ift6266: writeup/nips2010_submission.tex annotate

annotate writeup/nips2010_submission.tex @ 631:510220effb14

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author	Yoshua Bengio <bengioy@iro.umontreal.ca>
date	Sat, 19 Mar 2011 22:44:53 -0400
parents	9ebb335ca904
children

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}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	3 \usepackage{wrapfig}
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}
581 df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	14 \author{
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	15 Frédéric Bastien ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	16 Yoshua Bengio ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	17 Arnaud Bergeron ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	18 Nicolas Boulanger-Lewandowski ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	19 Thomas Breuel ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	20 Youssouf Chherawala ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	21 Moustapha Cisse ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	22 Myriam Côté ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	23 Dumitru Erhan ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	24 Jeremy Eustache ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	25 Xavier Glorot ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	26 Xavier Muller ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	27 Sylvain Pannetier Lebeuf ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	28 Razvan Pascanu ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	29 Salah Rifai ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	30 Francois Savard ,
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	31 Guillaume Sicard
df749e70f637 ajoute les auteurs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 569 diff changeset	32 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	33
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	34 \begin{document}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	35
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	36 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	37 \maketitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	38
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	39 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	40 \begin{abstract}
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	41 Recent theoretical and empirical work in statistical machine learning has
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	42 demonstrated the importance of learning algorithms for deep
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	43 architectures, i.e., function classes obtained by composing multiple
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	44 non-linear transformations. Self-taught learning (exploiting unlabeled
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	45 examples or examples from other distributions) has already been applied
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	46 to deep learners, but mostly to show the advantage of unlabeled
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	47 examples. Here we explore the advantage brought by {\em out-of-distribution examples}.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	48 For this purpose we
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	49 developed a powerful generator of stochastic variations and noise
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	50 processes for character images, including not only affine transformations
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	51 but also slant, local elastic deformations, changes in thickness,
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	52 background images, grey level changes, contrast, occlusion, and various
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	53 types of noise. The out-of-distribution examples are obtained from these
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	54 highly distorted images or by including examples of object classes
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	55 different from those in the target test set.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	56 We show that {\em deep learners benefit
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	57 more from them than a corresponding shallow learner}, at least in the area of
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	58 handwritten character recognition. In fact, we show that they reach
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	59 human-level performance on both handwritten digit classification and
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	60 62-class handwritten character recognition.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	61 \end{abstract}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	62 \vspace*{-3mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	63
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	64 \section{Introduction}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	65 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	66
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	67 {\bf 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	68 statistical machine learning (see~\citet{Bengio-2009} for a review).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	69 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	70 of useful representations of data, which are better suited to the task at hand.
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	71 This is in part inspired by observations of the mammalian visual cortex,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	72 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	73 different representation of the raw visual input. In fact,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	74 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	75 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	76 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	77 more invariant to factors of variation (such as camera movement) in
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	78 higher layers~\citep{Goodfellow2009}.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	79 Learning a hierarchy of features increases the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	80 ease and practicality of developing representations that are at once
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	81 tailored to specific tasks, yet are able to borrow statistical strength
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	82 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	83 feature representation can lead to higher-level (more abstract, more
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	84 general) features that are more robust to unanticipated sources of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	85 variance extant in real data.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	86
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	87 {\bf Self-taught learning}~\citep{RainaR2007} is a paradigm that combines principles
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	88 of semi-supervised and multi-task learning: the learner can exploit examples
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	89 that are unlabeled and possibly come from a distribution different from the target
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	90 distribution, e.g., from other classes than those of interest.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	91 It has already been shown that deep learners can clearly take advantage of
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	92 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	93 but more needs to be done to explore the impact
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	94 of {\em out-of-distribution} examples and of the multi-task setting
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	95 (one exception is~\citep{CollobertR2008}, which uses a different kind
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	96 of learning algorithm). In particular the {\em relative
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	97 advantage} of deep learning for these settings has not been evaluated.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	98 The hypothesis discussed in the conclusion is that a deep hierarchy of features
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	99 may be better able to provide sharing of statistical strength
