ift6266: writeup/nips2010_submission.tex annotate

annotate writeup/nips2010_submission.tex @ 551:8f365abf171d

separete the transmo image

author	Frederic Bastien <nouiz@nouiz.org>
date	Wed, 02 Jun 2010 17:00:11 -0400
parents	662299f265ab
children	35c611363291

rev	line source
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	1 \documentclass{article} % For LaTeX2e
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	2 \usepackage{nips10submit_e,times}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	3
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	4 \usepackage{amsthm,amsmath,bbm}
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	5 \usepackage[psamsfonts]{amssymb}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	6 \usepackage{algorithm,algorithmic}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	7 \usepackage[utf8]{inputenc}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	8 \usepackage{graphicx,subfigure}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	9 \usepackage[numbers]{natbib}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	10
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	11 %\setlength\parindent{0mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	12
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	13 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	14 \author{The IFT6266 Gang}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	15
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	16 \begin{document}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	17
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	18 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	19 \maketitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	20
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	21 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	22 \begin{abstract}
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	23 Recent theoretical and empirical work in statistical machine learning has
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	24 demonstrated the importance of learning algorithms for deep
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	25 architectures, i.e., function classes obtained by composing multiple
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	26 non-linear transformations. Self-taught learning (exploiting unlabeled
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	27 examples or examples from other distributions) has already been applied
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	28 to deep learners, but mostly to show the advantage of unlabeled
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	29 examples. Here we explore the advantage brought by {\em out-of-distribution
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	30 examples} and show that {\em deep learners benefit more from them than a
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	31 corresponding shallow learner}, in the area
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	32 of handwritten character recognition. In fact, we show that they reach
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	33 human-level performance on both handwritten digit classification and
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	34 62-class handwritten character recognition. For this purpose we
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	35 developed a powerful generator of stochastic variations and noise
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	36 processes for character images, including not only affine transformations but
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	37 also slant, local elastic deformations, changes in thickness, background
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	38 images, grey level changes, contrast, occlusion, and various types of
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	39 noise. The out-of-distribution examples are
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	40 obtained from these highly distorted images or
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	41 by including examples of object classes different from those in the target test set.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	42 \end{abstract}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	43 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	44
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	45 \section{Introduction}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	46 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	47
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	48 Deep Learning has emerged as a promising new area of research in
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	49 statistical machine learning (see~\citet{Bengio-2009} for a review).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	50 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	51 of useful representations of data, which are better suited to the task at hand.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	52 This is in great part inspired by observations of the mammalian visual cortex,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	53 which consists of a chain of processing elements, each of which is associated with a
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	54 different representation of the raw visual input. In fact,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	55 it was found recently that the features learnt in deep architectures resemble
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	56 those observed in the first two of these stages (in areas V1 and V2
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	57 of visual cortex)~\citep{HonglakL2008}, and that they become more and
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	58 more invariant to factors of variation (such as camera movement) in
501 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
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	76 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}),
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	77 which
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	78 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	79 Machines in terms of unsupervised extraction of a hierarchy of features
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	80 useful for classification. The principle is that each layer starting from
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	81 the bottom is trained to encode its input (the output of the previous
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	82 layer) and to reconstruct it from a corrupted version. After this
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	83 unsupervised initialization, the stack of DAs can be
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	84 converted into a deep supervised feedforward neural network and fine-tuned by
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	85 stochastic gradient descent.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	86
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	87 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	88 of semi-supervised and multi-task learning: the learner can exploit examples
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	89 that are unlabeled and/or come from a distribution different from the target
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	90 distribution, e.g., from other classes than those of interest.
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	91 It has already been shown that deep learners can clearly take advantage of
2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	92 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	93 but more needs to be done to explore the impact
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	94 of {\em out-of-distribution} examples and of the multi-task setting
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	95 (one exception is~\citep{CollobertR2008}, which uses very different kinds
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	96 of learning algorithms). In particular the {\em relative
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	97 advantage} of deep learning for these settings has not been evaluated.
