ift6266: writeup/nips2010_submission.tex annotate

annotate writeup/nips2010_submission.tex @ 517:0a5945249f2b

section 2, quick first pass

author	Dumitru Erhan <dumitru.erhan@gmail.com>
date	Tue, 01 Jun 2010 11:14:48 -0700
parents	d057941417ed
children	460a4e78c9a4

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
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	10 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	11 \author{The IFT6266 Gang}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	12
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	13 \begin{document}
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 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	16 \maketitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	17
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	18 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	19 \begin{abstract}
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	20 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	21 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	22 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	23 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	24 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	25 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	26 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	27 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	28 corresponding shallow learner}, in the area
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	29 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	30 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	31 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	32 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	33 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	34 also slant, local elastic deformations, changes in thickness, background
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	35 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	36 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	37 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	38 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	39 \end{abstract}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	40 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	41
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	42 \section{Introduction}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	43 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	44
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	45 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	46 statistical machine learning (see~\citet{Bengio-2009} for a review).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	47 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	48 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	49 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	50 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	51 different representation of the raw visual input. In fact,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	52 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	53 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	54 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	55 more invariant to factors of variation (such as camera movement) in
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	56 higher layers~\citep{Goodfellow2009}.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	57 Learning a hierarchy of features increases the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	58 ease and practicality of developing representations that are at once
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	59 tailored to specific tasks, yet are able to borrow statistical strength
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	60 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	61 feature representation can lead to higher-level (more abstract, more
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	62 general) features that are more robust to unanticipated sources of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	63 variance extant in real data.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	64
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	65 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	66 shallow one in terms of representation, depth appears to render the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	67 training problem more difficult in terms of optimization and local minima.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	68 It is also only recently that successful algorithms were proposed to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	69 overcome some of these difficulties. All are based on unsupervised
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	70 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	71 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	72 applied here, is the Denoising
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	73 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	74 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	75 Machines in terms of unsupervised extraction of a hierarchy of features
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	76 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	77 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	78 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	79 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	80 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	81 stochastic gradient descent.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	82
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	83 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	84 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	85 that are unlabeled and/or come from a distribution different from the target
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	86 distribution, e.g., from other classes that those of interest. Whereas
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	87 it has already been shown that deep learners can clearly take advantage of
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	88 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	89 and multi-task learning, not much has been done yet to explore the impact
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	90 of {\em out-of-distribution} examples and of the multi-task setting
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	91 (but see~\citep{CollobertR2008}). In particular the {\em relative
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	92 advantage} of deep learning for this settings has not been evaluated.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	93
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	94 % 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	95
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	96 In this paper we ask the following questions:
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	97
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	98 %\begin{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	99 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	100 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	101 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	102 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	103
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	104 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	105 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	106 noise, affine transformations, background images) make the resulting
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	107 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	108 the {\em original clean examples}?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	109
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	110 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	111 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	112 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	113
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	114 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	115 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	116 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	117 a corresponding shallow and purely supervised architecture?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	118 %\end{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	119
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	120 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	121
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	122 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	123 \section{Perturbation and Transformation of Character Images}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	124 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	125
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	126 This section describes the different transformations we used to stochastically
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	127 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	128 be found in this technical report~\citep{ift6266-tr-anonymous}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	129 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	130 {\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	131 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	132 amount of deformation or noise introduced.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	133
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	134 There are two main parts in the pipeline. The first one,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	135 from slant to pinch below, performs transformations. The second
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	136 part, from blur to contrast, adds different kinds of noise.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	137
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	138 \begin{figure}[h]
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	139 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\
506 8bf07979b8ba desiderata Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 503 diff changeset	140 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	141 \caption{Illustration of each transformation applied alone to the same image
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	142 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	143 thickness, affine transformation (translation, rotation, shear),
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	144 local elastic deformation; second row (from left to right) :
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	145 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	146 background image, salt and pepper noise, spatially Gaussian noise, scratches,
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	147 grey level and contrast changes.}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	148 \label{fig:transfo}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	149 \end{figure}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	150
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	151 {\large\bf Transformations}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	152
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	153 \vspace*{2mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	154
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	155 {\bf Slant.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	156 We mimic slant by shifting each row of the image
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	157 proportionally to its height: $shift = round(slant \times height)$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	158 The $slant$ coefficient can be negative or positive with equal probability
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	159 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	160 $slant \sim U[0,complexity]$, so the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	161 maximum displacement for the lowest or highest pixel line is of
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	162 $round(complexity \times 32)$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	163 {\bf Thickness.}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	164 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	165 are applied. The neighborhood of each pixel is multiplied
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	166 element-wise with a {\em structuring element} matrix.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	167 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	168 matrix, respectively for dilation or erosion. Ten different structural elements with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	169 increasing dimensions (largest is $5\times5$) were used. For each image,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	170 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	171 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	172 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	173 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	174 chosen no transformation is applied. Erosion allows only the six
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	175 smallest structural elements because when the character is too thin it may
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	176 be completely erased.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	177 {\bf Affine Transformations.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	178 A $2 \times 3$ affine transform matrix (with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	179 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	180 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	181 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	182 produces scaling, translation, rotation and shearing.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	183 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	184 forbid important rotations (not to confuse classes) but to give good
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	185 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	186 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	187 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	188 complexity]$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	189 {\bf Local Elastic Deformations.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	190 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	191 which provides more details.