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	100 between different regions in input space or different tasks.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	101
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	102 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	103 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	104 shallow one in terms of representation, depth appears to render the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	105 training problem more difficult in terms of optimization and local minima.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	106 It is also only recently that successful algorithms were proposed to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	107 overcome some of these difficulties. All are based on unsupervised
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	108 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	109 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	110 applied here, is the Denoising
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	111 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}),
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	112 which
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	113 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	114 Machines in terms of unsupervised extraction of a hierarchy of features
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	115 useful for classification. Each layer is trained to denoise its
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	116 input, creating a layer of features that can be used as input for the next layer.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	117 \fi
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	118 %The principle is that each layer starting from
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	119 %the bottom is trained to encode its input (the output of the previous
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	120 %layer) and to reconstruct it from a corrupted version. After this
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	121 %unsupervised initialization, the stack of DAs can be
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	122 %converted into a deep supervised feedforward neural network and fine-tuned by
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	123 %stochastic gradient descent.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	124
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	125 %
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	126 In this paper we ask the following questions:
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	127
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	128 %\begin{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	129 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	130 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	131 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	132 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	133
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	134 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	135 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	136 noise, affine transformations, background images) make the resulting
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	137 classifiers better not only on similarly perturbed images but also on
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	138 the {\em original clean examples}? We study this question in the
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	139 context of the 62-class and 10-class tasks of the NIST special database 19.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	140
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	141 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	142 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	143 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	144 We use highly perturbed examples to generate out-of-distribution examples.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	145
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	146 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	147 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	148 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	149 a corresponding shallow and purely supervised architecture?
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	150 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case)
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	151 to answer this question.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	152 %\end{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	153
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	154 Our experimental results provide positive evidence towards all of these questions.
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	155 To achieve these results, we introduce in the next section a sophisticated system
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	156 for stochastically transforming character images and then explain the methodology,
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	157 which is based on training with or without these transformed images and testing on
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	158 clean ones. We measure the relative advantage of out-of-distribution examples
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	159 for a deep learner vs a supervised shallow one.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	160 Code for generating these transformations as well as for the deep learning
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	161 algorithms are made available.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	162 We also estimate the relative advantage for deep learners of training with
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	163 other classes than those of interest, by comparing learners trained with
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	164 62 classes with learners trained with only a subset (on which they
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	165 are then tested).
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	166 The conclusion discusses
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	167 the more general question of why deep learners may benefit so much from
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	168 the self-taught learning framework.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	169
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	170 \vspace*{-3mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	171 \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	172 \label{s:perturbations}
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	173 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	174
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	175 \begin{wrapfigure}[8]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	176 %\begin{minipage}[b]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	177 \vspace*{-5mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	178 \begin{center}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	179 \includegraphics[scale=.4]{images/Original.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	180 {\bf Original}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	181 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	182 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	183 %\vspace{0.7cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	184 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	185 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	186 This section describes the different transformations we used to stochastically
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	187 transform $32 \times 32$ source images (such as the one on the left)
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	188 in order to obtain data from a larger distribution which
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	189 covers a domain substantially larger than the clean characters distribution from
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	190 which we start.
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	191 Although character transformations have been used before to
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	192 improve character recognizers, this effort is on a large scale both
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	193 in number of classes and in the complexity of the transformations, hence
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	194 in the complexity of the learning task.
