ift6266: writeup/nips2010_submission.tex annotate

annotate writeup/nips2010_submission.tex @ 532:2e33885730cf

changements aux charts.ods

author	Yoshua Bengio <bengioy@iro.umontreal.ca>
date	Tue, 01 Jun 2010 21:19:54 -0400
parents	4354c3c8f49c
children	22d5cd82d5f0

rev	line source
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	1 \documentclass{article} % For LaTeX2e
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	2 \usepackage{nips10submit_e,times}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	3
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	4 \usepackage{amsthm,amsmath,amssymb,bbold,bbm}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	5 \usepackage{algorithm,algorithmic}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	6 \usepackage[utf8]{inputenc}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	7 \usepackage{graphicx,subfigure}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	8 \usepackage[numbers]{natbib}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	9
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	10 %\setlength\parindent{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	11
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	12 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	13 \author{The IFT6266 Gang}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	14
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	15 \begin{document}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	16
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	17 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	18 \maketitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	19
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	20 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	21 \begin{abstract}
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	22 Recent theoretical and empirical work in statistical machine learning has
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	23 demonstrated the importance of learning algorithms for deep
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	24 architectures, i.e., function classes obtained by composing multiple
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	25 non-linear transformations. Self-taught learning (exploiting unlabeled
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	26 examples or examples from other distributions) has already been applied
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	27 to deep learners, but mostly to show the advantage of unlabeled
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	28 examples. Here we explore the advantage brought by {\em out-of-distribution
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	29 examples} and show that {\em deep learners benefit more from them than a
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	30 corresponding shallow learner}, in the area
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	31 of handwritten character recognition. In fact, we show that they reach
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	32 human-level performance on both handwritten digit classification and
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	33 62-class handwritten character recognition. For this purpose we
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	34 developed a powerful generator of stochastic variations and noise
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	35 processes character images, including not only affine transformations but
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	36 also slant, local elastic deformations, changes in thickness, background
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	37 images, grey level changes, contrast, occlusion, and various types of pixel and
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	38 spatially correlated noise. The out-of-distribution examples are
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	39 obtained by training with these highly distorted images or
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	40 by including object classes different from those in the target test set.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	41 \end{abstract}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	42 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	43
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	44 \section{Introduction}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	45 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	46
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	47 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	48 statistical machine learning (see~\citet{Bengio-2009} for a review).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	49 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	50 of useful representations of data, which are better suited to the task at hand.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	51 This is in great part inspired by observations of the mammalian visual cortex,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	52 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	53 different representation of the raw visual input. In fact,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	54 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	55 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	56 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	57 more invariant to factors of variation (such as camera movement) in
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	58 higher layers~\citep{Goodfellow2009}.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	59 Learning a hierarchy of features increases the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	60 ease and practicality of developing representations that are at once
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	61 tailored to specific tasks, yet are able to borrow statistical strength
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	62 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	63 feature representation can lead to higher-level (more abstract, more
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	64 general) features that are more robust to unanticipated sources of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	65 variance extant in real data.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	66
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	67 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	68 shallow one in terms of representation, depth appears to render the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	69 training problem more difficult in terms of optimization and local minima.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	70 It is also only recently that successful algorithms were proposed to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	71 overcome some of these difficulties. All are based on unsupervised
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	72 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	73 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	74 applied here, is the Denoising
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	75 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	76 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	77 Machines in terms of unsupervised extraction of a hierarchy of features
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	78 useful for classification. The principle is that each layer starting from
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	79 the bottom is trained to encode its input (the output of the previous
d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	80 layer) and to reconstruct it from a corrupted version of it. After this
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	81 unsupervised initialization, the stack of denoising auto-encoders can be
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	82 converted into a deep supervised feedforward neural network and fine-tuned by
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	83 stochastic gradient descent.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	84
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	85 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	86 of semi-supervised and multi-task learning: the learner can exploit examples
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	87 that are unlabeled and/or come from a distribution different from the target
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	88 distribution, e.g., from other classes that those of interest.
2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	89 It has already been shown that deep learners can clearly take advantage of
2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	90 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	91 but more needs to be done to explore the impact
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	92 of {\em out-of-distribution} examples and of the multi-task setting
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	93 (one exception is~\citep{CollobertR2008}, but using very different kinds
2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	94 of learning algorithms). In particular the {\em relative
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	95 advantage} of deep learning for this settings has not been evaluated.
