTP)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
652 but only marginally helped (5\% relative improvement on all classes)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
653 or even hurt (10\% relative loss on digits)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
654 with respect to clean examples . On the other hand, the deep SDAs
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
655 were significantly boosted by these out-of-distribution examples.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
656 Similarly, whereas the improvement due to the multi-task setting was marginal or
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
657 negative for the MLP (from +5.6\% to -3.6\% relative change),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
658 it was quite significant for the SDA (from +13\% to +27\% relative change),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
659 which may be explained by the arguments below.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
660 %\end{itemize}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
661
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
662 In the original self-taught learning framework~\citep{RainaR2007}, the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
663 out-of-sample examples were used as a source of unsupervised data, and
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
664 experiments showed its positive effects in a \emph{limited labeled data}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
665 scenario. However, many of the results by \citet{RainaR2007} (who used a
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
666 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
667 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
668 We note instead that, for deep
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
669 architectures, our experiments show that such a positive effect is accomplished
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
670 even in a scenario with a \emph{large number of labeled examples},
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
671 i.e., here, the relative gain of self-taught learning is probably preserved
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
672 in the asymptotic regime.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
673
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
674 {\bf Why would deep learners benefit more from the self-taught learning
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
675 framework and out-of-distribution examples}?
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
676 The key idea is that the lower layers of the predictor compute a hierarchy
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
677 of features that can be shared across tasks or across variants of the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
678 input distribution. A theoretical analysis of generalization improvements
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
679 due to sharing of intermediate features across tasks already points
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
680 towards that explanation~\cite{baxter95a}.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
681 Intermediate features that can be used in different
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
682 contexts can be estimated in a way that allows to share statistical
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
683 strength. Features extracted through many levels are more likely to
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
684 be more abstract and more invariant to some of the factors of variation
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
685 in the underlying distribution (as the experiments in~\citet{Goodfellow2009} suggest),
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
686 increasing the likelihood that they would be useful for a larger array
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
687 of tasks and input conditions.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
688 Therefore, we hypothesize that both depth and unsupervised
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
689 pre-training play a part in explaining the advantages observed here, and future
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
690 experiments could attempt at teasing apart these factors.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
691 And why would deep learners benefit from the self-taught learning
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
692 scenarios even when the number of labeled examples is very large?
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
693 We hypothesize that this is related to the hypotheses studied
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
694 in~\citet{Erhan+al-2010}. In~\citet{Erhan+al-2010}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
695 it was found that online learning on a huge dataset did not make the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
696 advantage of the deep learning bias vanish, and a similar phenomenon
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
697 may be happening here. We hypothesize that unsupervised pre-training
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
698 of a deep hierarchy with out-of-distribution examples initializes the
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
699 model in the basin of attraction of supervised gradient descent
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
700 that corresponds to better generalization. Furthermore, such good
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
701 basins of attraction are not discovered by pure supervised learning
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
702 (with or without out-of-distribution examples) from random initialization, and more labeled examples
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
703 does not allow the shallow or purely supervised models to discover
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
704 the kind of better basins associated
603
eb6244c6d861 aistats submission
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 602
diff changeset
705 with deep learning and out-of-distribution examples.
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
706
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
707 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
602
203c6071e104 aistats submission looking good
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 600
diff changeset
708 can be executed on-line at the anonymous site {\tt http://deep.host22.com}.
600
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
709
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
710 \iffalse
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
711 \section*{Appendix I: Detailed Numerical Results}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
712
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
713 These tables correspond to Figures 2 and 3 and contain the raw error rates for each model and dataset considered.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
714 They also contain additional data such as test errors on P07 and standard errors.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
715
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
716 \begin{table}[ht]
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
717 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
718 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
719 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
720 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
721 and using a validation set to select hyper-parameters and other training choices.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
722 \{SDA,MLP\}0 are trained on NIST,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
723 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
724 The human error rate on digits is a lower bound because it does not count digits that were
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
725 recognized as letters. For comparison, the results found in the literature
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
726 on NIST digits classification using the same test set are included.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
727 \label{tab:sda-vs-mlp-vs-humans}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
728 \begin{center}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
729 \begin{tabular}{|l|r|r|r|r|} \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
730 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
731 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
732 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
733 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
734 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
735 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
736 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
737 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
738 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
739 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
740 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
741 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
742 \end{tabular}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
743 \end{center}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
744 \end{table}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
745
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
746 \begin{table}[ht]
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
747 \caption{Relative change in error rates due to the use of perturbed training data,
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
748 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
749 A positive value indicates that training on the perturbed data helped for the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
750 given test set (the first 3 columns on the 62-class tasks and the last one is
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
751 on the clean 10-class digits). Clearly, the deep learning models did benefit more
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
752 from perturbed training data, even when testing on clean data, whereas the MLP
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
753 trained on perturbed data performed worse on the clean digits and about the same
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
754 on the clean characters. }
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
755 \label{tab:perturbation-effect}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
756 \begin{center}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
757 \begin{tabular}{|l|r|r|r|r|} \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
758 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
759 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
760 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
761 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
762 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
763 \end{tabular}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
764 \end{center}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
765 \end{table}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
766
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
767 \begin{table}[ht]
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
768 \caption{Test error rates and relative change in error rates due to the use of
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
769 a multi-task setting, i.e., training on each task in isolation vs training
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
770 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
771 more from the multi-task setting. All experiments on only on the
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
772 unperturbed NIST data, using validation error for model selection.
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
773 Relative improvement is 1 - single-task error / multi-task error.}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
774 \label{tab:multi-task}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
775 \begin{center}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
776 \begin{tabular}{|l|r|r|r|} \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
777 & single-task & multi-task & relative \\
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
778 & setting & setting & improvement \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
779 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
780 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
781 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
782 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
783 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
784 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
785 \end{tabular}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
786 \end{center}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
787 \end{table}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
788
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
789 \fi
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
790
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
791 %\afterpage{\clearpage}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
792 %\clearpage
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
793 {
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
794 %\bibliographystyle{spbasic} % basic style, author-year citations
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
795 \bibliographystyle{plainnat}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
796 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,specials,aigaion-shorter}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
797 %\bibliographystyle{unsrtnat}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
798 %\bibliographystyle{apalike}
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
799 }
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
800
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
801
1f5d2d01b84d draft submission to AISTATS 2011
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
802 \end{document}