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	195 More details can
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	196 be found in this technical report~\citep{ift6266-tr-anonymous}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	197 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	198 {\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	199 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	200 amount of deformation or noise introduced.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	201 There are two main parts in the pipeline. The first one,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	202 from slant to pinch below, performs transformations. The second
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	203 part, from blur to contrast, adds different kinds of noise.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	204 %\end{minipage}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	205
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	206 \vspace*{1mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	207 %\subsection{Transformations}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	208 {\large\bf 2.1 Transformations}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	209 \vspace*{1mm}
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	210
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	211
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	212 \begin{wrapfigure}[7]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	213 %\begin{minipage}[b]{0.14\linewidth}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	214 %\centering
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	215 \begin{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	216 \vspace*{-5mm}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	217 \includegraphics[scale=.4]{images/Thick_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	218 {\bf Thickness}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	219 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	220 %\vspace{.6cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	221 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	222 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	223 \end{wrapfigure}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	224 To change character {\bf thickness}, morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	225 are applied. The neighborhood of each pixel is multiplied
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	226 element-wise with a {\em structuring element} matrix.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	227 The pixel value is replaced by the maximum or the minimum of the resulting
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	228 matrix, respectively for dilation or erosion. Ten different structural elements with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	229 increasing dimensions (largest is $5\times5$) were used. For each image,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	230 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	231 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	232 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	233 A neutral element (no transformation)
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	234 is always present in the set.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	235 %\vspace{.4cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	236 %\end{minipage}
582 9ebb335ca904 techreport.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 581 diff changeset	237 \vspace*{3mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	238
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	239 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	240 \centering
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	241 \includegraphics[scale=.4]{images/Slant_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	242 {\bf Slant}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	243 \end{minipage}%
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	244 \hspace{0.3cm}
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	245 \begin{minipage}[b]{0.83\linewidth}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	246 %\centering
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	247 To produce {\bf slant}, each row of the image is shifted
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	248 proportionally to its height: $shift = round(slant \times height)$.
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	249 $slant \sim U[-complexity,complexity]$.
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	250 The shift is randomly chosen to be either to the left or to the right.
582 9ebb335ca904 techreport.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 581 diff changeset	251 \vspace{8mm}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	252 \end{minipage}
582 9ebb335ca904 techreport.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 581 diff changeset	253 \vspace*{3mm}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	254
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	255 %\begin{minipage}[b]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	256 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	257 \begin{wrapfigure}[8]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	258 \vspace*{-6mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	259 \begin{center}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	260 \includegraphics[scale=.4]{images/Affine_only.png}\\
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	261 {\small {\bf Affine \mbox{Transformation}}}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	262 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	263 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	264 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	265 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	266 A $2 \times 3$ {\bf affine transform} matrix (with
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	267 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$.
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	268 Output pixel $(x,y)$ takes the value of input pixel
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	269 nearest to $(ax+by+c,dx+ey+f)$,
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	270 producing scaling, translation, rotation and shearing.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	271 Marginal distributions of $(a,b,c,d,e,f)$ have been tuned to
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	272 forbid large rotations (to avoid confusing classes) but to give good
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	273 variability of the transformation: $a$ and $d$ $\sim U[1-3
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	274 complexity,1+3\,complexity]$, $b$ and $e$ $\sim U[-3 \,complexity,3\,
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	275 complexity]$, and $c$ and $f \sim U[-4 \,complexity, 4 \,
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	276 complexity]$.\\
582 9ebb335ca904 techreport.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 581 diff changeset	277 \end{minipage}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	278
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	279 \vspace*{-4.5mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	280
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	281 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	282 \begin{wrapfigure}[7]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	283 %\hspace*{-8mm}\begin{minipage}[b]{0.25\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	284 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	285 \begin{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	286 \vspace*{-4mm}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	287 \includegraphics[scale=.4]{images/Localelasticdistorsions_only.png}\\
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	288 {\bf Local Elastic Deformation}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	289 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	290 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	291 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	292 %\hspace{-3mm}\begin{minipage}[b]{0.85\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	293 %\vspace*{-20mm}
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	294 The {\bf local elastic deformation}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	295 module induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	296 which provides more details.
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	297 The intensity of the displacement fields is given by
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	298 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	299 convolved with a Gaussian 2D kernel (resulting in a blur) of
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	300 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	301 %\vspace{.9cm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	302 \end{minipage}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	303
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	304 \vspace*{7mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	305
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	306 %\begin{minipage}[b]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	307 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	308 \begin{wrapfigure}[7]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	309 \vspace*{-5mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	310 \begin{center}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	311 \includegraphics[scale=.4]{images/Pinch_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	312 {\bf Pinch}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	313 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	314 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	315 %\vspace{.6cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	316 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	317 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	318 The {\bf pinch} module applies the ``Whirl and pinch'' GIMP filter with whirl set to 0.