512 6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	96 The hypothesis explored here is that a deep hierarchy of features
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	97 may be better able to provide sharing of statistical strength
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	98 between different regions in input space or different tasks,
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	99 as discussed in the conclusion.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	100
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	101 % TODO: why we care to evaluate this relative advantage
d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	102
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	103 In this paper we ask the following questions:
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	104
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	105 %\begin{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	106 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	107 Do the good results previously obtained with deep architectures on the
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	108 MNIST digit images generalize to the setting of a much larger and richer (but similar)
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	109 dataset, the NIST special database 19, with 62 classes and around 800k examples?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	110
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	111 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	112 To what extent does the perturbation of input images (e.g. adding
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	113 noise, affine transformations, background images) make the resulting
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	114 classifiers better not only on similarly perturbed images but also on
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	115 the {\em original clean examples}?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	116
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	117 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	118 Do deep architectures {\em benefit more from such out-of-distribution}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	119 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	120
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	121 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	122 Similarly, does the feature learning step in deep learning algorithms benefit more
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	123 training with similar but different classes (i.e. a multi-task learning scenario) than
6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	124 a corresponding shallow and purely supervised architecture?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	125 %\end{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	126
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	127 Our experimental results provide positive evidence towards all of these questions.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	128
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	129 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	130 \section{Perturbation and Transformation of Character Images}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	131 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	132
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	133 This section describes the different transformations we used to stochastically
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	134 transform source images in order to obtain data. More details can
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	135 be found in this technical report~\citep{ift6266-tr-anonymous}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	136 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	137 {\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	138 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	139 amount of deformation or noise introduced.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	140
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	141 There are two main parts in the pipeline. The first one,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	142 from slant to pinch below, performs transformations. The second
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	143 part, from blur to contrast, adds different kinds of noise.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	144
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	145 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	146 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}}
506 8bf07979b8ba desiderata Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 503 diff changeset	147 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	148 \caption{Illustration of each transformation applied alone to the same image
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	149 of an upper-case h (top left). First row (from left to right) : original image, slant,
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	150 thickness, affine transformation (translation, rotation, shear),
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	151 local elastic deformation; second row (from left to right) :
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	152 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to right) :
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	153 background image, salt and pepper noise, spatially Gaussian noise, scratches,
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	154 grey level and contrast changes.}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	155 \label{fig:transfo}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	156 \end{figure}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	157
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	158 {\large\bf Transformations}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	159
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	160 \vspace*{2mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	161
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	162 {\bf Slant.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	163 We mimic slant by shifting each row of the image
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	164 proportionally to its height: $shift = round(slant \times height)$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	165 The $slant$ coefficient can be negative or positive with equal probability
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	166 and its value is randomly sampled according to the complexity level:
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	167 $slant \sim U[0,complexity]$, so the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	168 maximum displacement for the lowest or highest pixel line is of
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	169 $round(complexity \times 32)$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	170 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	171
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	172 {\bf Thickness.}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	173 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	174 are applied. The neighborhood of each pixel is multiplied
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	175 element-wise with a {\em structuring element} matrix.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	176 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	177 matrix, respectively for dilation or erosion. Ten different structural elements with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	178 increasing dimensions (largest is $5\times5$) were used. For each image,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	179 randomly sample the operator type (dilation or erosion) with equal probability and one structural
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	180 element from a subset of the $n$ smallest structuring elements where $n$ is
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	181 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	182 for erosion. A neutral element is always present in the set, and if it is
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	183 chosen no transformation is applied. Erosion allows only the six
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	184 smallest structural elements because when the character is too thin it may
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	185 be completely erased.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	186 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	187
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	188 {\bf Affine Transformations.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	189 A $2 \times 3$ affine transform matrix (with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	190 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	191 Each pixel $(x,y)$ of the output image takes the value of the pixel
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	192 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	193 produces scaling, translation, rotation and shearing.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	194 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	195 forbid important rotations (not to confuse classes) but to give good
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	196 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	197 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	198 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	199 complexity]$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	200 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	201
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	202 {\bf Local Elastic Deformations.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	203 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	204 which provides more details.