512 6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	98 The hypothesis explored here is that a deep hierarchy of features
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	99 may be better able to provide sharing of statistical strength
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	100 between different regions in input space or different tasks,
6f042a71be23 todo done Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 507 diff changeset	101 as discussed in the conclusion.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	102
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	103 In this paper we ask the following questions:
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	104
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	105 %\begin{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	106 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	107 Do the good results previously obtained with deep architectures on the
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	108 MNIST digit images generalize to the setting of a much larger and richer (but similar)
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	109 dataset, the NIST special database 19, with 62 classes and around 800k examples?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	110
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	111 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	112 To what extent does the perturbation of input images (e.g. adding
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	113 noise, affine transformations, background images) make the resulting
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	114 classifiers better not only on similarly perturbed images but also on
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	115 the {\em original clean examples}?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	116
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	117 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	118 Do deep architectures {\em benefit more from such out-of-distribution}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	119 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	120
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	121 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	122 Similarly, does the feature learning step in deep learning algorithms benefit more
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	123 from training with moderately different classes (i.e. a multi-task learning scenario) than
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	124 a corresponding shallow and purely supervised architecture?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	125 %\end{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	126
511 d057941417ed a few changes in the first section Dumitru Erhan <dumitru.erhan@gmail.com> parents: 510 diff changeset	127 Our experimental results provide positive evidence towards all of these questions.
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	128 To achieve these results, we introduce in the next section a sophisticated system
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	129 for stochastically transforming character images. The conclusion discusses
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	130 the more general question of why deep learners may benefit so much from
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	131 the self-taught learning framework.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	132
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	133 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	134 \section{Perturbation and Transformation of Character Images}
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	135 \label{s:perturbations}
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	136 {\large\bf Transformations}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	137
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	138 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	139
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	140 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	141 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	142 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	143 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	144 \vspace{1.2cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	145 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	146 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	147 {\bf Original:}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	148 This section describes the different transformations we used to stochastically
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	149 transform source images in order to obtain data from a larger distribution which
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	150 covers a domain substantially larger than the clean characters distribution from
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	151 which we start. Although character transformations have been used before to
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	152 improve character recognizers, this effort is on a large scale both
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	153 in number of classes and in the complexity of the transformations, hence
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	154 in the complexity of the learning task.
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	155 More details can
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	156 be found in this technical report~\citep{ift6266-tr-anonymous}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	157 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	158 {\tt http://anonymous.url.net}. All the modules in the pipeline share
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	159 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	160 amount of deformation or noise introduced.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	161
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	162 There are two main parts in the pipeline. The first one,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	163 from slant to pinch below, performs transformations. The second
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	164 part, from blur to contrast, adds different kinds of noise.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	165 \end{minipage}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	166
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	167
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	168 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	169 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	170 \includegraphics[scale=.45]{images/Slant_only.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	171 \label{fig:Slant}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	172 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	173 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	174 %\centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	175 {\bf Slant:}
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	176 Each row of the image is shifted
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	177 proportionally to its height: $shift = round(slant \times height)$.
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	178 $slant \sim U[-complexity,complexity]$.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	179 \vspace{1.2cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	180 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	181
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	182
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	183 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	184 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	185 \includegraphics[scale=.45]{images/Thick_only.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	186 \label{fig:Think}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	187 \vspace{.9cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	188 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	189 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	190 {\bf Thinkness:}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	191 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	192 are applied. The neighborhood of each pixel is multiplied
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	193 element-wise with a {\em structuring element} matrix.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	194 The pixel value is replaced by the maximum or the minimum of the resulting
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	195 matrix, respectively for dilation or erosion. Ten different structural elements with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	196 increasing dimensions (largest is $5\times5$) were used. For each image,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	197 randomly sample the operator type (dilation or erosion) with equal probability and one structural
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	198 element from a subset of the $n=round(m \times complexity)$ smallest structuring elements
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	199 where $m=10$ for dilation and $m=6$ for erosion (to avoid completely erasing thin characters).
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	200 A neutral element (no transformation)
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	201 is always present in the set. is applied.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	202 \vspace{.4cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	203 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	204 \vspace{-.7cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	205
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	206
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	207 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	208 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	209 \includegraphics[scale=.45]{images/Affine_only.png}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	210 \label{fig:Affine}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	211 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	212 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	213 {\bf Affine Transformations:}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	214 A $2 \times 3$ affine transform matrix (with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	215 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	216 Output pixel $(x,y)$ takes the value of input pixel
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	217 nearest to $(ax+by+c,dx+ey+f)$,
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	218 producing scaling, translation, rotation and shearing.
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	219 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	220 forbid large rotations (not to confuse classes) but to give good
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	221 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	222 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	223 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	224 complexity]$.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	225 \end{minipage}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	226
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	227 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	228 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	229 \includegraphics[scale=.45]{images/Localelasticdistorsions_only.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	230 \label{fig:Elastic}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	231 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	232 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	233 {\bf Local Elastic Deformations:}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	234 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	235 which provides more details.
