annotate writeup/nips2010_submission.tex @ 552:35c611363291

added the real picture
author Frederic Bastien <nouiz@nouiz.org>
date Wed, 02 Jun 2010 17:28:43 -0400
parents 8f365abf171d
children 8f6c09d1140f
rev   line source
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
1 \documentclass{article} % For LaTeX2e
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
2 \usepackage{nips10submit_e,times}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
3
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
4 \usepackage{amsthm,amsmath,bbm}
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
5 \usepackage[psamsfonts]{amssymb}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
6 \usepackage{algorithm,algorithmic}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
7 \usepackage[utf8]{inputenc}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
8 \usepackage{graphicx,subfigure}
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
9 \usepackage[numbers]{natbib}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
10
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
11 %\setlength\parindent{0mm}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
12
482
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
13 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
14 \author{The IFT6266 Gang}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
15
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
16 \begin{document}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
17
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
18 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
19 \maketitle
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
20
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
21 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
22 \begin{abstract}
482
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
23 Recent theoretical and empirical work in statistical machine learning has
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
24 demonstrated the importance of learning algorithms for deep
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
25 architectures, i.e., function classes obtained by composing multiple
511
d057941417ed a few changes in the first section
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 510
diff changeset
26 non-linear transformations. Self-taught learning (exploiting unlabeled
482
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
27 examples or examples from other distributions) has already been applied
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
28 to deep learners, but mostly to show the advantage of unlabeled
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
29 examples. Here we explore the advantage brought by {\em out-of-distribution
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
30 examples} and show that {\em deep learners benefit more from them than a
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
31 corresponding shallow learner}, in the area
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
32 of handwritten character recognition. In fact, we show that they reach
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
33 human-level performance on both handwritten digit classification and
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
34 62-class handwritten character recognition. For this purpose we
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
35 developed a powerful generator of stochastic variations and noise
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
36 processes for character images, including not only affine transformations but
482
ce69aa9204d8 changement au titre et reecriture abstract
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 480
diff changeset
37 also slant, local elastic deformations, changes in thickness, background
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
38 images, grey level changes, contrast, occlusion, and various types of
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
39 noise. The out-of-distribution examples are
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
40 obtained from these highly distorted images or
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
41 by including examples of object classes different from those in the target test set.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
42 \end{abstract}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
43 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
44
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
45 \section{Introduction}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
46 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
47
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
48 Deep Learning has emerged as a promising new area of research in
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
49 statistical machine learning (see~\citet{Bengio-2009} for a review).
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
50 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
51 of useful representations of data, which are better suited to the task at hand.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
52 This is in great part inspired by observations of the mammalian visual cortex,
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
53 which consists of a chain of processing elements, each of which is associated with a
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
54 different representation of the raw visual input. In fact,
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
55 it was found recently that the features learnt in deep architectures resemble
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
56 those observed in the first two of these stages (in areas V1 and V2
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
57 of visual cortex)~\citep{HonglakL2008}, and that they become more and
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
58 more invariant to factors of variation (such as camera movement) in
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
59 higher layers~\citep{Goodfellow2009}.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
60 Learning a hierarchy of features increases the
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
61 ease and practicality of developing representations that are at once
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
62 tailored to specific tasks, yet are able to borrow statistical strength
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
63 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
64 feature representation can lead to higher-level (more abstract, more
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
65 general) features that are more robust to unanticipated sources of
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
66 variance extant in real data.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
67
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
68 Whereas a deep architecture can in principle be more powerful than a
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
69 shallow one in terms of representation, depth appears to render the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
70 training problem more difficult in terms of optimization and local minima.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
71 It is also only recently that successful algorithms were proposed to
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
72 overcome some of these difficulties. All are based on unsupervised
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
73 learning, often in an greedy layer-wise ``unsupervised pre-training''
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
74 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
75 applied here, is the Denoising
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
76 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
77 which
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
78 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
79 Machines in terms of unsupervised extraction of a hierarchy of features
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
80 useful for classification. The principle is that each layer starting from
511
d057941417ed a few changes in the first section
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 510
diff changeset
81 the bottom is trained to encode its input (the output of the previous
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
82 layer) and to reconstruct it from a corrupted version. After this
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
83 unsupervised initialization, the stack of DAs can be
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
84 converted into a deep supervised feedforward neural network and fine-tuned by
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
85 stochastic gradient descent.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
86
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
87 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
88 of semi-supervised and multi-task learning: the learner can exploit examples
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
89 that are unlabeled and/or come from a distribution different from the target
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
90 distribution, e.g., from other classes than those of interest.