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	205 Two ``displacements'' fields are generated and applied, for horizontal
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	206 and vertical displacements of pixels.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	207 To generate a pixel in either field, first a value between -1 and 1 is
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	208 chosen from a uniform distribution. Then all the pixels, in both fields, are
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	209 multiplied by a constant $\alpha$ which controls the intensity of the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	210 displacements (larger $\alpha$ translates into larger wiggles).
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	211 Each field is convoluted with a Gaussian 2D kernel of
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	212 standard deviation $\sigma$. Visually, this results in a blur.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	213 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	214 \sqrt[3]{complexity}$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	215 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	216
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	217 {\bf Pinch.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	218 This is a GIMP filter called ``Whirl and
0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	219 pinch'', but whirl was set to 0. 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	220 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	221 For a square input image, this is akin to drawing a circle of
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	222 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	223 that disk (region inside circle) will have its value recalculated by taking
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	224 the value of another ``source'' pixel in the original image. The position of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	225 that source pixel is found on the line that goes through $C$ and $P$, but
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	226 at some other distance $d_2$. Define $d_1$ to be the distance between $P$
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	227 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	228 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	229 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	230 around the (non-integer) source position thus found.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	231 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	232
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	233 \vspace*{1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	234
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	235 {\large\bf Injecting Noise}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	236
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	237 \vspace*{1mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	238
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	239 {\bf Motion Blur.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	240 This is a ``linear motion blur'' in GIMP
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	241 terminology, with two parameters, $length$ and $angle$. The value of
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	242 a pixel in the final image is approximately the mean value of the $length$ first pixels
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	243 found by moving in the $angle$ direction.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	244 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	245 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	246
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	247 {\bf Occlusion.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	248 Selects a random rectangle from an {\em occluder} character
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	249 images and places it over the original {\em occluded} character
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	250 image. Pixels are combined by taking the max(occluder,occluded),
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	251 closer to black. The rectangle corners
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	252 are sampled so that larger complexity gives larger rectangles.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	253 The destination position in the occluded image are also sampled
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	254 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	255 This filter has a probability of 60\% of not being applied.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	256 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	257
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	258 {\bf Pixel Permutation.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	259 This filter permutes neighbouring pixels. It selects first
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	260 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	261 sequentially exchanged with one other pixel in its $V4$ neighbourhood. The number
0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	262 of exchanges to the left, right, top, bottom is equal or does not differ
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	263 from more than 1 if the number of selected pixels is not a multiple of 4.
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	264 % TODO: The previous sentence is hard to parse
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	265 This filter has a probability of 80\% of not being applied.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	266 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	267
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	268 {\bf Gaussian Noise.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	269 This filter simply adds, to each pixel of the image independently, a
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	270 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	271 It has a probability of 70\% of not being applied.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	272 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	273
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	274 {\bf Background Images.}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	275 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	276 background behind the letter. The background is chosen by first selecting,
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	277 at random, an image from a set of images. Then a 32$\times$32 sub-region
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	278 of that image is chosen as the background image (by sampling position
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	279 uniformly while making sure not to cross image borders).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	280 To combine the original letter image and the background image, contrast
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	281 adjustments are made. We first get the maximal values (i.e. maximal
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	282 intensity) for both the original image and the background image, $maximage$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	283 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	284 Each background pixel value is multiplied by $\frac{max(maximage -
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	285 contrast, 0)}{maxbg}$ (higher contrast yield darker
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	286 background). The output image pixels are max(background,original).
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	287 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	288
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	289 {\bf Salt and Pepper Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	290 This filter adds noise $\sim U[0,1]$ to random subsets of pixels.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	291 The number of selected pixels is $0.2 \times complexity$.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	292 This filter has a probability of not being applied at all of 75\%.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	293 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	294
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	295 {\bf Spatially Gaussian Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	296 Different regions of the image are spatially smoothed.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	297 The image is convolved with a symmetric Gaussian kernel of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	298 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	299 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	300 between $0$ and $1$. We also create a symmetric averaging window, of the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	301 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	302 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	303 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	304 initialize to zero a mask matrix of the image size. For each selected pixel
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	305 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	306 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	307 image \times mask}{mask+1}$.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	308 This filter has a probability of not being applied at all of 75\%.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	309 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	310
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	311 {\bf Scratches.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	312 The scratches module places line-like white patches on the image. The
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	313 lines are heavily transformed images of the digit ``1'' (one), chosen
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	314 at random among five thousands such 1 images. The 1 image is
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	315 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	316 complexity)^2$, using bi-cubic interpolation,
5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	317 Two passes of a grey-scale morphological erosion filter
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	318 are applied, reducing the width of the line
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	319 by an amount controlled by $complexity$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	320 This filter is only applied only 15\% of the time. When it is applied, 50\%
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	321 of the time, only one patch image is generated and applied. In 30\% of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	322 cases, two patches are generated, and otherwise three patches are
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	323 generated. The patch is applied by taking the maximal value on any given
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	324 patch or the original image, for each of the 32x32 pixel locations.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	325 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	326
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	327 {\bf Grey Level and Contrast Changes.}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	328 This filter changes the contrast and may invert the image polarity (white
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	329 on black to black on white). The contrast $C$ is defined here as the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	330 difference between the maximum and the minimum pixel value of the image.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	331 Contrast $\sim U[1-0.85 \times complexity,1]$ (so contrast $\geq 0.15$).