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	236 The intensity of the displacement fields is given by
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	237 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	238 convolved with a Gaussian 2D kernel (resulting in a blur) of
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	239 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	240 \vspace{.4cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	241 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	242 \vspace{-.7cm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	243
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	244 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	245 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	246 \includegraphics[scale=.45]{images/Pinch_only.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	247 \label{fig:Pinch}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	248 \vspace{.6cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	249 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	250 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	251 {\bf Pinch:}
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	252 This is the ``Whirl and pinch'' GIMP filter but with whirl was set to 0.
8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	253 A pinch is ``similar to projecting the image onto an elastic
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	254 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	255 For a square input image, this is akin to drawing a circle of
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	256 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	257 that disk (region inside circle) will have its value recalculated by taking
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	258 the value of another ``source'' pixel in the original image. The position of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	259 that source pixel is found on the line that goes through $C$ and $P$, but
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	260 at some other distance $d_2$. Define $d_1$ to be the distance between $P$
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	261 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	262 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	263 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	264 around the (non-integer) source position thus found.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	265 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	266 %\vspace{1.5cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	267 \end{minipage}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	268
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	269 \vspace{.1cm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	270
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	271 {\large\bf Injecting Noise}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	272
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	273 \vspace*{-.2cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	274 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	275 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	276 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	277 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	278 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	279 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	280 {\bf Motion Blur:}
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	281 This is GIMP's ``linear motion blur''
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	282 with parameters $length$ and $angle$. The value of
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	283 a pixel in the final image is approximately the mean value of the first $length$ pixels
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	284 found by moving in the $angle$ direction.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	285 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	286 \vspace{.7cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	287 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	288
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	289 \vspace*{-5mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	290
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	291 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	292 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	293 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	294 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	295 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	296 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	297 {\bf Occlusion:}
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	298 Selects a random rectangle from an {\em occluder} character
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	299 image and places it over the original {\em occluded}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	300 image. Pixels are combined by taking the max(occluder,occluded),
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	301 closer to black. The rectangle corners
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	302 are sampled so that larger complexity gives larger rectangles.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	303 The destination position in the occluded image are also sampled
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	304 according to a normal distribution (more details in~\citet{ift6266-tr-anonymous}).
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	305 This filter is skipped with probability 60\%.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	306 \vspace{.4cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	307 \end{minipage}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	308
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	309 \vspace*{-5mm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	310 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	311 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	312 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	313 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	314 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	315 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	316 {\bf Pixel Permutation:}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	317 This filter permutes neighbouring pixels. It first selects
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	318 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each of them are then
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	319 sequentially exchanged with one other in as $V4$ neighbourhood.
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	320 This filter is skipped with probability 80\%.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	321 \vspace{.8cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	322 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	323
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	324
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	325 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	326 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	327 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	328 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	329 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	330 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	331 {\bf Gaussian Noise:}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	332 This filter simply adds, to each pixel of the image independently, a
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	333 noise $\sim Normal(0,(\frac{complexity}{10})^2)$.
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	334 This filter is skipped with probability 70\%.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	335 \vspace{1.1cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	336 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	337 \vspace{-.7cm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	338
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	339 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	340 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	341 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	342 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	343 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	344 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	345 {\bf Background Images:}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	346 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	347 background behind the letter, from a randomly chosen natural image,
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	348 with contrast adjustments depending on $complexity$, to preserve
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	349 more or less of the original character image.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	350 \vspace{.8cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	351 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	352 \vspace{-.7cm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	353
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	354 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	355 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	356 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	357 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	358 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	359 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	360 {\bf Salt and Pepper Noise:}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	361 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	362 The number of selected pixels is $0.2 \times complexity$.
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	363 This filter is skipped with probability 75\%.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	364 \vspace{.9cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	365 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	366 \vspace{-.7cm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	367
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	368 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	369 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	370 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	371 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	372 \vspace{.5cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	373 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	374 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	375 {\bf Spatially Gaussian Noise:}
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	376 Different regions of the image are spatially smoothed by convolving
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	377 the image is convolved with a symmetric Gaussian kernel of
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	378 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	379 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	380 between $0$ and $1$. We also create a symmetric averaging window, of the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	381 kernel size, with maximum value at the center. For each image we sample
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	382 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	383 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	384 initialize to zero a mask matrix of the image size. For each selected pixel
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	385 we add to the mask the averaging window centered to it. The final image is
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	386 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	387 image \times mask}{mask+1}$.