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	192 Two ``displacements'' fields are generated and applied, for horizontal
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	193 and vertical displacements of pixels.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	194 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	195 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	196 multiplied by a constant $\alpha$ which controls the intensity of the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	197 displacements (larger $\alpha$ translates into larger wiggles).
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	198 Each field is convoluted with a Gaussian 2D kernel of
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	199 standard deviation $\sigma$. Visually, this results in a blur.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	200 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	201 \sqrt[3]{complexity}$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	202 {\bf Pinch.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	203 This is a GIMP filter called ``Whirl and
0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	204 pinch'', but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
509 860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	205 surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}.
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	206 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	207 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	208 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	209 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	210 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	211 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	212 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	213 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	214 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	215 around the (non-integer) source position thus found.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	216 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	217
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	218 \vspace*{1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	219
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	220 {\large\bf Injecting Noise}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	221
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	222 \vspace*{1mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	223
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	224 {\bf Motion Blur.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	225 This is a ``linear motion blur'' in GIMP
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	226 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	227 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	228 found by moving in the $angle$ direction.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	229 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	230 {\bf Occlusion.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	231 Selects a random rectangle from an {\em occluder} character
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	232 images and places it over the original {\em occluded} character
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	233 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	234 closer to black. The rectangle corners
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	235 are sampled so that larger complexity gives larger rectangles.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	236 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	237 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	238 This filter has a probability of 60\% of not being applied.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	239 {\bf Pixel Permutation.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	240 This filter permutes neighbouring pixels. It selects first
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	241 $\frac{complexity}{3}$ 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	242 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	243 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	244 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	245 % TODO: The previous sentence is hard to parse
0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	246 This filter has a probability of 80\% of not being applied.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	247 {\bf Gaussian Noise.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	248 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	249 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	250 It has a probability of 70\% of not being applied.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	251 {\bf Background Images.}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	252 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	253 background behind the letter. The background is chosen by first selecting,
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	254 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	255 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	256 uniformly while making sure not to cross image borders).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	257 To combine the original letter image and the background image, contrast
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	258 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	259 intensity) for both the original image and the background image, $maximage$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	260 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	261 Each background pixel value is multiplied by $\frac{max(maximage -
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	262 contrast, 0)}{maxbg}$ (higher contrast yield darker
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	263 background). The output image pixels are max(background,original).\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	264 {\bf Salt and Pepper Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	265 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	266 The number of selected pixels is $0.2 \times complexity$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	267 This filter has a probability of not being applied at all of 75\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	268 {\bf Spatially Gaussian Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	269 Different regions of the image are spatially smoothed.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	270 The image is convolved with a symmetric Gaussian kernel of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	271 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	272 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	273 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	274 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	275 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	276 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	277 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	278 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	279 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	280 image \times mask}{mask+1}$.
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	281 This filter has a probability of not being applied at all of 75\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	282 {\bf Scratches.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	283 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	284 lines are heavily transformed images of the digit ``1'' (one), chosen
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	285 at random among five thousands such 1 images. The 1 image is
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	286 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	287 complexity)^2$, using bi-cubic interpolation,
5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	288 Two passes of a grey-scale morphological erosion filter
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	289 are applied, reducing the width of the line
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	290 by an amount controlled by $complexity$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	291 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	292 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	293 cases, two patches are generated, and otherwise three patches are
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	294 generated. The patch is applied by taking the maximal value on any given
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	295 patch or the original image, for each of the 32x32 pixel locations.\\
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	296 {\bf Grey Level and Contrast Changes.}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	297 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	298 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	299 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	300 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	301 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	302 polarity is inverted with $0.5$ probability.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	303
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	304 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	305 \begin{figure}[h]
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	306 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	307 \caption{Illustration of the pipeline of stochastic
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	308 transformations applied to the image of a lower-case t
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	309 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	310 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	311 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	312 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	313 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	314 \end{figure}
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	315 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	316
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	317
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	318 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	319 \section{Experimental Setup}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	320 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	321
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	322 Whereas much previous work on deep learning algorithms had been performed on
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	323 the MNIST digits classification task~\citep{Hinton06,ranzato-07,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	324 with 60~000 examples, and variants involving 10~000
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	325 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	326 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	327 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	328 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	329 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	330 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	331 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	332 image.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	333
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	334 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	335 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	336 of human performance obtained via Amazon's Mechanical Turk (AMT)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	337 service\footnote{http://mturk.com}.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	338 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	339 of money to perform tasks for which human intelligence is required.
