ift6266: writeup/nips2010_submission.tex annotate

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author	Dumitru Erhan <dumitru.erhan@gmail.com>
date	Tue, 01 Jun 2010 18:28:09 -0700
parents	85f2337d47d2
children	47894d0ecbde

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464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	1 \documentclass{article} % For LaTeX2e
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	2 \usepackage{nips10submit_e,times}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	3
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	4 \usepackage{amsthm,amsmath,bbm}
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	5 \usepackage[psamsfonts]{amssymb}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	6 \usepackage{algorithm,algorithmic}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	7 \usepackage[utf8]{inputenc}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	8 \usepackage{graphicx,subfigure}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	9 \usepackage[numbers]{natbib}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	10
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	11 %\setlength\parindent{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	12
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	13 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	14 \author{The IFT6266 Gang}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	15
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	16 \begin{document}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	17
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	18 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	19 \maketitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	20
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	21 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	22 \begin{abstract}
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	23 Recent theoretical and empirical work in statistical machine learning has
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	24 demonstrated the importance of learning algorithms for deep
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	25 architectures, i.e., function classes obtained by composing multiple
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	26 non-linear transformations. Self-taught learning (exploiting unlabeled
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	27 examples or examples from other distributions) has already been applied
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	28 to deep learners, but mostly to show the advantage of unlabeled
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	29 examples. Here we explore the advantage brought by {\em out-of-distribution
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	30 examples} and show that {\em deep learners benefit more from them than a
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	31 corresponding shallow learner}, in the area
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	32 of handwritten character recognition. In fact, we show that they reach
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	33 human-level performance on both handwritten digit classification and
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	34 62-class handwritten character recognition. For this purpose we
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	35 developed a powerful generator of stochastic variations and noise
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	36 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	37 also slant, local elastic deformations, changes in thickness, background
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	38 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	39 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	40 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	41 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	42 \end{abstract}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	43 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	44
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	45 \section{Introduction}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	46 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	47
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	48 Deep Learning has emerged as a promising new area of research in
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	49 statistical machine learning (see~\citet{Bengio-2009} for a review).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	50 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	51 of useful representations of data, which are better suited to the task at hand.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	52 This is in great part inspired by observations of the mammalian visual cortex,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	53 which consists of a chain of processing elements, each of which is associated with a
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	54 different representation of the raw visual input. In fact,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	55 it was found recently that the features learnt in deep architectures resemble
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	56 those observed in the first two of these stages (in areas V1 and V2
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	57 of visual cortex)~\citep{HonglakL2008}, and that they become more and
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	58 more invariant to factors of variation (such as camera movement) in
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	59 higher layers~\citep{Goodfellow2009}.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	60 Learning a hierarchy of features increases the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	61 ease and practicality of developing representations that are at once
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	62 tailored to specific tasks, yet are able to borrow statistical strength
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	63 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	64 feature representation can lead to higher-level (more abstract, more
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	65 general) features that are more robust to unanticipated sources of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	66 variance extant in real data.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	67
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	68 Whereas a deep architecture can in principle be more powerful than a
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	69 shallow one in terms of representation, depth appears to render the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	70 training problem more difficult in terms of optimization and local minima.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	71 It is also only recently that successful algorithms were proposed to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	72 overcome some of these difficulties. All are based on unsupervised
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	73 learning, often in an greedy layer-wise ``unsupervised pre-training''
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	74 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	75 applied here, is the Denoising
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	76 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	77 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	78 Machines in terms of unsupervised extraction of a hierarchy of features
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	79 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	80 the bottom is trained to encode its input (the output of the previous
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	81 layer) and to reconstruct it from a corrupted version. After this
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	82 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	83 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	84 stochastic gradient descent.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	85
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	86 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	87 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	88 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	89 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	90 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	91 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	92 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	93 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	94 (but see~\citep{CollobertR2008}). In particular the {\em relative
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	95 advantage} of deep learning for this settings has not been evaluated.