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	388 This filter is skipped with probability 75\%.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	389 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	390 \vspace{-.7cm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	391
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	392 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	393 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	394 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	395 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	396 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	397 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	398 \vspace{.4cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	399 {\bf Scratches:}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	400 The scratches module places line-like white patches on the image. The
517 0a5945249f2b section 2, quick first pass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 511 diff changeset	401 lines are heavily transformed images of the digit ``1'' (one), chosen
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	402 at random among 500 such 1 images,
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	403 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	404 complexity)^2$, using bi-cubic interpolation.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	405 Two passes of a grey-scale morphological erosion filter
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	406 are applied, reducing the width of the line
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	407 by an amount controlled by $complexity$.
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	408 This filter is skipped with probability 85\%. The probabilities
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	409 of applying 1, 2, or 3 patches are (50\%,30\%,20\%).
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	410 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	411 \vspace{-.7cm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	412
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	413 \begin{minipage}[b]{0.14\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	414 \centering
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	415 \includegraphics[scale=.45]{images/Original.PNG}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	416 \label{fig:Original}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	417 \end{minipage}%
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	418 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	419 {\bf Grey Level and Contrast Changes:}
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	420 This filter changes the contrast and may invert the image polarity (white
544 1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	421 to black and black to white). The contrast is $C \sim U[1-0.85 \times complexity,1]$
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	422 so the image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
1cdfc17e890f ca fitte maintenant Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 541 diff changeset	423 polarity is inverted with probability 50\%.
551 8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	424 \vspace{.7cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	425 \end{minipage}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	426 \vspace{-.7cm}
8f365abf171d separete the transmo image Frederic Bastien <nouiz@nouiz.org> parents: 550 diff changeset	427
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	428
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	429 \iffalse
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	430 \begin{figure}[ht]
538 f0ee2212ea7c typos and stuff Dumitru Erhan <dumitru.erhan@gmail.com> parents: 537 534 diff changeset	431 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	432 \caption{Illustration of the pipeline of stochastic
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	433 transformations applied to the image of a lower-case \emph{t}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	434 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	435 left to right, first top line, then bottom line) shows the result
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	436 of applying one of the modules in the pipeline. The last image
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	437 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	438 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	439 \end{figure}
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	440 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	441
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	442
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	443 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	444 \section{Experimental Setup}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	445 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	446
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	447 Whereas much previous work on deep learning algorithms had been performed on
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	448 the MNIST digits classification task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	449 with 60~000 examples, and variants involving 10~000
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	450 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	451 to focus here on the case of much larger training sets, from 10 times to
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	452 to 1000 times larger.
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	453
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	454 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
499 2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	455 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
2b58eda9fc08 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 495 diff changeset	456 and {\bf OCR data} (scanned machine printed characters). Once a character
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	457 is sampled from one of these sources (chosen randomly), the second step is to
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	458 apply a pipeline of transformations and/or noise processes described in section \ref{s:perturbations}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	459
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	460 To provide a baseline of error rate comparison we also estimate human performance
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	461 on both the 62-class task and the 10-class digits task.
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	462 We compare the best MLPs against
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	463 the best SDAs (both models' hyper-parameters are selected to minimize the validation set error),
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	464 along with a comparison against a precise estimate
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	465 of human performance obtained via Amazon's Mechanical Turk (AMT)
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	466 service (http://mturk.com).
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	467 AMT users are paid small amounts
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	468 of money to perform tasks for which human intelligence is required.
522 d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	469 Mechanical Turk has been used extensively in natural language processing and vision.
d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	470 %processing \citep{SnowEtAl2008} and vision
d41926a68993 remis les choses qui avaient disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 521 diff changeset	471 %\citep{SorokinAndForsyth2008,whitehill09}.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	472 AMT users were presented
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	473 with 10 character images and asked to choose 10 corresponding ASCII
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	474 characters. They were forced to make a hard choice among the
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	475 62 or 10 character classes (all classes or digits only).
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	476 A total 2500 images/dataset were classified by XXX subjects,
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	477 with 3 subjects classifying each image, allowing
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	478 us to estimate inter-human variability (e.g a standard error of 0.1\%
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	479 on the average 18\% error done by humans on the 62-class task).