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	332 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	333 polarity is inverted with $0.5$ probability.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	334
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	335 \iffalse
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	336 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	337 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	338 \caption{Illustration of the pipeline of stochastic
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	339 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	340 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	341 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	342 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	343 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	344 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	345 \end{figure}
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	346 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	347
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	348
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	349 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	350 \section{Experimental Setup}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	351 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	352
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	353 Whereas much previous work on deep learning algorithms had been performed on
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	354 the MNIST digits classification task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	355 with 60~000 examples, and variants involving 10~000
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	356 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	357 to focus here on the case of much larger training sets, from 10 times to
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	358 to 1000 times larger. The larger datasets are obtained by first sampling from
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	359 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	360 and {\bf OCR data} (scanned machine printed characters). Once a character
2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	361 is sampled from one of these sources (chosen randomly), a pipeline of
2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	362 the above transformations and/or noise processes is applied to the
2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	363 image.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	364
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	365 We compare the best MLP (according to validation set error) that we found against
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	366 the best SDA (again according to validation set error), along with a precise estimate
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	367 of human performance obtained via Amazon's Mechanical Turk (AMT)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	368 service\footnote{http://mturk.com}.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	369 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	370 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	371 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	372 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	373 %\citep{SorokinAndForsyth2008,whitehill09}.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	374 AMT users where presented
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	375 with 10 character images and asked to type 10 corresponding ASCII
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	376 characters. They were forced to make a hard choice among the
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	377 62 or 10 character classes (all classes or digits only).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	378 Three users classified each image, allowing
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	379 to estimate inter-human variability.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	380
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	381 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	382 \subsection{Data Sources}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	383 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	384
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	385 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	386 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	387 {\bf NIST.}
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	388 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	389 widely used for training and testing character
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	390 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	391 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	392 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	393 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	394 The fourth partition, $hsf_4$, 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	395 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}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	396 for that purpose. We randomly split the remainder into a training set and a validation set for
480 150203d2b5c3 added number of train test and valid for NIST Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 479 diff changeset	397 model selection. The sizes of these data sets are: 651668 for training, 80000 for validation,
150203d2b5c3 added number of train test and valid for NIST Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 479 diff changeset	398 and 82587 for testing.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	399 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	400 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	401 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	402 Note that the distribution of the classes in the NIST training and test sets differs
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	403 substantially, with relatively many more digits in the test set, and more uniform distribution
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	404 of letters in the test set, compared to the training set (in the latter, the letters are distributed
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	405 more like the natural distribution of letters in text).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	406
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	407 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	408 {\bf Fonts.}
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	409 In order to have a good variety of sources we downloaded an important number of free fonts from:
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	410 {\tt http://cg.scs.carleton.ca/~luc/freefonts.html}
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	411 % TODO: pointless to anonymize, it's not pointing to our work
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	412 Including operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	413 The {\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	414 directly as input to our models.