512 6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	96 The hypothesis explored here is that a deep hierarchy of features
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	97 may be better able to provide sharing of statistical strength
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	98 between different regions in input space or different tasks,
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	99 as discussed in the conclusion.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	100
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	101 In this paper we ask the following questions:
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	102
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	103 %\begin{enumerate}
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 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	106 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	107 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	108
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	109 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	110 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	111 noise, affine transformations, background images) make the resulting
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	112 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	113 the {\em original clean examples}?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	114
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	115 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	116 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	117 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	118
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	119 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	120 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	121 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	122 a corresponding shallow and purely supervised architecture?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	123 %\end{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	124
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	125 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	126
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	127 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	128 \section{Perturbation and Transformation of Character Images}
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	129 \label{s:perturbations}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	130 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	131
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	132 This section describes the different transformations we used to stochastically
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	133 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	134 be found in this technical report~\citep{ift6266-tr-anonymous}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	135 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	136 {\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	137 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	138 amount of deformation or noise introduced.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	139
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	140 There are two main parts in the pipeline. The first one,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	141 from slant to pinch below, performs transformations. The second
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	142 part, from blur to contrast, adds different kinds of noise.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	143
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	144 \begin{figure}[ht]
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	145 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/transfo.png}}}
506 8bf07979b8ba desiderata Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 503 diff changeset	146 % TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	147 \caption{Illustration of each transformation applied alone to the same image
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	148 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	149 thickness, affine transformation (translation, rotation, shear),
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	150 local elastic deformation; second row (from left to right) :
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	151 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	152 background image, salt and pepper noise, spatially Gaussian noise, scratches,
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	153 grey level and contrast changes.}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	154 \label{fig:transfo}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	155 \end{figure}
5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	156
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	157 {\large\bf Transformations}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	158
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	159 \vspace*{2mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	160
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	161 {\bf Slant.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	162 We mimic slant by shifting each row of the image
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	163 proportionally to its height: $shift = round(slant \times height)$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	164 The $slant$ coefficient can be negative or positive with equal probability
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	165 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	166 $slant \sim U[0,complexity]$, so the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	167 maximum displacement for the lowest or highest pixel line is of
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	168 $round(complexity \times 32)$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	169 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	170
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	171 {\bf Thickness.}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	172 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	173 are applied. The neighborhood of each pixel is multiplied
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	174 element-wise with a {\em structuring element} matrix.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	175 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	176 matrix, respectively for dilation or erosion. Ten different structural elements with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	177 increasing dimensions (largest is $5\times5$) were used. For each image,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	178 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	179 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	180 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	181 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	182 chosen no transformation is applied. Erosion allows only the six
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	183 smallest structural elements because when the character is too thin it may
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	184 be completely erased.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	185 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	186
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	187 {\bf Affine Transformations.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	188 A $2 \times 3$ affine transform matrix (with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	189 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	190 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	191 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	192 produces scaling, translation, rotation and shearing.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	193 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	194 forbid important rotations (not to confuse classes) but to give good
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	195 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	196 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	197 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	198 complexity]$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	199 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	200
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	201 {\bf Local Elastic Deformations.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	202 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	203 which provides more details.
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	204 Two ``displacements'' fields are generated and applied, for horizontal
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	205 and vertical displacements of pixels.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	206 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	207 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	208 multiplied by a constant $\alpha$ which controls the intensity of the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	209 displacements (larger $\alpha$ translates into larger wiggles).
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	210 Each field is convoluted with a Gaussian 2D kernel of
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	211 standard deviation $\sigma$. Visually, this results in a blur.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	212 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	213 \sqrt[3]{complexity}$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	214 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	215
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	216 {\bf Pinch.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	217 This is a GIMP filter called ``Whirl and
0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	218 pinch'', but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	219 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	220 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	221 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	222 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	223 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	224 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	225 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	226 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	227 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	228 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	229 around the (non-integer) source position thus found.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	230 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	231
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	232 \vspace*{1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	233
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	234 {\large\bf Injecting Noise}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	235
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	236 \vspace*{1mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	237
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	238 {\bf Motion Blur.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	239 This is a ``linear motion blur'' in GIMP
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	240 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	241 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	242 found by moving in the $angle$ direction.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	243 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	244 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	245
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	246 {\bf Occlusion.}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	247 Selects a random rectangle from an {\em occluder} character
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	248 images and places it over the original {\em occluded} character
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	249 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	250 closer to black. The rectangle corners
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	251 are sampled so that larger complexity gives larger rectangles.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	252 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	253 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	254 This filter has a probability of 60\% of not being applied.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	255 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	256
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	257 {\bf Pixel Permutation.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	258 This filter permutes neighbouring pixels. It selects first
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	259 $\frac{complexity}{3}$ 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	260 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	261 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	262 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	263 % TODO: The previous sentence is hard to parse
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	264 This filter has a probability of 80\% of not being applied.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	265 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	266
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	267 {\bf Gaussian Noise.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	268 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	269 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	270 It has a probability of 70\% of not being applied.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	271 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	272
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	273 {\bf Background Images.}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	274 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	275 background behind the letter. The background is chosen by first selecting,
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	276 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	277 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	278 uniformly while making sure not to cross image borders).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	279 To combine the original letter image and the background image, contrast
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	280 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	281 intensity) for both the original image and the background image, $maximage$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	282 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	283 Each background pixel value is multiplied by $\frac{max(maximage -
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	284 contrast, 0)}{maxbg}$ (higher contrast yield darker
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	285 background). The output image pixels are max(background,original).