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	480
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	481 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	482 \subsection{Data Sources}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	483 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	484
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	485 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	486 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	487 {\bf NIST.}
501 5927432d8b8d - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 500 diff changeset	488 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	489 widely used for training and testing character
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	490 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	491 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	492 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	493 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
534 4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	494 The fourth partition (called $hsf_4$, 82587 examples),
4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	495 experimentally recognized to be the most difficult one, is the one recommended
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	496 by NIST as a testing set and is used in our work as well as some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
534 4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	497 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for
4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	498 model selection.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	499 The performances reported by previous work on that dataset mostly use only the digits.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	500 Here we use all the classes both in the training and testing phase. This is especially
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	501 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	502 Note that the distribution of the classes in the NIST training and test sets differs
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	503 substantially, with relatively many more digits in the test set, and more uniform distribution
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	504 of letters in the test set, compared to the training set (in the latter, the letters are distributed
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	505 more like the natural distribution of letters in text).
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	506 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	507
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	508 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	509 {\bf Fonts.}
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	510 In order to have a good variety of sources we downloaded an important number of free fonts from:
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	511 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	512 % TODO: pointless to anonymize, it's not pointing to our work
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	513 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	514 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	515 directly as input to our models.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	516 \vspace*{-1mm}
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	517
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	518 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	519 {\bf Captchas.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	520 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	521 generating characters of the same format as the NIST dataset. This software is based on
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	522 a random character class generator and various kinds of transformations similar to those described in the previous sections.
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	523 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	524 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	525 depending on the value of the complexity parameter provided by the user of the data source.
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	526 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	527 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	528
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	529 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	530 {\bf OCR data.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	531 A large set (2 million) of scanned, OCRed and manually verified machine-printed
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	532 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	533 additional source. This set is part of a larger corpus being collected by the Image Understanding
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	534 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	535 ({\tt http://www.iupr.com}), and which will be publicly released.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	536 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	537 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	538
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	539 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	540 \subsection{Data Sets}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	541 \vspace*{-1mm}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	542
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	543 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	544 from one of the 62 character classes.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	545 %\begin{itemize}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	546 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	547
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	548 %\item
534 4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	549 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	550 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	551 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	552
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	553 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	554 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	555 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	556 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	557 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	558 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	559 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	560 \vspace*{-1mm}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	561
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	562 %\item
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	563 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	564 except that we only apply
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	565 transformations from slant to pinch. Therefore, the character is
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	566 transformed but no additional noise is added to the image, giving images
534 4d6493d171f6 added all sizes Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 533 diff changeset	567 closer to the NIST dataset.
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	568 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	569 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	570
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	571 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	572 \subsection{Models and their Hyperparameters}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	573 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	574
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	575 The experiments are performed with Multi-Layer Perceptrons (MLP) with a single
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	576 hidden layer and with Stacked Denoising Auto-Encoders (SDA).
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	577 \emph{Note that all hyper-parameters are selected based on performance on the {\bf NISTP} validation set.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	578
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	579 {\bf Multi-Layer Perceptrons (MLP).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	580 Whereas previous work had compared deep architectures to both shallow MLPs and
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	581 SVMs, we only compared to MLPs here because of the very large datasets used
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	582 (making the use of SVMs computationally challenging because of their quadratic
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	583 scaling behavior).
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	584 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	585 exponentials) on the output layer for estimating $P(class \| image)$.
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	586 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	587 Training examples are presented in minibatches of size 20. A constant learning
8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	588 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	589 through preliminary experiments (measuring performance on a validation set),
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	590 and $0.1$ was then selected for optimizing on the whole training sets.
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	591 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	592
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	593
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	594 {\bf Stacked Denoising Auto-Encoders (SDA).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	595 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	596 can be used to initialize the weights of each layer of a deep MLP (with many hidden
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	597 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	598 apparently setting parameters in the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	599 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	600 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	601 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	602 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	603 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	604 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	605 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	606 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	607 compositions of simpler ones through a deep hierarchy).