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	319 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	320 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	321 For a square input image, draw a radius-$r$ disk
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	322 around its center $C$. Any pixel $P$ belonging to
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	323 that disk has its value replaced by
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	324 the value of a ``source'' pixel in the original image,
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	325 on the line that goes through $C$ and $P$, but
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	326 at some other distance $d_2$. Define $d_1=distance(P,C)$
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	327 and $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	328 d_1$, where $pinch$ is a parameter of the filter.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	329 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	330 around the (non-integer) source position thus found.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	331 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	332 %\vspace{1.5cm}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	333 %\end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	334
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	335 \vspace{1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	336
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	337 {\large\bf 2.2 Injecting Noise}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	338 %\subsection{Injecting Noise}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	339 \vspace{2mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	340
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	341 %\vspace*{-.2cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	342 \begin{minipage}[t]{0.14\linewidth}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	343 \centering
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	344 \vspace*{-2mm}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	345 \includegraphics[scale=.4]{images/Motionblur_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	346 {\bf Motion Blur}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	347 \end{minipage}%
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	348 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	349 %\vspace*{.5mm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	350 The {\bf motion blur} module is GIMP's ``linear motion blur'', which
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	351 has parameters $length$ and $angle$. The value of
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	352 a pixel in the final image is approximately the mean of the first $length$ pixels
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	353 found by moving in the $angle$ direction,
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	354 $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	355 \vspace{5mm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	356 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	357
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	358 \vspace*{1mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	359
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	360 \begin{minipage}[t]{0.14\linewidth}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	361 \centering
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	362 \includegraphics[scale=.4]{images/occlusion_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	363 {\bf Occlusion}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	364 %\vspace{.5cm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	365 \end{minipage}%
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	366 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	367 \vspace*{-18mm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	368 The {\bf occlusion} module selects a random rectangle from an {\em occluder} character
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	369 image and places it over the original {\em occluded}
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	370 image. Pixels are combined by taking the max(occluder, occluded),
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	371 i.e. keeping the lighter ones.
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	372 The rectangle corners
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	373 are sampled so that larger complexity gives larger rectangles.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	374 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	375 according to a normal distribution (more details in~\citet{ift6266-tr-anonymous}).
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	376 This module is skipped with probability 60\%.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	377 %\vspace{7mm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	378 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	379
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	380 \vspace*{1mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	381
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	382 \begin{wrapfigure}[8]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	383 \vspace*{-6mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	384 \begin{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	385 %\begin{minipage}[t]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	386 %\centering
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	387 \includegraphics[scale=.4]{images/Bruitgauss_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	388 {\bf Gaussian Smoothing}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	389 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	390 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	391 %\vspace{.5cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	392 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	393 %\hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	394 With the {\bf Gaussian smoothing} module,
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	395 different regions of the image are spatially smoothed.
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	396 This is achieved by first convolving
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	397 the image with an isotropic Gaussian kernel of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	398 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	399 complexity]$ and $[2,2 + 6 \times complexity]$. This filtered image is normalized
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	400 between $0$ and $1$. We also create an isotropic weighted averaging window, of the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	401 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	402 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	403 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	404 initialize to zero a mask matrix of the image size. For each selected pixel
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	405 we add to the mask the averaging window centered on it. The final image is
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	406 computed from the following element-wise operation: $\frac{image + filtered\_image
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	407 \times mask}{mask+1}$.
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	408 This module is skipped with probability 75\%.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	409 %\end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	410
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	411 \newpage
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	412
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	413 \vspace*{-9mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	414
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	415 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	416 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	417 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	418 \begin{wrapfigure}[7]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	419 \vspace*{-5mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	420 \begin{center}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	421 \includegraphics[scale=.4]{images/Permutpixel_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	422 {\small\bf Permute Pixels}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	423 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	424 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	425 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	426 %\hspace{-0cm}\begin{minipage}[t]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	427 %\vspace*{-20mm}
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	428 This module {\bf permutes neighbouring pixels}. It first selects a
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	429 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	430 of these pixels is then sequentially exchanged with a random pixel
dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	431 among its four nearest neighbors (on its left, right, top or bottom).