532
2e33885730cf changements aux charts.ods
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 529
diff changeset
91 It has already been shown that deep learners can clearly take advantage of
2e33885730cf changements aux charts.ods
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 529
diff changeset
92 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
2e33885730cf changements aux charts.ods
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 529
diff changeset
93 but more needs to be done to explore the impact
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
94 of {\em out-of-distribution} examples and of the multi-task setting
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
95 (one exception is~\citep{CollobertR2008}, which uses very different kinds
532
2e33885730cf changements aux charts.ods
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 529
diff changeset
96 of learning algorithms). In particular the {\em relative
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
97 advantage} of deep learning for these settings has not been evaluated.
512
6f042a71be23 todo done
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 507
diff changeset
98 The hypothesis explored here is that a deep hierarchy of features
6f042a71be23 todo done
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 507
diff changeset
99 may be better able to provide sharing of statistical strength
6f042a71be23 todo done
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 507
diff changeset
100 between different regions in input space or different tasks,
6f042a71be23 todo done
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 507
diff changeset
101 as discussed in the conclusion.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
102
466
6205481bf33f asking the questions
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 464
diff changeset
103 In this paper we ask the following questions:
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
104
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
105 %\begin{enumerate}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
106 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
107 Do the good results previously obtained with deep architectures on the
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
108 MNIST digit images generalize to the setting of a much larger and richer (but similar)
466
6205481bf33f asking the questions
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 464
diff changeset
109 dataset, the NIST special database 19, with 62 classes and around 800k examples?
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
110
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
111 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
112 To what extent does the perturbation of input images (e.g. adding
466
6205481bf33f asking the questions
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 464
diff changeset
113 noise, affine transformations, background images) make the resulting
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
114 classifiers better not only on similarly perturbed images but also on
466
6205481bf33f asking the questions
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 464
diff changeset
115 the {\em original clean examples}?
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
116
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
117 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
118 Do deep architectures {\em benefit more from such out-of-distribution}
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
119 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
120
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
121 $\bullet$ %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
122 Similarly, does the feature learning step in deep learning algorithms benefit more
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
123 from training with moderately different classes (i.e. a multi-task learning scenario) than
466
6205481bf33f asking the questions
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 464
diff changeset
124 a corresponding shallow and purely supervised architecture?
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
125 %\end{enumerate}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
126
511
d057941417ed a few changes in the first section
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 510
diff changeset
127 Our experimental results provide positive evidence towards all of these questions.
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
128 To achieve these results, we introduce in the next section a sophisticated system
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
129 for stochastically transforming character images. The conclusion discusses
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
130 the more general question of why deep learners may benefit so much from
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
131 the self-taught learning framework.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
132
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
133 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
134 \section{Perturbation and Transformation of Character Images}
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
135 \label{s:perturbations}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
136 {\large\bf Transformations}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
137
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
138 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
139
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
140 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
141 \centering
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
142 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
143 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
144 \vspace{1.2cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
145 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
146 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
147 {\bf Original:}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
148 This section describes the different transformations we used to stochastically
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
149 transform source images in order to obtain data from a larger distribution which
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
150 covers a domain substantially larger than the clean characters distribution from
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
151 which we start. Although character transformations have been used before to
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
152 improve character recognizers, this effort is on a large scale both
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
153 in number of classes and in the complexity of the transformations, hence
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
154 in the complexity of the learning task.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
155 More details can
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
156 be found in this technical report~\citep{ift6266-tr-anonymous}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
157 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
158 {\tt http://anonymous.url.net}. All the modules in the pipeline share
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
159 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
160 amount of deformation or noise introduced.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
161
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
162 There are two main parts in the pipeline. The first one,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
163 from slant to pinch below, performs transformations. The second
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
164 part, from blur to contrast, adds different kinds of noise.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
165 \end{minipage}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
166
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
167
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
168 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
169 \centering
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
170 \includegraphics[scale=.45]{images/Slant_only.PNG}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
171 \label{fig:Slant}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
172 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
173 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
174 %\centering
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
175 {\bf Slant:}
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
176 Each row of the image is shifted
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
177 proportionally to its height: $shift = round(slant \times height)$.