530 8fe77eac344f Clarifying the experimental setup, typos here and there Dumitru Erhan <dumitru.erhan@gmail.com> parents: 524 diff changeset	608
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	609 \begin{figure}[ht]
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	610 \vspace*{-2mm}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	611 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{images/denoising_autoencoder_small.pdf}}}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	612 \vspace*{-2mm}
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	613 \caption{Illustration of the computations and training criterion for the denoising
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	614 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	615 the layer (i.e. raw input or output of previous layer)
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	616 is corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	617 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	618 is compared to the uncorrupted input $x$ through the loss function
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	619 $L_H(x,z)$, whose expected value is approximately minimized during training
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	620 by tuning $\theta$ and $\theta'$.}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	621 \label{fig:da}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	622 \vspace*{-2mm}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	623 \end{figure}
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	624
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	625 Here we chose to use the Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	626 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	627 these deep hierarchies of features, as it is very simple to train and
532 2e33885730cf changements aux charts.ods Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 529 diff changeset	628 explain (see Figure~\ref{fig:da}, as well as
521 13816dbef6ed des choses ont disparu Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 520 diff changeset	629 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	630 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	631 comparable or better than RBMs in series of experiments
519 eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	632 \citep{VincentPLarochelleH2008}. During training, a Denoising
eaa595ea2402 section 3 quickpass Dumitru Erhan <dumitru.erhan@gmail.com> parents: 518 diff changeset	633 Auto-Encoder is presented with a stochastically corrupted version
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	634 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	635 forcing the hidden units to represent the leading regularities in
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	636 the data. Once it is trained, in a purely unsupervised way,
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	637 its hidden units' activations can
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	638 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	639 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	640 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	641 the same standard procedure used to train them (see previous section).
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	642 The SDA hyper-parameters are the same as for the MLP, with the addition of the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	643 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	644 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	645 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	646 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	647 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	648 of hidden layers but it was fixed to 3 based on previous work with
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	649 SDAs on MNIST~\citep{VincentPLarochelleH2008}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	650
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	651 \vspace*{-1mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	652
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	653 \begin{figure}[ht]
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	654 \vspace*{-2mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	655 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	656 \vspace*{-3mm}
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	657 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	658 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
548 34cb28249de0 suggestions de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 547 diff changeset	659 of all models, on NIST and NISTP test sets.
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	660 Right: error rates on NIST test digits only, along with the previous results from
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	661 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	662 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	663 \label{fig:error-rates-charts}
541 8aad1c6ec39a reduction espace Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 539 diff changeset	664 \vspace*{-2mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	665 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	666
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	667
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	668 \section{Experimental Results}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	669 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	670
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	671 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	672 %\subsection{SDA vs MLP vs Humans}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	673 %\vspace*{-1mm}
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	674 The models are either trained on NIST (MLP0 and SDA0),
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	675 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	676 on either NIST, NISTP or P07, either on the 62-class task
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	677 or on the 10-digits task.
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	678 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	679 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	680 SDA2), along with the previous results on the digits NIST special database
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	681 19 test set from the literature respectively based on ARTMAP neural
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	682 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
516 092dae9a5040 make the reference more compact. Frederic Bastien <nouiz@nouiz.org> parents: 514 diff changeset	683 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	684 ~\citep{Milgram+al-2005}. More detailed and complete numerical results
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	685 (figures and tables, including standard errors on the error rates) can be
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	686 found in Appendix I of the supplementary material.
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	687 The deep learner not only outperformed the shallow ones and
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	688 previously published performance (in a statistically and qualitatively
535 caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	689 significant way) but when trained with perturbed data
caf7769ca19c typo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 534 diff changeset	690 reaches human performance on both the 62-class task
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	691 and the 10-class (digits) task.
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	692 17\% error (SDA1) or 18\% error (humans) may seem large but a large
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	693 majority of the errors from humans and from SDA1 are from out-of-context
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	694 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	695 ``c'' and a ``C'' are often indistinguishible).
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	696
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	697 \begin{figure}[ht]
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	698 \vspace*{-3mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	699 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	700 \vspace*{-3mm}
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	701 \caption{Relative improvement in error rate due to self-taught learning.
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	702 Left: Improvement (or loss, when negative)
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	703 induced by out-of-distribution examples (perturbed data).
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	704 Right: Improvement (or loss, when negative) induced by multi-task
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	705 learning (training on all classes and testing only on either digits,
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	706 upper case, or lower-case). The deep learner (SDA) benefits more from
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	707 both self-taught learning scenarios, compared to the shallow MLP.}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	708 \label{fig:improvements-charts}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	709 \vspace*{-2mm}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	710 \end{figure}
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	711
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	712 In addition, as shown in the left of
c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	713 Figure~\ref{fig:improvements-charts}, the relative improvement in error
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	714 rate brought by self-taught learning is greater for the SDA, and these
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	715 differences with the MLP are statistically and qualitatively
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	716 significant.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	717 The left side of the figure shows the improvement to the clean
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	718 NIST test set error brought by the use of out-of-distribution examples
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	719 (i.e. the perturbed examples examples from NISTP or P07).