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	432 This module is skipped with probability 80\%.\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	433 \vspace*{1mm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	434 \end{minipage}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	435
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	436 \vspace{-3mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	437
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	438 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	439 \begin{wrapfigure}[7]{l}{0.15\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	440 %\vspace*{-3mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	441 \begin{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	442 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	443 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	444 \vspace*{-5mm}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	445 \includegraphics[scale=.4]{images/Distorsiongauss_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	446 {\small \bf Gauss. Noise}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	447 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	448 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	449 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	450 %\hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	451 \vspace*{12mm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	452 The {\bf Gaussian noise} module simply adds, to each pixel of the image independently, a
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	453 noise $\sim Normal(0,(\frac{complexity}{10})^2)$.
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	454 This module is skipped with probability 70\%.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	455 %\vspace{1.1cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	456 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	457
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	458 \vspace*{1.2cm}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	459
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	460 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	461 \begin{minipage}[t]{0.14\linewidth}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	462 \centering
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	463 \includegraphics[scale=.4]{images/background_other_only.png}\\
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	464 {\small \bf Bg Image}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	465 \end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	466 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	467 \vspace*{-18mm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	468 Following~\citet{Larochelle-jmlr-2009}, the {\bf background image} module adds a random
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	469 background image behind the letter, from a randomly chosen natural image,
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	470 with contrast adjustments depending on $complexity$, to preserve
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	471 more or less of the original character image.
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	472 %\vspace{.8cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	473 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	474 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	475 %\vspace{-.7cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	476
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	477 \begin{minipage}[t]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	478 \centering
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	479 \includegraphics[scale=.4]{images/Poivresel_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	480 {\small \bf Salt \& Pepper}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	481 \end{minipage}%
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	482 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	483 \vspace*{-18mm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	484 The {\bf salt and pepper noise} module adds noise $\sim U[0,1]$ to random subsets of pixels.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	485 The number of selected pixels is $0.2 \times complexity$.
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	486 This module is skipped with probability 75\%.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	487 %\vspace{.9cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	488 \end{minipage}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	489 %\vspace{-.7cm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	490
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	491 \vspace{1mm}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	492
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	493 \begin{minipage}[t]{\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	494 \begin{wrapfigure}[7]{l}{0.14\textwidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	495 %\begin{minipage}[t]{0.14\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	496 %\centering
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	497 \begin{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	498 \vspace*{-4mm}
558 143a1467f157 Fixed compilation: .PNG -> .png Olivier Delalleau <delallea@iro> parents: 555 diff changeset	499 \hspace*{-1mm}\includegraphics[scale=.4]{images/Rature_only.png}\\
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	500 {\bf Scratches}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	501 %\end{minipage}%
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	502 \end{center}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	503 \end{wrapfigure}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	504 %\hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	505 %\vspace{.4cm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	506 The {\bf 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	507 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	508 at random among 500 such 1 images,
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	509 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
554 e95395f51d72 minor Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 553 diff changeset	510 complexity)^2$ (in degrees), using bi-cubic interpolation.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	511 Two passes of a grey-scale morphological erosion filter
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	512 are applied, reducing the width of the line
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	513 by an amount controlled by $complexity$.
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	514 This module is skipped with probability 85\%. The probabilities
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	515 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	516 \end{minipage}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	517
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	518 \vspace*{1mm}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	519
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	520 \begin{minipage}[t]{0.25\linewidth}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	521 \centering
559 cf5a7ee2d892 Merged Olivier Delalleau <delallea@iro> parents: 558 557 diff changeset	522 \hspace*{-16mm}\includegraphics[scale=.4]{images/Contrast_only.png}\\
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	523 {\bf Grey Level \& Contrast}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	524 \end{minipage}%
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	525 \hspace{-12mm}\begin{minipage}[t]{0.82\linewidth}
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	526 \vspace*{-18mm}
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	527 The {\bf grey level and contrast} module changes the contrast by changing grey levels, and may invert the image polarity (white
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	528 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	529 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	530 polarity is inverted with probability 50\%.