509 860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	340 Mechanical Turk has been used extensively in natural language
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	341 processing \citep{SnowEtAl2008} and vision
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	342 \citep{SorokinAndForsyth2008,whitehill09}.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	343 AMT users where presented
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	344 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	345 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	346 62 or 10 character classes (all classes or digits only).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	347 Three users classified each image, allowing
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	348 to estimate inter-human variability.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	349
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	350 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	351 \subsection{Data Sources}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	352 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	353
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	354 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	355 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	356 {\bf NIST.}
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	357 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	358 widely used for training and testing character
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	359 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}.
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	360 The dataset is composed with 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	361 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	362 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity.
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	363 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one is recommended
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	364 by NIST as testing set and is used in our work and some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	365 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	366 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	367 and 82587 for testing.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	368 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	369 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	370 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	371 Note that the distribution of the classes in the NIST training and test sets differs
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	372 substantially, with relatively many more digits in the test set, and uniform distribution
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	373 of letters in the test set, not in the training set (more like the natural distribution
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	374 of letters in text).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	375
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	376 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	377 {\bf Fonts.}
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	378 In order to have a good variety of sources we downloaded an important number of free fonts from: {\tt http://anonymous.url.net}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	379 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	380 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	381 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	382 directly as input to our models.
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	383
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	384 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	385 {\bf Captchas.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	386 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	387 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	388 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	389 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	390 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	391 depending on the value of the complexity parameter provided by the user of the data source. Two levels of complexity are
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	392 allowed and can be controlled via an easy to use facade class.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	393
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	394 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	395 {\bf OCR data.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	396 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	397 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	398 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	399 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	400 ({\tt http://www.iupr.com}), and which will be publicly released.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	401 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	402
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	403 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	404 \subsection{Data Sets}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	405 \vspace*{-1mm}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	406
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	407 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	408 from one of the 62 character classes.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	409 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	410
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	411 %\item
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	412 {\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	413
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	414 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	415 {\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	416 and sending them through the above transformation pipeline.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	417 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	418 $25\%$ 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	419 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	420
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	421 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	422 {\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	423 except that we only apply
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	424 transformations from slant to pinch. Therefore, the character is
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	425 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	426 closer to the NIST dataset.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	427 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	428
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	429 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	430 \subsection{Models and their Hyperparameters}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	431 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	432
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	433 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	434 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	435 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	436
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	437 {\bf Multi-Layer Perceptrons (MLP).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	438 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	439 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	440 (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	441 scaling behavior).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	442 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	443 exponentials) on the output layer for estimating P(class \| image).
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	444 The hyper-parameters are the following: number of hidden units, taken in
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	445 $\{300,500,800,1000,1500\}$. The optimization procedure is as follows. Training
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	446 examples are presented in minibatches of size 20. A constant learning
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	447 rate is chosen in $10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	448 through preliminary experiments, and 0.1 was selected.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	449
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	450 {\bf Stacked Denoising Auto-Encoders (SDA).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	451 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	452 can be used to initialize the weights of each layer of a deep MLP (with many hidden
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	453 layers)~\citep{Hinton06,ranzato-07,Bengio-nips-2006}
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	454 enabling better generalization, apparently setting parameters in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	455 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	456 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	457 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	458 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	459 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	460 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	461 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	462 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	463 compositions of simpler ones through a deep hierarchy).
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	464 Here we chose to use the Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	465 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	466 % AJOUTER UNE IMAGE?