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	415
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	416 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	417 {\bf Captchas.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	418 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	419 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	420 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	421 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	422 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	423 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	424 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	425
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	426 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	427 {\bf OCR data.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	428 A large set (2 million) of scanned, OCRed and manually verified machine-printed
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	429 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	430 additional source. This set is part of a larger corpus being collected by the Image Understanding
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	431 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	432 ({\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	433 %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	434 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	435
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	436 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	437 \subsection{Data Sets}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	438 \vspace*{-1mm}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	439
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	440 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	441 from one of the 62 character classes.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	442 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	443
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	444 %\item
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	445 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	446
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	447 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	448 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	449 and sending them through the above transformation pipeline.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	450 For each new example to generate, a source is selected with probability $10\%$ from the fonts,
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	451 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	452 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	453
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	454 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	455 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion)
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	456 except that we only apply
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	457 transformations from slant to pinch. Therefore, the character is
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	458 transformed but no additional noise is added to the image, giving images
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	459 closer to the NIST dataset.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	460 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	461
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	462 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	463 \subsection{Models and their Hyperparameters}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	464 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	465
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	466 The experiments are performed with Multi-Layer Perceptrons (MLP) with a single
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	467 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	468 All hyper-parameters are selected based on performance on the NISTP validation set.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	469
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	470 {\bf Multi-Layer Perceptrons (MLP).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	471 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	472 SVMs, we only compared to MLPs here because of the very large datasets used
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	473 (making the use of SVMs computationally inconvenient because of their quadratic
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	474 scaling behavior).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	475 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	476 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	477 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	478 The optimization procedure is as follows: training
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	479 examples are presented in minibatches of size 20, a constant learning
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	480 rate is chosen in $\{10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	481 through preliminary experiments (measuring performance on a validation set),
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	482 and $0.1$ was then selected.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	483
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	484 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	485 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	486 \caption{Illustration of the computations and training criterion for the denoising
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	487 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	488 the layer (i.e. raw input or output of previous layer)
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	489 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	490 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	491 is compared to the uncorrupted input $x$ through the loss function
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	492 $L_H(x,z)$, whose expected value is approximately minimized during training
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	493 by tuning $\theta$ and $\theta'$.}
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	494 \label{fig:da}
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	495 \end{figure}
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	496
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	497 {\bf Stacked Denoising Auto-Encoders (SDA).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	498 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	499 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	500 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	501 apparently setting parameters in the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	502 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	503 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	504 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	505 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	506 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	507 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	508 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	509 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	510 compositions of simpler ones through a deep hierarchy).
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	511 Here we chose to use the Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	512 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	513 these deep hierarchies of features, as it is very simple to train and
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	514 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	515 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	516 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	517 comparable or better than RBMs in series of experiments
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	518 \citep{VincentPLarochelleH2008}. During training, a Denoising
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	519 Auto-Encoder is presented with a stochastically corrupted version
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	520 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	521 forcing the hidden units to represent the leading regularities in
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	522 the data. Once it is trained, its hidden units activations can
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	523 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	524 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	525 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	526 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	527 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	528 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	529 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	530 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	531 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	532 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	533 of hidden layers but it was fixed to 3 based on previous work with
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	534 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	535
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	536 \vspace*{-1mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	537
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	538 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	539 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	540 \caption{Error bars indicate a 95\% confidence interval. 0 indicates training
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	541 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	542 of all models, on 3 different test sets corresponding to the three
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	543 datasets.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	544 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	545 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	546 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	547
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	548 \label{fig:error-rates-charts}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	549 \vspace*{-1mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	550 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	551
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	552
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	553 \section{Experimental Results}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	554
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	555 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	556 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	557 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	558
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	559 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	560 comparing Humans, three MLPs (MLP0, MLP1, MLP2) and three SDAs (SDA0, SDA1,
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	561 SDA2), along with the previous results on the digits NIST special database
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	562 19 test set from the literature respectively based on ARTMAP neural
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	563 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	564 ~\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	565 ~\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	566 (figures and tables, including standard errors on the error rates) can be
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	567 found in Appendix I of the supplementary material. The 3 kinds of model differ in the
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	568 training sets used: NIST only (MLP0,SDA0), NISTP (MLP1, SDA1), or P07
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	569 (MLP2, SDA2). The deep learner not only outperformed the shallow ones and
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	570 previously published performance (in a statistically and qualitatively
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	571 significant way) but reaches human performance on both the 62-class task
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	572 and the 10-class (digits) task.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	573
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	574 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	575 \vspace*{-2mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	576 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	577 \caption{Relative improvement in error rate due to self-taught learning.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	578 Left: Improvement (or loss, when negative)
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	579 induced by out-of-distribution examples (perturbed data).