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	531 %\vspace{.7cm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	532 \end{minipage}
555 b6dfba0a110c ameliorer l'aspect visuel, Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 554 diff changeset	533 \vspace{2mm}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	534
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	535
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	536 \iffalse
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	537 \begin{figure}[ht]
538 f0ee2212ea7c typos and stuff Dumitru Erhan <dumitru.erhan@gmail.com> parents: 537 534 diff changeset	538 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	539 \caption{Illustration of the pipeline of stochastic
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	540 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	541 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	542 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	543 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	544 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	545 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	546 \end{figure}
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	547 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	548
560 dc5c3f538a05 Small fixes (typos / precisions) Olivier Delalleau <delallea@iro> parents: 559 diff changeset	549 \vspace*{-3mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	550 \section{Experimental Setup}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	551 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	552
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	553 Much previous work on deep learning had been performed on
8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	554 the MNIST digits 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	555 with 60~000 examples, and variants involving 10~000
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	556 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}.
8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	557 The focus here is on much larger training sets, from 10 times to
8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	558 to 1000 times larger, and 62 classes.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	559
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	560 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	561 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	562 and {\bf OCR data} (scanned machine printed characters). Once a character
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	563 is sampled from one of these sources (chosen randomly), the second step is to
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	564 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	565
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	566 To provide a baseline of error rate comparison we also estimate human performance
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	567 on both the 62-class task and the 10-class digits task.
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	568 We compare the best Multi-Layer Perceptrons (MLP) against
b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	569 the best Stacked Denoising Auto-encoders (SDA), when
b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	570 both models' hyper-parameters are selected to minimize the validation set error.
b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	571 We also provide a comparison against a precise estimate
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	572 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	573 service (http://mturk.com).
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	574 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	575 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	576 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	577 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	578 %\citep{SorokinAndForsyth2008,whitehill09}.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	579 AMT users were presented
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	580 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	581 characters. They were forced to choose a single character class (either among the
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	582 62 or 10 character classes) for each image.
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	583 80 subjects classified 2500 images per (dataset,task) pair,
8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	584 with the guarantee that 3 different subjects classified each image, allowing
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	585 us to estimate inter-human variability (e.g a standard error of 0.1\%
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	586 on the average 18.2\% error done by humans on the 62-class task NIST test set).
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	587
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	588 \vspace*{-3mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	589 \subsection{Data Sources}
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	590 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	591
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	592 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	593 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	594 {\bf NIST.}
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	595 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	596 widely used for training and testing character
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	597 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	598 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	599 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	600 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	601 The fourth partition (called $hsf_4$, 82587 examples),
4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	602 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	603 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	604 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	605 model selection.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	606 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	607 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	608 useful to estimate the effect of a multi-task setting.
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	609 The distribution of the classes in the NIST training and test sets differs
8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	610 substantially, with relatively many more digits in the test set, and a more uniform distribution
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	611 of letters in the test set (whereas in the training set they are distributed
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	612 more like in natural text).
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	613 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	614
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	615 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	616 {\bf Fonts.}
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	617 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	618 {\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	619 % 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	620 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	621 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	622 directly as input to our models.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	623 \vspace*{-1mm}
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	624
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	625 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	626 {\bf Captchas.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	627 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	628 generating characters of the same format as the NIST dataset. This software is based on
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	629 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	630 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	631 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	632 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	633 %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	634 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	635
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	636 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	637 {\bf OCR data.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	638 A large set (2 million) of scanned, OCRed and manually verified machine-printed
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	639 characters where included as an
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	640 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	641 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	642 ({\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	643 %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	644 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	645
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	646 \vspace*{-3mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	647 \subsection{Data Sets}
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	648 \vspace*{-2mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	649
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	650 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	651 from one of the 62 character classes.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	652 %\begin{itemize}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	653 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	654
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	655 %\item
534 4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	656 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	657 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	658 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	659
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	660 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	661 {\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	662 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	663 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	664 $25\%$ 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	665 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	666 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	667 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	668
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	669 %\item
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	670 {\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	671 except that we only apply
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	672 transformations from slant to pinch. Therefore, the character is
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	673 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	674 closer to the NIST dataset.
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	675 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	676 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	677
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	678 \vspace*{-3mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	679 \subsection{Models and their Hyperparameters}
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	680 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	681
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	682 The experiments are performed using MLPs (with a single
b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	683 hidden layer) and SDAs.