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	720 Relative percent change is measured by taking
548 34cb28249de0 suggestions de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 547 diff changeset	721 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	722 The right side of
523 c778d20ab6f8 space adjustments Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 522 diff changeset	723 Figure~\ref{fig:improvements-charts} shows the relative improvement
486 877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	724 brought by the use of a multi-task setting, in which the same model is
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	725 trained for more classes than the target classes of interest (i.e. training
877af97ee193 section resultats et appendice Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 485 diff changeset	726 with all 62 classes when the target classes are respectively the digits,
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	727 lower-case, or upper-case characters). Again, whereas the gain from the
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	728 multi-task setting is marginal or negative for the MLP, it is substantial
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	729 for the SDA. Note that to simplify these multi-task experiments, only the original
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	730 NIST dataset is used. For example, the MLP-digits bar shows the relative
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	731 percent improvement in MLP error rate on the NIST digits test set
548 34cb28249de0 suggestions de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 547 diff changeset	732 is $100\% \times$ (1 - single-task
493 a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	733 model's error / multi-task model's error). The single-task model is
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	734 trained with only 10 outputs (one per digit), seeing only digit examples,
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	735 whereas the multi-task model is trained with 62 outputs, with all 62
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	736 character classes as examples. Hence the hidden units are shared across
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	737 all tasks. For the multi-task model, the digit error rate is measured by
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	738 comparing the correct digit class with the output class associated with the
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	739 maximum conditional probability among only the digit classes outputs. The
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	740 setting is similar for the other two target classes (lower case characters
a194ce5a4249 difference stat. sign. Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 491 diff changeset	741 and upper case characters).
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	742 %\vspace*{-1mm}
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	743 %\subsection{Perturbed Training Data More Helpful for SDA}
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	744 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	745
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	746 %\vspace*{-1mm}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	747 %\subsection{Multi-Task Learning Effects}
6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	748 %\vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	749
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	750 \iffalse
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	751 As previously seen, the SDA is better able to benefit from the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	752 transformations applied to the data than the MLP. In this experiment we
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	753 define three tasks: recognizing digits (knowing that the input is a digit),
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	754 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	755 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	756 consider the digit classification task as the target task and we want to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	757 evaluate whether training with the other tasks can help or hurt, and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	758 whether the effect is different for MLPs versus SDAs. The goal is to find
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	759 out if deep learning can benefit more (or less) from multiple related tasks
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	760 (i.e. the multi-task setting) compared to a corresponding purely supervised
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	761 shallow learner.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	762
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	763 We use a single hidden layer MLP with 1000 hidden units, and a SDA
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	764 with 3 hidden layers (1000 hidden units per layer), pre-trained and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	765 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	766
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	767 Our results show that the MLP benefits marginally from the multi-task setting
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	768 in the case of digits (5\% relative improvement) but is actually hurt in the case
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	769 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
495 5764a2ae1fb5 typos Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 493 diff changeset	770 On the other hand the SDA benefited from the multi-task setting, with relative
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	771 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	772 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	773 \fi
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	774
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	775
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	776 \vspace*{-2mm}
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	777 \section{Conclusions and Discussion}
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	778 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	779
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	780 We have found that the self-taught learning framework is more beneficial
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	781 to a deep learner than to a traditional shallow and purely
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	782 supervised learner. More precisely,
520 18a6379999fd more after lunch :) Dumitru Erhan <dumitru.erhan@gmail.com> parents: 519 diff changeset	783 the answers are positive for all the questions asked in the introduction.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	784 %\begin{itemize}
487 21787ac4e5a0 - Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 486 diff changeset	785
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	786 $\bullet$ %\item
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	787 {\bf Do the good results previously obtained with deep architectures on the
549 ef172f4a322a ca fitte Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 548 diff changeset	788 MNIST digits generalize to a much larger and richer (but similar)
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	789 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	790 Yes, the SDA {\bf systematically outperformed the MLP and all the previously
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	791 published results on this dataset} (the ones that we are aware of), {\bf in fact reaching human-level
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	792 performance} at around 17\% error on the 62-class task and 1.4\% on the digits.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	793
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	794 $\bullet$ %\item
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	795 {\bf To what extent do self-taught learning scenarios help deep learners,
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	796 and do they help them more than shallow supervised ones}?