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	286 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	287
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	288 {\bf Salt and Pepper Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	289 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	290 The number of selected pixels is $0.2 \times complexity$.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	291 This filter has a probability of not being applied at all of 75\%.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	292 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	293
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	294 {\bf Spatially Gaussian Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	295 Different regions of the image are spatially smoothed.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	296 The image is convolved with a symmetric Gaussian kernel of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	297 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	298 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	299 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	300 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	301 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	302 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	303 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	304 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	305 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	306 image \times mask}{mask+1}$.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	307 This filter has a probability of not being applied at all of 75\%.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	308 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	309
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	310 {\bf Scratches.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	311 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	312 lines are heavily transformed images of the digit ``1'' (one), chosen
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	313 at random among five thousands such 1 images. The 1 image is
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	314 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	315 complexity)^2$, using bi-cubic interpolation,
5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	316 Two passes of a grey-scale morphological erosion filter
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	317 are applied, reducing the width of the line
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	318 by an amount controlled by $complexity$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	319 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	320 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	321 cases, two patches are generated, and otherwise three patches are
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	322 generated. The patch is applied by taking the maximal value on any given
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	323 patch or the original image, for each of the 32x32 pixel locations.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	324 \vspace*{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	325
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	326 {\bf Grey Level and Contrast Changes.}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	327 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	328 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	329 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	330 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	331 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	332 polarity is inverted with $0.5$ probability.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	333
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	334 \iffalse
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	335 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	336 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	337 \caption{Illustration of the pipeline of stochastic
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	338 transformations applied to the image of a lower-case \emph{t}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	339 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	340 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	341 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	342 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	343 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	344 \end{figure}
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	345 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	346
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	347
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	348 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	349 \section{Experimental Setup}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	350 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	351
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	352 Whereas much previous work on deep learning algorithms had been performed on
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	353 the MNIST digits classification task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	354 with 60~000 examples, and variants involving 10~000
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	355 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	356 to focus here on the case of much larger training sets, from 10 times to
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	357 to 1000 times larger.
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	358
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	359 The first step in constructing the larger datasets is to sample from
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	360 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	361 and {\bf OCR data} (scanned machine printed characters). Once a character
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	362 is sampled from one of these sources (chosen randomly), the pipeline of
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	363 the transformations and/or noise processes described in section \ref{s:perturbations}
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	364 is applied to the image.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	365
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	366 We compare the best MLP against
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	367 the best SDA (both models' hyper-parameters are selected to minimize the validation set error),
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	368 along with a comparison against a precise estimate
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	369 of human performance obtained via Amazon's Mechanical Turk (AMT)
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	370 service (http://mturk.com).
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	371 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	372 of money to perform tasks for which human intelligence is required.
522 d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	373 Mechanical Turk has been used extensively in natural language processing and vision.
d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	374 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	375 %\citep{SorokinAndForsyth2008,whitehill09}.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	376 AMT users were presented
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	377 with 10 character images and asked to choose 10 corresponding ASCII
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	378 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	379 62 or 10 character classes (all classes or digits only).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	380 Three users classified each image, allowing
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	381 to estimate inter-human variability. A total 2500 images/dataset were classified.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	382
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	383 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	384 \subsection{Data Sources}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	385 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	386
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	387 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	388 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	389 {\bf NIST.}
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	390 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	391 widely used for training and testing character
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	392 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	393 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	394 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	395 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	396 The fourth partition (called $hsf_4$), experimentally recognized to be the most difficult one, is the one recommended
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	397 by NIST as a testing set and is used in our work as well as some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	398 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	399 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	400 and 82587 for testing.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	401 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	402 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	403 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	404 Note that the distribution of the classes in the NIST training and test sets differs
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	405 substantially, with relatively many more digits in the test set, and more uniform distribution
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	406 of letters in the test set, compared to the training set (in the latter, the letters are distributed
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	407 more like the natural distribution of letters in text).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	408
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	409 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	410 {\bf Fonts.}
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	411 In order to have a good variety of sources we downloaded an important number of free fonts from:
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	412 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	413 % TODO: pointless to anonymize, it's not pointing to our work
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	414 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	415 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	416 directly as input to our models.