553 8f6c09d1140f ca fitte de nouveau Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 552 diff changeset	684 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	685
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	686 {\bf Multi-Layer Perceptrons (MLP).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	687 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	688 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	689 (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	690 scaling behavior).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	691 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	692 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	693 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	694 Training examples are presented in minibatches of size 20. A constant learning
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	695 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$.
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	696 %through preliminary experiments (measuring performance on a validation set),
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	697 %and $0.1$ (which was found to work best) was then selected for optimizing on
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	698 %the whole training sets.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	699 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	700
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	701
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	702 {\bf Stacked Denoising Auto-Encoders (SDA).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	703 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	704 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	705 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	706 apparently setting parameters in the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	707 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	708 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	709 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	710 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	711 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	712 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	713 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	714 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	715 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	716
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	717 \begin{figure}[ht]
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	718 \vspace*{-2mm}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	719 \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	720 \vspace*{-2mm}
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	721 \caption{Illustration of the computations and training criterion for the denoising
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	722 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	723 the layer (i.e. raw input or output of previous layer)
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	724 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	725 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	726 is compared to the uncorrupted input $x$ through the loss function
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	727 $L_H(x,z)$, whose expected value is approximately minimized during training
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	728 by tuning $\theta$ and $\theta'$.}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	729 \label{fig:da}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	730 \vspace*{-2mm}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	731 \end{figure}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	732
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	733 Here we chose to use the Denoising
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	734 Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	735 these deep hierarchies of features, as it is simple to train and
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	736 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	737 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	738 provides efficient inference, and yielded results
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	739 comparable or better than RBMs in series of experiments
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	740 \citep{VincentPLarochelleH2008}. During training, a Denoising
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	741 Auto-encoder is presented with a stochastically corrupted version
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	742 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	743 forcing the hidden units to represent the leading regularities in
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	744 the data. Here we use the random binary masking corruption
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	745 (which sets to 0 a random subset of the inputs).
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	746 Once it is trained, in a purely unsupervised way,
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	747 its hidden units' activations can
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	748 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	749 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	750 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	751 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	752 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	753 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	754 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	755 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	756 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	757 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	758 of hidden layers but it was fixed to 3 based on previous work with
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	759 SDAs on MNIST~\citep{VincentPLarochelleH2008}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	760
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	761 \vspace*{-1mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	762
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	763 \begin{figure}[ht]
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	764 \vspace*{-2mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	765 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	766 \vspace*{-3mm}
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	767 \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	768 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	769 of all models, on NIST and NISTP test sets.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	770 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	771 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	772 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	773 \label{fig:error-rates-charts}
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	774 \vspace*{-2mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	775 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	776
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	777
557 17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	778 \begin{figure}[ht]
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	779 \vspace*{-3mm}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	780 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	781 \vspace*{-3mm}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	782 \caption{Relative improvement in error rate due to self-taught learning.
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	783 Left: Improvement (or loss, when negative)
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	784 induced by out-of-distribution examples (perturbed data).
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	785 Right: Improvement (or loss, when negative) induced by multi-task
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	786 learning (training on all classes and testing only on either digits,
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	787 upper case, or lower-case). The deep learner (SDA) benefits more from
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	788 both self-taught learning scenarios, compared to the shallow MLP.}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	789 \label{fig:improvements-charts}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	790 \vspace*{-2mm}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	791 \end{figure}
17d16700e0c8 encore du visuel de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 555 diff changeset	792
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	793 \section{Experimental Results}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	794 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	795
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	796 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	797 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	798 %\vspace*{-1mm}
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	799 The models are either trained on NIST (MLP0 and SDA0),
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	800 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	801 on either NIST, NISTP or P07, either on the 62-class task
568 ae6ba0309bf9 nouveaux graphes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 566 diff changeset	802 or on the 10-digits task. Training (including about half
ae6ba0309bf9 nouveaux graphes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 566 diff changeset	803 for unsupervised pre-training, for DAs) on the larger
ae6ba0309bf9 nouveaux graphes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 566 diff changeset	804 datasets takes around one day on a GPU-285.
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	805 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	806 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	807 SDA2), along with the previous results on the digits NIST special database
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	808 19 test set from the literature, respectively based on ARTMAP neural
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	809 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	810 ~\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	811 ~\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	812 (figures and tables, including standard errors on the error rates) can be
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	813 found in Appendix I of the supplementary material.