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
178 $slant \sim U[-complexity,complexity]$.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
179 \vspace{1.2cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
180 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
181
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
182
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
183 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
184 \centering
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
185 \includegraphics[scale=.45]{images/Thick_only.PNG}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
186 \label{fig:Think}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
187 \vspace{.9cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
188 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
189 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
190 {\bf Thinkness:}
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
191 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
192 are applied. The neighborhood of each pixel is multiplied
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
193 element-wise with a {\em structuring element} matrix.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
194 The pixel value is replaced by the maximum or the minimum of the resulting
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
195 matrix, respectively for dilation or erosion. Ten different structural elements with
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
196 increasing dimensions (largest is $5\times5$) were used. For each image,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
197 randomly sample the operator type (dilation or erosion) with equal probability and one structural
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
198 element from a subset of the $n=round(m \times complexity)$ smallest structuring elements
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
199 where $m=10$ for dilation and $m=6$ for erosion (to avoid completely erasing thin characters).
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
200 A neutral element (no transformation)
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
201 is always present in the set. is applied.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
202 \vspace{.4cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
203 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
204 \vspace{-.7cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
205
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
206
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
207 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
208 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
209 \includegraphics[scale=.45]{images/Affine_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
210 \label{fig:Affine}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
211 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
212 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
213 {\bf Affine Transformations:}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
214 A $2 \times 3$ affine transform matrix (with
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
215 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
216 Output pixel $(x,y)$ takes the value of input pixel
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
217 nearest to $(ax+by+c,dx+ey+f)$,
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
218 producing scaling, translation, rotation and shearing.
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
219 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
220 forbid large rotations (not to confuse classes) but to give good
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
221 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
222 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
223 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
224 complexity]$.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
225 \end{minipage}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
226
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
227 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
228 \centering
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
229 \includegraphics[scale=.45]{images/Localelasticdistorsions_only.PNG}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
230 \label{fig:Elastic}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
231 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
232 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
233 {\bf Local Elastic Deformations:}
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
234 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
235 which provides more details.
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
236 The intensity of the displacement fields is given by
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
237 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
238 convolved with a Gaussian 2D kernel (resulting in a blur) of
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
239 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
240 \vspace{.4cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
241 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
242 \vspace{-.7cm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
243
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
244 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
245 \centering
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
246 \includegraphics[scale=.45]{images/Pinch_only.PNG}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
247 \label{fig:Pinch}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
248 \vspace{.6cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
249 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
250 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
251 {\bf Pinch:}
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
252 This is the ``Whirl and pinch'' GIMP filter but with whirl was set to 0.
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
253 A pinch is ``similar to projecting the image onto an elastic
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
254 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
255 For a square input image, this is akin to drawing a circle of
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
256 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
257 that disk (region inside circle) will have its value recalculated by taking
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
258 the value of another ``source'' pixel in the original image. The position of
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
259 that source pixel is found on the line that goes through $C$ and $P$, but
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
260 at some other distance $d_2$. Define $d_1$ to be the distance between $P$
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
261 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
262 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
263 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
264 around the (non-integer) source position thus found.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
265 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
266 %\vspace{1.5cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
267 \end{minipage}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
268
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
269 \vspace{.1cm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
270
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
271 {\large\bf Injecting Noise}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
272
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
273 \vspace*{-.2cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
274 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
275 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
276 \includegraphics[scale=.45]{images/Motionblur_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
277 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
278 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
279 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
280 {\bf Motion Blur:}
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
281 This is GIMP's ``linear motion blur''
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
282 with parameters $length$ and $angle$. The value of
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
283 a pixel in the final image is approximately the mean value of the first $length$ pixels
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
284 found by moving in the $angle$ direction.
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
285 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
286 \vspace{.7cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
287 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
288
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
289 \vspace*{-5mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
290
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
291 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
292 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
293 \includegraphics[scale=.45]{images/occlusion_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
294 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
295 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
296 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
297 {\bf Occlusion:}
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
298 Selects a random rectangle from an {\em occluder} character
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
299 image and places it over the original {\em occluded}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
300 image. Pixels are combined by taking the max(occluder,occluded),
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
301 closer to black. The rectangle corners
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
302 are sampled so that larger complexity gives larger rectangles.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
303 The destination position in the occluded image are also sampled
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
304 according to a normal distribution (more details in~\citet{ift6266-tr-anonymous}).
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
305 This filter is skipped with probability 60\%.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
306 \vspace{.4cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
307 \end{minipage}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
308
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
309 \vspace*{-5mm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
310 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
311 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
312 \includegraphics[scale=.45]{images/Permutpixel_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
313 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
314 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
315 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
316 {\bf Pixel Permutation:}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
317 This filter permutes neighbouring pixels. It first selects
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
318 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each of them are then
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
319 sequentially exchanged with one other in as $V4$ neighbourhood.