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	797 We found that distorted training examples not only made the resulting
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	798 classifier better on similarly perturbed images but also on
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	799 the {\em original clean examples}, and more importantly and more novel,
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	800 that deep architectures benefit more from such {\em out-of-distribution}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	801 examples. MLPs were helped by perturbed training examples when tested on perturbed input
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	802 images (65\% relative improvement on NISTP)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	803 but only marginally helped (5\% relative improvement on all classes)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	804 or even hurt (10\% relative loss on digits)
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	805 with respect to clean examples . On the other hand, the deep SDAs
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	806 were very significantly boosted by these out-of-distribution examples.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	807 Similarly, whereas the improvement due to the multi-task setting was marginal or
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	808 negative for the MLP (from +5.6\% to -3.6\% relative change),
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	809 it was very significant for the SDA (from +13\% to +27\% relative change),
316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	810 which may be explained by the arguments below.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	811 %\end{itemize}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	812
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	813 In the original self-taught learning framework~\citep{RainaR2007}, the
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	814 out-of-sample examples were used as a source of unsupervised data, and
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	815 experiments showed its positive effects in a \emph{limited labeled data}
07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	816 scenario. However, many of the results by \citet{RainaR2007} (who used a
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	817 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	818 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	819 We note instead that, for deep
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	820 architectures, our experiments show that such a positive effect is accomplished
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	821 even in a scenario with a \emph{very large number of labeled examples},
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	822 i.e., here, the relative gain of self-taught learning is probably preserved
662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	823 in the asymptotic regime.
524 07bc0ca8d246 added paragraph comparing "our" self-taught learning with "theirs" Dumitru Erhan <dumitru.erhan@gmail.com> parents: 523 diff changeset	824
547 316c7bdad5ad charts Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 544 diff changeset	825 {\bf Why would deep learners benefit more from the self-taught learning framework}?
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	826 The key idea is that the lower layers of the predictor compute a hierarchy
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	827 of features that can be shared across tasks or across variants of the
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	828 input distribution. Intermediate features that can be used in different
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	829 contexts can be estimated in a way that allows to share statistical
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	830 strength. Features extracted through many levels are more likely to
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	831 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	832 increasing the likelihood that they would be useful for a larger array
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	833 of tasks and input conditions.
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	834 Therefore, we hypothesize that both depth and unsupervised
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	835 pre-training play a part in explaining the advantages observed here, and future
2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	836 experiments could attempt at teasing apart these factors.
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	837 And why would deep learners benefit from the self-taught learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	838 scenarios even when the number of labeled examples is very large?
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	839 We hypothesize that this is related to the hypotheses studied
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	840 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	841 it was found that online learning on a huge dataset did not make the
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	842 advantage of the deep learning bias vanish, a similar phenomenon
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	843 may be happening here. We hypothesize that unsupervised pre-training
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	844 of a deep hierarchy with self-taught learning initializes the
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	845 model in the basin of attraction of supervised gradient descent
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	846 that corresponds to better generalization. Furthermore, such good
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	847 basins of attraction are not discovered by pure supervised learning
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	848 (with or without self-taught settings), and more labeled examples
550 662299f265ab suggestions from Ian Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 549 diff changeset	849 does not allow the model to go from the poorer basins of attraction discovered
529 4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	850 by the purely supervised shallow models to the kind of better basins associated
4354c3c8f49c longer conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 524 diff changeset	851 with deep learning and self-taught learning.
502 2b35a6e5ece4 changements de Myriam Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 501 diff changeset	852
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	853 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	854 can be executed on-line at {\tt http://deep.host22.com}.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	855
498 7ff00c27c976 add missing file for bibtex and make it smaller. Frederic Bastien <nouiz@nouiz.org> parents: 496 diff changeset	856 \newpage
496 e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	857 {
e41007dd40e9 make the reference shorter. Frederic Bastien <nouiz@nouiz.org> parents: 495 diff changeset	858 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,aigaion-shorter,specials}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	859 %\bibliographystyle{plainnat}
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	860 \bibliographystyle{unsrtnat}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	861 %\bibliographystyle{apalike}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	862 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	863
485 6beaf3328521 les tables enlevées Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 484 diff changeset	864
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	865 \end{document}

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