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	814 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	815 previously published performance (in a statistically and qualitatively
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	816 significant way) but when trained with perturbed data
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	817 reaches human performance on both the 62-class task
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	818 and the 10-class (digits) task.
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	819 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	820 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	821 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	822 ``c'' and a ``C'' are often indistinguishible).
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	823
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	824 In addition, as shown in the left of
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	825 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	826 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	827 differences with the MLP are statistically and qualitatively
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	828 significant.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	829 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	830 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	831 (i.e. the perturbed examples examples from NISTP or P07).
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	832 Relative percent change is measured by taking
548 34cb28249de0 suggestions de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 547 diff changeset	833 $100 \% \times$ (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	834 The right side of
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	835 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	836 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	837 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	838 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	839 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	840 multi-task setting is marginal or negative for the MLP, it is substantial
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	841 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	842 NIST dataset is used. For example, the MLP-digits bar shows the relative
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	843 percent improvement in MLP error rate on the NIST digits test set
566 b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	844 is $100\% \times$ (single-task
b9b811e886ae Small fixes Olivier Delalleau <delallea@iro> parents: 560 diff changeset	845 model's error / multi-task model's error - 1). The single-task model is
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	846 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	847 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	848 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	849 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	850 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	851 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	852 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	853 and upper case characters).
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	854 %\vspace*{-1mm}
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	855 %\subsection{Perturbed Training Data More Helpful for SDA}
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	856 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	857
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	858 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	859 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	860 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	861
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	862 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	863 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	864 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	865 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	866 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	867 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	868 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	869 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	870 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	871 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	872 (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	873 shallow learner.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	874
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	875 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	876 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	877 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	878
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	879 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	880 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	881 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	882 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	883 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	884 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	885 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	886
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	887
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	888 \vspace*{-2mm}
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	889 \section{Conclusions and Discussion}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	890 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	891
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	892 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	893 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	894 supervised learner. More precisely,
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	895 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	896 %\begin{itemize}
487 21787ac4e5a0 - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 486 diff changeset	897
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	898 $\bullet$ %\item
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	899 {\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	900 MNIST digits generalize to a much larger and richer (but similar)
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	901 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	902 Yes, the SDA {\em systematically outperformed the MLP and all the previously
9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	903 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	904 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	905
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	906 $\bullet$ %\item
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	907 {\bf To what extent do self-taught learning scenarios help deep learners,
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	908 and do they help them more than shallow supervised ones}?
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	909 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	910 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	911 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	912 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	913 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	914 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	915 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	916 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	917 with respect to clean examples . On the other hand, the deep SDAs
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	918 were significantly boosted by these out-of-distribution examples.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	919 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	920 negative for the MLP (from +5.6\% to -3.6\% relative change),
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	921 it was quite significant for the SDA (from +13\% to +27\% relative change),
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	922 which may be explained by the arguments below.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	923 %\end{itemize}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	924
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	925 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	926 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	927 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	928 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	929 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	930 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	931 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	932 architectures, our experiments show that such a positive effect is accomplished
569 9d01280ff1c1 commentaires de Joseph Turian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 568 diff changeset	933 even in a scenario with a \emph{large number of labeled examples},
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	934 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	935 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	936
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	937 {\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	938 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	939 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	940 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	941 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	942 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	943 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	944 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	945 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	946 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	947 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	948 experiments could attempt at teasing apart these factors.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	949 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	950 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	951 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	952 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	953 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	954 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	955 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	956 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	957 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	958 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	959 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	960 (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	961 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	962 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	963 with deep learning and self-taught learning.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	964
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	965 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	966 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	967
498 7ff00c27c976 add missing file for bibtex and make it smaller. Frederic Bastien <nouiz@nouiz.org> parents: 496 diff changeset	968 \newpage
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	969 {
e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	970 \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	971 %\bibliographystyle{plainnat}
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	972 \bibliographystyle{unsrtnat}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	973 %\bibliographystyle{apalike}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	974 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	975
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	976
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	977 \end{document}

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