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
320 This filter is skipped with probability 80\%.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
321 \vspace{.8cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
322 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
323
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
324
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
325 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
326 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
327 \includegraphics[scale=.45]{images/Distorsiongauss_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
328 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
329 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
330 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
331 {\bf Gaussian Noise:}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
332 This filter simply adds, to each pixel of the image independently, a
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
333 noise $\sim Normal(0,(\frac{complexity}{10})^2)$.
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
334 This filter is skipped with probability 70\%.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
335 \vspace{1.1cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
336 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
337 \vspace{-.7cm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
338
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
339 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
340 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
341 \includegraphics[scale=.45]{images/background_other_only.png}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
342 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
343 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
344 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
345 {\bf Background Images:}
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
346 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
347 background behind the letter, from a randomly chosen natural image,
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
348 with contrast adjustments depending on $complexity$, to preserve
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
349 more or less of the original character image.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
350 \vspace{.8cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
351 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
352 \vspace{-.7cm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
353
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
354 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
355 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
356 \includegraphics[scale=.45]{images/Poivresel_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
357 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
358 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
359 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
360 {\bf Salt and Pepper Noise:}
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
361 This filter adds noise $\sim U[0,1]$ to random subsets of pixels.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
362 The number of selected pixels is $0.2 \times complexity$.
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
363 This filter is skipped with probability 75\%.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
364 \vspace{.9cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
365 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
366 \vspace{-.7cm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
367
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
368 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
369 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
370 \includegraphics[scale=.45]{images/Bruitgauss_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
371 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
372 \vspace{.5cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
373 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
374 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
375 {\bf Spatially Gaussian Noise:}
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
376 Different regions of the image are spatially smoothed by convolving
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
377 the image is convolved with a symmetric Gaussian kernel of
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
378 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
379 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
380 between $0$ and $1$. We also create a symmetric averaging window, of the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
381 kernel size, with maximum value at the center. For each image we sample
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
382 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
383 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
384 initialize to zero a mask matrix of the image size. For each selected pixel
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
385 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
386 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
387 image \times mask}{mask+1}$.
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
388 This filter is skipped with probability 75\%.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
389 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
390 \vspace{-.7cm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
391
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
392 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
393 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
394 \includegraphics[scale=.45]{images/Rature_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
395 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
396 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
397 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
398 \vspace{.4cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
399 {\bf Scratches:}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
400 The scratches module places line-like white patches on the image. The
517
0a5945249f2b section 2, quick first pass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 511
diff changeset
401 lines are heavily transformed images of the digit ``1'' (one), chosen
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
402 at random among 500 such 1 images,
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
403 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
404 complexity)^2$, using bi-cubic interpolation.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
405 Two passes of a grey-scale morphological erosion filter
467
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
406 are applied, reducing the width of the line
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 466
diff changeset
407 by an amount controlled by $complexity$.
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
408 This filter is skipped with probability 85\%. The probabilities
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
409 of applying 1, 2, or 3 patches are (50\%,30\%,20\%).
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
410 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
411 \vspace{-.7cm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
412
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
413 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
414 \centering
552
35c611363291 added the real picture
Frederic Bastien <nouiz@nouiz.org>
parents: 551
diff changeset
415 \includegraphics[scale=.45]{images/Contrast_only.PNG}
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
416 \label{fig:Original}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
417 \end{minipage}%
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
418 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
419 {\bf Grey Level and Contrast Changes:}
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
420 This filter changes the contrast and may invert the image polarity (white
544
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
421 to black and black to white). The contrast is $C \sim U[1-0.85 \times complexity,1]$
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
422 so the image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
1cdfc17e890f ca fitte maintenant
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 541
diff changeset
423 polarity is inverted with probability 50\%.
551
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
424 \vspace{.7cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
425 \end{minipage}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
426 \vspace{-.7cm}
8f365abf171d separete the transmo image
Frederic Bastien <nouiz@nouiz.org>
parents: 550
diff changeset
427
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
428
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
429 \iffalse
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
430 \begin{figure}[ht]
538
f0ee2212ea7c typos and stuff
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 537 534
diff changeset
431 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
432 \caption{Illustration of the pipeline of stochastic
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
433 transformations applied to the image of a lower-case \emph{t}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
434 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
435 left to right, first top line, then bottom line) shows the result
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
436 of applying one of the modules in the pipeline. The last image
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
437 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
438 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
439 \end{figure}
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
440 \fi
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
441
479
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
442
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
443 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
444 \section{Experimental Setup}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
445 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
446
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
447 Whereas much previous work on deep learning algorithms had been performed on
516
092dae9a5040 make the reference more compact.
Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
448 the MNIST digits classification task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
449 with 60~000 examples, and variants involving 10~000
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
450 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
451 to focus here on the case of much larger training sets, from 10 times to
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
452 to 1000 times larger.
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
453
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
454 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
499
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
455 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
2b58eda9fc08 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 495
diff changeset
456 and {\bf OCR data} (scanned machine printed characters). Once a character
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
457 is sampled from one of these sources (chosen randomly), the second step is to
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
458 apply a pipeline of transformations and/or noise processes described in section \ref{s:perturbations}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
459
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
460 To provide a baseline of error rate comparison we also estimate human performance
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
461 on both the 62-class task and the 10-class digits task.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
462 We compare the best MLPs against
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
463 the best SDAs (both models' hyper-parameters are selected to minimize the validation set error),
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
464 along with a comparison against a precise estimate
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
465 of human performance obtained via Amazon's Mechanical Turk (AMT)
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
466 service (http://mturk.com).
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
467 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
468 of money to perform tasks for which human intelligence is required.
522
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
469 Mechanical Turk has been used extensively in natural language processing and vision.
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
470 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 521
diff changeset
471 %\citep{SorokinAndForsyth2008,whitehill09}.
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
472 AMT users were presented
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
473 with 10 character images and asked to choose 10 corresponding ASCII
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
474 characters. They were forced to make a hard choice among the
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
475 62 or 10 character classes (all classes or digits only).
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
476 A total 2500 images/dataset were classified by XXX subjects,
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
477 with 3 subjects classifying each image, allowing
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
478 us to estimate inter-human variability (e.g a standard error of 0.1\%
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
479 on the average 18\% error done by humans on the 62-class task).
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
480
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
481 \vspace*{-1mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
482 \subsection{Data Sources}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
483 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
484
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
485 %\begin{itemize}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
486 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
487 {\bf NIST.}
501
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 500
diff changeset
488 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
489 widely used for training and testing character
516
092dae9a5040 make the reference more compact.
Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
490 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
491 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
492 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
493 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
494 The fourth partition (called $hsf_4$, 82587 examples),
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
495 experimentally recognized to be the most difficult one, is the one recommended
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
496 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}
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
497 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
498 model selection.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
499 The performances reported by previous work on that dataset mostly use only the digits.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
500 Here we use all the classes both in the training and testing phase. This is especially
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
501 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
502 Note that the distribution of the classes in the NIST training and test sets differs
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
503 substantially, with relatively many more digits in the test set, and more uniform distribution
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
504 of letters in the test set, compared to the training set (in the latter, the letters are distributed
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
505 more like the natural distribution of letters in text).
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
506 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
507
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
508 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
509 {\bf Fonts.}
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
510 In order to have a good variety of sources we downloaded an important number of free fonts from:
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
511 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
512 % TODO: pointless to anonymize, it's not pointing to our work
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
513 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
514 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
479
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
515 directly as input to our models.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
516 \vspace*{-1mm}
479
6593e67381a3 Added transformation figure
Xavier Glorot <glorotxa@iro.umontreal.ca>
parents: 476
diff changeset
517
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
518 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
519 {\bf Captchas.}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
520 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
521 generating characters of the same format as the NIST dataset. This software is based on
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
522 a random character class generator and various kinds of transformations similar to those described in the previous sections.
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
523 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
524 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
525 depending on the value of the complexity parameter provided by the user of the data source.
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
526 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
527 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
528
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
529 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
530 {\bf OCR data.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
531 A large set (2 million) of scanned, OCRed and manually verified machine-printed
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
532 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
533 additional source. This set is part of a larger corpus being collected by the Image Understanding
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
534 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
535 ({\tt http://www.iupr.com}), and which will be publicly released.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
536 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
537 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
538
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
539 \vspace*{-1mm}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
540 \subsection{Data Sets}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
541 \vspace*{-1mm}
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
542
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
543 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
544 from one of the 62 character classes.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
545 %\begin{itemize}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
546 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
547
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
548 %\item
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
549 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
550 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
551 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
552
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
553 %\item
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
554 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
555 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
556 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
557 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
558 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
559 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
560 \vspace*{-1mm}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
561
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
562 %\item
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
563 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
564 except that we only apply
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
565 transformations from slant to pinch. Therefore, the character is
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
566 transformed but no additional noise is added to the image, giving images
534
4d6493d171f6 added all sizes
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 533
diff changeset
567 closer to the NIST dataset.