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	417
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	418 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	419 {\bf Captchas.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	420 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	421 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	422 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	423 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	424 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	425 depending on the value of the complexity parameter provided by the user of the data source.
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	426 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	427
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	428 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	429 {\bf OCR data.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	430 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	431 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	432 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	433 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	434 ({\tt http://www.iupr.com}), and which will be publicly released.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	435 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	436 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	437
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	438 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	439 \subsection{Data Sets}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	440 \vspace*{-1mm}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	441
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	442 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	443 from one of the 62 character classes.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	444 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	445
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	446 %\item
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	447 {\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	448
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	449 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	450 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	451 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	452 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	453 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	454 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	455
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	456 %\item
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	457 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	458 except that we only apply
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	459 transformations from slant to pinch. Therefore, the character is
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	460 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	461 closer to the NIST dataset.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	462 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	463
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	464 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	465 \subsection{Models and their Hyperparameters}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	466 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	467
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	468 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	469 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	470 \emph{Note that all hyper-parameters are selected based on performance on the {\bf NISTP} validation set.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	471
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	472 {\bf Multi-Layer Perceptrons (MLP).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	473 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	474 SVMs, we only compared to MLPs here because of the very large datasets used
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	475 (making the use of SVMs computationally challenging because of their quadratic
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	476 scaling behavior).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	477 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	478 exponentials) on the output layer for estimating $P(class \| image)$.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	479 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	480 Training examples are presented in minibatches of size 20. A constant learning
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	481 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	482 through preliminary experiments (measuring performance on a validation set),
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	483 and $0.1$ was then selected for optimizing on the whole training sets.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	484
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	485 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	486 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	487 \caption{Illustration of the computations and training criterion for the denoising
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	488 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	489 the layer (i.e. raw input or output of previous layer)
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	490 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	491 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	492 is compared to the uncorrupted input $x$ through the loss function
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	493 $L_H(x,z)$, whose expected value is approximately minimized during training
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	494 by tuning $\theta$ and $\theta'$.}
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	495 \label{fig:da}
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	496 \end{figure}
13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	497
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	498 {\bf Stacked Denoising Auto-Encoders (SDA).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	499 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	500 can be used to initialize the weights of each layer of a deep MLP (with many hidden
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	501 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	502 apparently setting parameters in the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	503 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	504 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	505 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	506 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	507 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	508 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	509 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	510 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	511 compositions of simpler ones through a deep hierarchy).
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	512
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	513 Here we chose to use the Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	514 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	515 these deep hierarchies of features, as it is very simple to train and
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	516 teach (see Figure~\ref{fig:da}, as well as
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	517 tutorial and code at {\tt http://deeplearning.net/tutorial}),
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	518 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	519 comparable or better than RBMs in series of experiments
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	520 \citep{VincentPLarochelleH2008}. During training, a Denoising
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	521 Auto-Encoder is presented with a stochastically corrupted version
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	522 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	523 forcing the hidden units to represent the leading regularities in
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	524 the data. Once it is trained, its hidden units activations can
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	525 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	526 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	527 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	528 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	529 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	530 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	531 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	532 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	533 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	534 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	535 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	536 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	537
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	538 \vspace*{-1mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	539
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	540 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	541 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	542 \caption{Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	543 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	544 of all models, on 3 different test sets (NIST, NISTP, P07).
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	545 Right: error rates on NIST test digits only, along with the previous results from
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	546 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	547 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	548
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	549 \label{fig:error-rates-charts}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	550 \vspace*{-1mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	551 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	552
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	553
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	554 \section{Experimental Results}
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{SDA vs MLP vs Humans}
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 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	561 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	562 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	563 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	564 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	565 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	566 ~\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	567 (figures and tables, including standard errors on the error rates) can be
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	568 found in Appendix I of the supplementary material. The 3 kinds of model differ in the
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	569 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	570 (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	571 previously published performance (in a statistically and qualitatively
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	572 significant way) but reaches human performance on both the 62-class task
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	573 and the 10-class (digits) task.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	574
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	575 \begin{figure}[ht]
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	576 \vspace*{-2mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	577 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	578 \caption{Relative improvement in error rate due to self-taught learning.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	579 Left: Improvement (or loss, when negative)
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	580 induced by out-of-distribution examples (perturbed data).