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	467 these deep hierarchies of features, as it is very simple to train and
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	468 teach (see tutorial and code there: {\tt http://deeplearning.net/tutorial}),
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	469 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	470 comparable or better than RBMs in series of experiments
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	471 \citep{VincentPLarochelleH2008}. During training of a Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	472 Auto-Encoder, it is presented with a stochastically corrupted version
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	473 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	474 forcing the hidden units to represent the leading regularities in
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	475 the data. Once it is trained, its hidden units activations can
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	476 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	477 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	478 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	479 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	480 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	481 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	482 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	483 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	484 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	485 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	486 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	487 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	488
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	489 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	490 \section{Experimental Results}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	491
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	492 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	493 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	494 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	495
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	496 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	497 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	498 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	499 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	500 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	501 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002}, and SVMs
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	502 ~\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	503 (figures and tables, including standard errors on the error rates) can be
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	504 found in the supplementary material. The 3 kinds of model differ in the
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	505 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	506 (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	507 previously published performance (in a statistically and qualitatively
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	508 significant way) but reaches human performance on both the 62-class task
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	509 and the 10-class (digits) task. In addition, as shown in the left of
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	510 Figure~\ref{fig:fig:improvements-charts}, the relative improvement in error
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	511 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	512 differences with the MLP are statistically and qualitatively
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	513 significant.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	514 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	515 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	516 (i.e. the perturbed examples examples from NISTP or P07).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	517 Relative change is measured by taking
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	518 (original model's error / perturbed-data model's error - 1).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	519 The right side of
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	520 Figure~\ref{fig:fig:improvements-charts} shows the relative improvement
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	521 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	522 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	523 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	524 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	525 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	526 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	527 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	528 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	529 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	530 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	531 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	532 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	533 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	534 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	535 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	536 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	537 and upper case characters).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	538
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	539 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	540 \resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}\\
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	541 \caption{Error bars indicate a 95\% confidence interval. 0 indicates training
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	542 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	543 of all models, on 3 different test sets corresponding to the three
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	544 datasets.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	545 Right: error rates on NIST test digits only, along with the previous results from
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	546 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	547 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	548
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	549 \label{fig:error-rates-charts}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	550 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	551
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	552 %\vspace*{-1mm}
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	553 %\subsection{Perturbed Training Data More Helpful for SDA}
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	554 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	555
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	556 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	557 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	558 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	559
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	560 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	561 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	562 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	563 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	564 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	565 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	566 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	567 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	568 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	569 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	570 (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	571 shallow learner.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	572
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	573 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	574 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	575 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	576
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	577 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	578 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	579 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	580 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	581 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	582 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	583 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	584
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	585
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	586 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	587 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\
509 860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	588 \caption{Relative improvement in error rate due to self-taught learning.
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	589 Left: Improvement (or loss, when negative)
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	590 induced by out-of-distribution examples (perturbed data).
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	591 Right: Improvement (or loss, when negative) induced by multi-task
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	592 learning (training on all classes and testing only on either digits,
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	593 upper case, or lower-case). The deep learner (SDA) benefits more from
860c755ddcff argh, sorry about that Dumitru Erhan <dumitru.erhan@gmail.com> parents: 505 diff changeset	594 both self-taught learning scenarios, compared to the shallow MLP.}
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	595 \label{fig:improvements-charts}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	596 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	597
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	598 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	599 \section{Conclusions}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	600 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	601
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	602 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	603 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	604 supervised learner. More precisely,
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	605 the conclusions 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	606 %\begin{itemize}
487 21787ac4e5a0 - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 486 diff changeset	607
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	608 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	609 Do the good results previously obtained with deep architectures on the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	610 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	611 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	612 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	613 published results on this dataset (as far as we know), in fact reaching human-level
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	614 performance} at round 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	615
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	616 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	617 To what extent does the perturbation of input images (e.g. adding
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	618 noise, affine transformations, background images) make the resulting
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	619 classifier better not only on similarly perturbed images but also on
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	620 the {\em original clean examples}? Do deep architectures benefit more from such {\em out-of-distribution}
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	621 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	622 MLPs were helped by perturbed training examples when tested on perturbed input
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	623 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	624 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	625 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	626 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	627 were very significantly boosted by these out-of-distribution examples.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	628
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	629 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	630 Similarly, does the feature learning step in deep learning algorithms benefit more
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	631 training with similar but different classes (i.e. a multi-task learning scenario) than
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	632 a corresponding shallow and purely supervised architecture?
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	633 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	634 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	635 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	636 %\end{itemize}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	637
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	638 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	639 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	640 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	641 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	642 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	643 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	644 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	645 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	646 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	647 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	648 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	649 experiments could attempt at teasing apart these factors.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	650
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	651 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	652 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	653
498 7ff00c27c976 add missing file for bibtex and make it smaller. Frederic Bastien <nouiz@nouiz.org> parents: 496 diff changeset	654 \newpage
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	655 {
e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	656 \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	657 %\bibliographystyle{plainnat}
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	658 \bibliographystyle{unsrtnat}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	659 %\bibliographystyle{apalike}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	660 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	661
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	662
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	663 \end{document}

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