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
568 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
569 %\end{itemize}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
570
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
571 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
572 \subsection{Models and their Hyperparameters}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
573 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
574
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
575 The experiments are performed with Multi-Layer Perceptrons (MLP) with a single
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
576 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
577 \emph{Note that all hyper-parameters are selected based on performance on the {\bf NISTP} validation set.}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
578
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
579 {\bf Multi-Layer Perceptrons (MLP).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
580 Whereas previous work had compared deep architectures to both shallow MLPs and
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
581 SVMs, we only compared to MLPs here because of the very large datasets used
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
582 (making the use of SVMs computationally challenging because of their quadratic
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
583 scaling behavior).
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
584 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
585 exponentials) on the output layer for estimating $P(class | image)$.
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
586 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
587 Training examples are presented in minibatches of size 20. A constant learning
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
588 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
589 through preliminary experiments (measuring performance on a validation set),
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
590 and $0.1$ was then selected for optimizing on the whole training sets.
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
591 \vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
592
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
593
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
594 {\bf Stacked Denoising Auto-Encoders (SDA).}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
595 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
596 can be used to initialize the weights of each layer of a deep MLP (with many hidden
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
597 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
598 apparently setting parameters in the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
599 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
600 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
601 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
602 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
603 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
604 $P(y|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
605 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
606 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
607 compositions of simpler ones through a deep hierarchy).
530
8fe77eac344f Clarifying the experimental setup, typos here and there
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 524
diff changeset
608
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
609 \begin{figure}[ht]
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
610 \vspace*{-2mm}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
611 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
612 \vspace*{-2mm}
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
613 \caption{Illustration of the computations and training criterion for the denoising
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
614 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
615 the layer (i.e. raw input or output of previous layer)
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
616 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
617 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
618 is compared to the uncorrupted input $x$ through the loss function
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
619 $L_H(x,z)$, whose expected value is approximately minimized during training
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
620 by tuning $\theta$ and $\theta'$.}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
621 \label{fig:da}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
622 \vspace*{-2mm}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
623 \end{figure}
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
624
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
625 Here we chose to use the Denoising
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
626 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
627 these deep hierarchies of features, as it is very simple to train and
532
2e33885730cf changements aux charts.ods
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 529
diff changeset
628 explain (see Figure~\ref{fig:da}, as well as
521
13816dbef6ed des choses ont disparu
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 520
diff changeset
629 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
630 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
631 comparable or better than RBMs in series of experiments
519
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
632 \citep{VincentPLarochelleH2008}. During training, a Denoising
eaa595ea2402 section 3 quickpass
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 518
diff changeset
633 Auto-Encoder is presented with a stochastically corrupted version
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
634 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
635 forcing the hidden units to represent the leading regularities in
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
636 the data. Once it is trained, in a purely unsupervised way,
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
637 its hidden units' activations can
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
638 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
639 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
640 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
641 the same standard procedure used to train them (see previous section).
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
642 The SDA hyper-parameters are the same as for the MLP, with the addition of the
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
643 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
644 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
645 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
646 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
647 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
648 of hidden layers but it was fixed to 3 based on previous work with
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
649 SDAs on MNIST~\citep{VincentPLarochelleH2008}.
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
650
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
651 \vspace*{-1mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
652
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
653 \begin{figure}[ht]
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
654 \vspace*{-2mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
655 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
656 \vspace*{-3mm}
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
657 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
658 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
548
34cb28249de0 suggestions de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 547
diff changeset
659 of all models, on NIST and NISTP test sets.
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
660 Right: error rates on NIST test digits only, along with the previous results from
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
661 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
662 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
663 \label{fig:error-rates-charts}
541
8aad1c6ec39a reduction espace
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 539
diff changeset
664 \vspace*{-2mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
665 \end{figure}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
666
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
667
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
668 \section{Experimental Results}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
669 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
670
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
671 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
672 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
673 %\vspace*{-1mm}
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
674 The models are either trained on NIST (MLP0 and SDA0),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
675 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
676 on either NIST, NISTP or P07, either on the 62-class task
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
677 or on the 10-digits task.
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
678 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
679 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
680 SDA2), along with the previous results on the digits NIST special database
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
681 19 test set from the literature respectively based on ARTMAP neural
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
682 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
516
092dae9a5040 make the reference more compact.
Frederic Bastien <nouiz@nouiz.org>
parents: 514
diff changeset
683 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
684 ~\citep{Milgram+al-2005}. More detailed and complete numerical results
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
685 (figures and tables, including standard errors on the error rates) can be
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
686 found in Appendix I of the supplementary material.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
687 The deep learner not only outperformed the shallow ones and
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
688 previously published performance (in a statistically and qualitatively
535
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
689 significant way) but when trained with perturbed data
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 534
diff changeset
690 reaches human performance on both the 62-class task
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
691 and the 10-class (digits) task.