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	581 Right: Improvement (or loss, when negative) induced by multi-task
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	582 learning (training on all classes and testing only on either digits,
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	583 upper case, or lower-case). The deep learner (SDA) benefits more from
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	584 both self-taught learning scenarios, compared to the shallow MLP.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	585 \label{fig:improvements-charts}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	586 \vspace*{-2mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	587 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	588
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	589 In addition, as shown in the left of
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	590 Figure~\ref{fig:improvements-charts}, the relative improvement in error
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	591 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	592 differences with the MLP are statistically and qualitatively
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	593 significant.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	594 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	595 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	596 (i.e. the perturbed examples examples from NISTP or P07).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	597 Relative change is measured by taking
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	598 (original model's error / perturbed-data model's error - 1).
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	599 The right side of
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	600 Figure~\ref{fig:improvements-charts} shows the relative improvement
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	601 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	602 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	603 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	604 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	605 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	606 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	607 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	608 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	609 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	610 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	611 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	612 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	613 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	614 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	615 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	616 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	617 and upper case characters).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	618
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	619 %\vspace*{-1mm}
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	620 %\subsection{Perturbed Training Data More Helpful for SDA}
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	621 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	622
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	623 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	624 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	625 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	626
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	627 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	628 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	629 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	630 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	631 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	632 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	633 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	634 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	635 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	636 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	637 (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	638 shallow learner.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	639
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	640 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	641 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	642 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	643
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	644 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	645 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	646 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	647 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	648 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	649 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	650 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	651
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	652
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	653 \vspace*{-1mm}
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	654 \section{Conclusions and Discussion}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	655 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	656
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	657 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	658 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	659 supervised learner. More precisely,
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	660 the answers are positive for all the questions asked in the introduction.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	661 %\begin{itemize}
487 21787ac4e5a0 - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 486 diff changeset	662
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	663 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	664 Do the good results previously obtained with deep architectures on the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	665 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	666 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	667 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	668 published results on this dataset} (the ones that we are aware of), {\bf in fact reaching human-level
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	669 performance} at around 17\% error on the 62-class task and 1.4\% on the digits.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	670
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	671 $\bullet$ %\item
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	672 To what extent do self-taught learning scenarios help deep learners,
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	673 and do they help them more than shallow supervised ones?
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	674 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	675 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	676 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	677 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	678 examples. MLPs were helped by perturbed training examples when tested on perturbed input
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	679 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	680 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	681 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	682 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	683 were very significantly boosted by these out-of-distribution examples.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	684 Similarly, whereas the improvement due to the multi-task setting was marginal or
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	685 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	686 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	687 %\end{itemize}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	688
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	689 In the original self-taught learning framework~\citep{RainaR2007}, the
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	690 out-of-sample examples were used as a source of unsupervised data, and
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	691 experiments showed its positive effects in a \emph{limited labeled data}
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	692 scenario. However, many of the results by \citet{RainaR2007} (who used a
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	693 shallow, sparse coding approach) suggest that the relative gain of self-taught
536 5157a5830125 One comma Dumitru Erhan <dumitru.erhan@gmail.com> parents: 531 diff changeset	694 learning diminishes as the number of labeled examples increases (essentially,
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	695 a ``diminishing returns'' scenario occurs). We note instead that, for deep
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	696 architectures, our experiments show that such a positive effect is accomplished
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	697 even in a scenario with a \emph{very large number of labeled examples}.
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	698
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	699 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	700 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	701 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	702 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	703 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	704 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	705 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	706 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	707 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	708 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	709 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	710 experiments could attempt at teasing apart these factors.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	711 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	712 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	713 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	714 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	715 it was found that online learning on a huge dataset did not make the
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	716 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	717 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	718 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	719 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	720 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	721 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	722 (with or without self-taught settings), and more labeled examples
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	723 does not allow to go from the poorer basins of attraction discovered
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	724 by the purely supervised shallow models to the kind of better basins associated
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	725 with deep learning and self-taught learning.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	726
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	727 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	728 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	729
498 7ff00c27c976 add missing file for bibtex and make it smaller. Frederic Bastien <nouiz@nouiz.org> parents: 496 diff changeset	730 \newpage
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	731 {
e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	732 \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	733 %\bibliographystyle{plainnat}
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	734 \bibliographystyle{unsrtnat}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	735 %\bibliographystyle{apalike}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	736 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	737
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	738
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	739 \end{document}

Mercurial > ift6266

annotate writeup/nips2010_submission.tex @ 536:5157a5830125