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	580 Right: Improvement (or loss, when negative) induced by multi-task
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	581 learning (training on all classes and testing only on either digits,
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	582 upper case, or lower-case). The deep learner (SDA) benefits more from
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	583 both self-taught learning scenarios, compared to the shallow MLP.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	584 \label{fig:improvements-charts}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	585 \vspace*{-2mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	586 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	587
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	588 In addition, as shown in the left of
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	589 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	590 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	591 differences with the MLP are statistically and qualitatively
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	592 significant.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	593 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	594 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	595 (i.e. the perturbed examples examples from NISTP or P07).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	596 Relative change is measured by taking
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	597 (original model's error / perturbed-data model's error - 1).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	598 The right side of
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	599 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	600 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	601 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	602 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	603 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	604 multi-task setting is marginal or negative for the MLP, it is substantial
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	605 for the SDA. Note that for these multi-task experiment, only the original
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	606 NIST dataset is used. For example, the MLP-digits bar shows the relative
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	607 improvement in MLP error rate on the NIST digits test set (1 - single-task
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	608 model's error / multi-task model's error). The single-task model is
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	609 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	610 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	611 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	612 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	613 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	614 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	615 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	616 and upper case characters).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	617
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	618 %\vspace*{-1mm}
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	619 %\subsection{Perturbed Training Data More Helpful for SDA}
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	620 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	621
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	622 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	623 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	624 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	625
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	626 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	627 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	628 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	629 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	630 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	631 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	632 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	633 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	634 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	635 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	636 (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	637 shallow learner.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	638
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	639 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	640 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	641 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	642
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	643 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	644 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	645 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	646 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	647 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	648 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	649 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	650
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	651
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	652 \vspace*{-1mm}
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	653 \section{Conclusions and Discussion}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	654 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	655
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	656 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	657 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	658 supervised learner. More precisely,
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	659 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	660 %\begin{itemize}
487 21787ac4e5a0 - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 486 diff changeset	661
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	662 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	663 Do the good results previously obtained with deep architectures on the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	664 MNIST digits generalize to the setting of a much larger and richer (but similar)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	665 dataset, the NIST special database 19, with 62 classes and around 800k examples?
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	666 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	667 published results on this dataset} (the ones that we are aware of), {\bf in fact reaching human-level
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	668 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	669
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	670 $\bullet$ %\item
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	671 To what extent do self-taught learning scenarios help deep learners,
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	672 and do they help them more than shallow supervised ones?
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	673 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	674 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	675 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	676 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	677 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	678 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	679 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	680 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	681 with respect to clean examples . On the other hand, the deep SDAs
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	682 were very significantly boosted by these out-of-distribution examples.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	683 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	684 negative for the MLP (from +5.6\% to -3.6\% relative change),
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	685 it was very significant for the SDA (from +13\% to +27\% relative change).
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	686 %\end{itemize}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	687
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	688 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	689 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	690 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	691 scenario. However, many of the results by \citet{RainaR2007} (who used a
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	692 shallow, sparse coding approach) suggest that the relative gain of self-taught
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	693 learning diminishes as the number of labeled examples increases, (essentially,
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	694 a ``diminishing returns'' scenario occurs). 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	695 architectures, our experiments show that such a positive effect is accomplished
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	696 even in a scenario with a \emph{very large number of labeled examples}.
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	697
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	698 Why would deep learners benefit more from the self-taught learning framework?
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	699 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	700 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	701 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	702 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	703 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	704 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	705 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	706 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	707 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	708 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	709 experiments could attempt at teasing apart these factors.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	710 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	711 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	712 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	713 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	714 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	715 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	716 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	717 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	718 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	719 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	720 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	721 (with or without self-taught settings), and more labeled examples
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	722 does not allow to go from the poorer basins of attraction discovered
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	723 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	724 with deep learning and self-taught learning.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	725
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	726 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	727 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	728
498 7ff00c27c976 add missing file for bibtex and make it smaller. Frederic Bastien <nouiz@nouiz.org> parents: 496 diff changeset	729 \newpage
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	730 {
e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	731 \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	732 %\bibliographystyle{plainnat}
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	733 \bibliographystyle{unsrtnat}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	734 %\bibliographystyle{apalike}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	735 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	736
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	737
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	738 \end{document}

Mercurial > ift6266

annotate writeup/nips2010_submission.tex @ 532:2e33885730cf