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
692 17\% error (SDA1) or 18\% error (humans) may seem large but a large
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
693 majority of the errors from humans and from SDA1 are from out-of-context
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
694 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
695 ``c'' and a ``C'' are often indistinguishible).
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
696
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
697 \begin{figure}[ht]
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
698 \vspace*{-3mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
699 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
700 \vspace*{-3mm}
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
701 \caption{Relative improvement in error rate due to self-taught learning.
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
702 Left: Improvement (or loss, when negative)
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
703 induced by out-of-distribution examples (perturbed data).
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
704 Right: Improvement (or loss, when negative) induced by multi-task
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
705 learning (training on all classes and testing only on either digits,
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
706 upper case, or lower-case). The deep learner (SDA) benefits more from
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
707 both self-taught learning scenarios, compared to the shallow MLP.}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
708 \label{fig:improvements-charts}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
709 \vspace*{-2mm}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
710 \end{figure}
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
711
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
712 In addition, as shown in the left of
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
713 Figure~\ref{fig:improvements-charts}, the relative improvement in error
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
714 rate brought by self-taught learning is greater for the SDA, and these
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
715 differences with the MLP are statistically and qualitatively
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
716 significant.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
717 The left side of the figure shows the improvement to the clean
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
718 NIST test set error brought by the use of out-of-distribution examples
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
719 (i.e. the perturbed examples examples from NISTP or P07).
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
720 Relative percent change is measured by taking
548
34cb28249de0 suggestions de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 547
diff changeset
721 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
722 The right side of
523
c778d20ab6f8 space adjustments
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 522
diff changeset
723 Figure~\ref{fig:improvements-charts} shows the relative improvement
486
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
724 brought by the use of a multi-task setting, in which the same model is
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
725 trained for more classes than the target classes of interest (i.e. training
877af97ee193 section resultats et appendice
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 485
diff changeset
726 with all 62 classes when the target classes are respectively the digits,
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
727 lower-case, or upper-case characters). Again, whereas the gain from the
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
728 multi-task setting is marginal or negative for the MLP, it is substantial
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
729 for the SDA. Note that to simplify these multi-task experiments, only the original
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
730 NIST dataset is used. For example, the MLP-digits bar shows the relative
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
731 percent improvement in MLP error rate on the NIST digits test set
548
34cb28249de0 suggestions de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 547
diff changeset
732 is $100\% \times$ (1 - single-task
493
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
733 model's error / multi-task model's error). The single-task model is
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
734 trained with only 10 outputs (one per digit), seeing only digit examples,
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
735 whereas the multi-task model is trained with 62 outputs, with all 62
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
736 character classes as examples. Hence the hidden units are shared across
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
737 all tasks. For the multi-task model, the digit error rate is measured by
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
738 comparing the correct digit class with the output class associated with the
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
739 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
740 setting is similar for the other two target classes (lower case characters
a194ce5a4249 difference stat. sign.
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 491
diff changeset
741 and upper case characters).
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
742 %\vspace*{-1mm}
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
743 %\subsection{Perturbed Training Data More Helpful for SDA}
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
744 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
745
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
746 %\vspace*{-1mm}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
747 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
748 %\vspace*{-1mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
749
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
750 \iffalse
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
751 As previously seen, the SDA is better able to benefit from the
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
752 transformations applied to the data than the MLP. In this experiment we
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
753 define three tasks: recognizing digits (knowing that the input is a digit),
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
754 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
755 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
756 consider the digit classification task as the target task and we want to
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
757 evaluate whether training with the other tasks can help or hurt, and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
758 whether the effect is different for MLPs versus SDAs. The goal is to find
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
759 out if deep learning can benefit more (or less) from multiple related tasks
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
760 (i.e. the multi-task setting) compared to a corresponding purely supervised
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
761 shallow learner.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
762
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
763 We use a single hidden layer MLP with 1000 hidden units, and a SDA
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
764 with 3 hidden layers (1000 hidden units per layer), pre-trained and
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
765 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
766
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
767 Our results show that the MLP benefits marginally from the multi-task setting
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
768 in the case of digits (5\% relative improvement) but is actually hurt in the case
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
769 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
495
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 493
diff changeset
770 On the other hand the SDA benefited from the multi-task setting, with relative
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
771 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
772 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
773 \fi
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
774
475
ead3085c1c66 Added charts to nips2010_submission.tex
fsavard
parents: 469
diff changeset
775
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
776 \vspace*{-2mm}
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
777 \section{Conclusions and Discussion}
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
778 \vspace*{-2mm}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
779
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
780 We have found that the self-taught learning framework is more beneficial
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
781 to a deep learner than to a traditional shallow and purely
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
782 supervised learner. More precisely,
520
18a6379999fd more after lunch :)
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 519
diff changeset
783 the answers are positive for all the questions asked in the introduction.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
784 %\begin{itemize}
487
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 486
diff changeset
785
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
786 $\bullet$ %\item
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
787 {\bf Do the good results previously obtained with deep architectures on the
549
ef172f4a322a ca fitte
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 548
diff changeset
788 MNIST digits generalize to a much larger and richer (but similar)
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
789 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
790 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
791 published results on this dataset} (the ones that we are aware of), {\bf in fact reaching human-level
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
792 performance} at around 17\% error on the 62-class task and 1.4\% on the digits.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
793
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
794 $\bullet$ %\item
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
795 {\bf To what extent do self-taught learning scenarios help deep learners,
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
796 and do they help them more than shallow supervised ones}?
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
797 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
798 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
799 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
800 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
801 examples. MLPs were helped by perturbed training examples when tested on perturbed input
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
802 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
803 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
804 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
805 with respect to clean examples . On the other hand, the deep SDAs
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
806 were very significantly boosted by these out-of-distribution examples.
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
807 Similarly, whereas the improvement due to the multi-task setting was marginal or
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
808 negative for the MLP (from +5.6\% to -3.6\% relative change),
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
809 it was very significant for the SDA (from +13\% to +27\% relative change),
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
810 which may be explained by the arguments below.
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
811 %\end{itemize}
472
2dd6e8962df1 conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 469
diff changeset
812
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
813 In the original self-taught learning framework~\citep{RainaR2007}, the
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
814 out-of-sample examples were used as a source of unsupervised data, and
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
815 experiments showed its positive effects in a \emph{limited labeled data}
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
816 scenario. However, many of the results by \citet{RainaR2007} (who used a
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
817 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
818 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
819 We note instead that, for deep
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
820 architectures, our experiments show that such a positive effect is accomplished
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
821 even in a scenario with a \emph{very large number of labeled examples},
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
822 i.e., here, the relative gain of self-taught learning is probably preserved
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
823 in the asymptotic regime.
524
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs"
Dumitru Erhan <dumitru.erhan@gmail.com>
parents: 523
diff changeset
824
547
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 544
diff changeset
825 {\bf Why would deep learners benefit more from the self-taught learning framework}?
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
826 The key idea is that the lower layers of the predictor compute a hierarchy
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
827 of features that can be shared across tasks or across variants of the
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
828 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
829 contexts can be estimated in a way that allows to share statistical
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
830 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
831 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
832 increasing the likelihood that they would be useful for a larger array
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
833 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
834 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
835 pre-training play a part in explaining the advantages observed here, and future
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
836 experiments could attempt at teasing apart these factors.
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
837 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
838 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
839 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
840 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
841 it was found that online learning on a huge dataset did not make the
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
842 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
843 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
844 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
845 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
846 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
847 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
848 (with or without self-taught settings), and more labeled examples
550
662299f265ab suggestions from Ian
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 549
diff changeset
849 does not allow the model to go from the poorer basins of attraction discovered
529
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
850 by the purely supervised shallow models to the kind of better basins associated
4354c3c8f49c longer conclusion
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 524
diff changeset
851 with deep learning and self-taught learning.
502
2b35a6e5ece4 changements de Myriam
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 501
diff changeset
852
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
853 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
854 can be executed on-line at {\tt http://deep.host22.com}.
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
855
498
7ff00c27c976 add missing file for bibtex and make it smaller.
Frederic Bastien <nouiz@nouiz.org>
parents: 496
diff changeset
856 \newpage
496
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
857 {
e41007dd40e9 make the reference shorter.
Frederic Bastien <nouiz@nouiz.org>
parents: 495
diff changeset
858 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,aigaion-shorter,specials}
469
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
859 %\bibliographystyle{plainnat}
d02d288257bf redone bib style
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 467
diff changeset
860 \bibliographystyle{unsrtnat}
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
861 %\bibliographystyle{apalike}
484
9a757d565e46 reduction de taille
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 483
diff changeset
862 }
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
863
485
6beaf3328521 les tables enlevées
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents: 484
diff changeset
864
464
24f4a8b53fcc nips2010_submission.tex
Yoshua Bengio <bengioy@iro.umontreal.ca>
parents:
diff changeset
865 \end{document}