ift6266: writeup/nips2010_submission.tex annotate

annotate writeup/nips2010_submission.tex @ 484:9a757d565e46

reduction de taille

author	Yoshua Bengio <bengioy@iro.umontreal.ca>
date	Mon, 31 May 2010 20:42:22 -0400
parents	b9cdb464de5f
children	6beaf3328521

rev	line source
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	1 \documentclass{article} % For LaTeX2e
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	2 \usepackage{nips10submit_e,times}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	3
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	4 \usepackage{amsthm,amsmath,amssymb,bbold,bbm}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	5 \usepackage{algorithm,algorithmic}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	6 \usepackage[utf8]{inputenc}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	7 \usepackage{graphicx,subfigure}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	8 \usepackage[numbers]{natbib}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	9
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	10 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	11 \author{The IFT6266 Gang}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	12
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	13 \begin{document}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	14
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	15 %\makeanontitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	16 \maketitle
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	17
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	18 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	19 \begin{abstract}
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	20 Recent theoretical and empirical work in statistical machine learning has
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	21 demonstrated the importance of learning algorithms for deep
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	22 architectures, i.e., function classes obtained by composing multiple
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	23 non-linear transformations. The self-taught learning (exploitng unlabeled
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	24 examples or examples from other distributions) has already been applied
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	25 to deep learners, but mostly to show the advantage of unlabeled
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	26 examples. Here we explore the advantage brought by {\em out-of-distribution
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	27 examples} and show that {\em deep learners benefit more from them than a
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	28 corresponding shallow learner}, in the area
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	29 of handwritten character recognition. In fact, we show that they reach
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	30 human-level performance on both handwritten digit classification and
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	31 62-class handwritten character recognition. For this purpose we
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	32 developed a powerful generator of stochastic variations and noise
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	33 processes character images, including not only affine transformations but
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	34 also slant, local elastic deformations, changes in thickness, background
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	35 images, color, contrast, occlusion, and various types of pixel and
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	36 spatially correlated noise. The out-of-distribution examples are
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	37 obtained by training with these highly distorted images or
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	38 by including object classes different from those in the target test set.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	39 \end{abstract}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	40 \vspace*{-2mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	41
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	42 \section{Introduction}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	43 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	44
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	45 Deep Learning has emerged as a promising new area of research in
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	46 statistical machine learning (see~\citet{Bengio-2009} for a review).
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	47 Learning algorithms for deep architectures are centered on the learning
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	48 of useful representations of data, which are better suited to the task at hand.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	49 This is in great part inspired by observations of the mammalian visual cortex,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	50 which consists of a chain of processing elements, each of which is associated with a
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	51 different representation of the raw visual input. In fact,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	52 it was found recently that the features learnt in deep architectures resemble
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	53 those observed in the first two of these stages (in areas V1 and V2
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	54 of visual cortex)~\citep{HonglakL2008}, and that they become more and
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	55 more invariant to factors of variation (such as camera movement) in
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	56 higher layers~\cite{Goodfellow2009}.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	57 Learning a hierarchy of features increases the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	58 ease and practicality of developing representations that are at once
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	59 tailored to specific tasks, yet are able to borrow statistical strength
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	60 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	61 feature representation can lead to higher-level (more abstract, more
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	62 general) features that are more robust to unanticipated sources of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	63 variance extant in real data.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	64
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	65 Whereas a deep architecture can in principle be more powerful than a
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	66 shallow one in terms of representation, depth appears to render the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	67 training problem more difficult in terms of optimization and local minima.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	68 It is also only recently that successful algorithms were proposed to
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	69 overcome some of these difficulties. All are based on unsupervised
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	70 learning, often in an greedy layer-wise ``unsupervised pre-training''
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	71 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	72 applied here, is the Denoising
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	73 Auto-Encoder~(DEA)~\citep{VincentPLarochelleH2008-very-small}, which
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	74 performed similarly or better than previously proposed Restricted Boltzmann
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	75 Machines in terms of unsupervised extraction of a hierarchy of features
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	76 useful for classification. The principle is that each layer starting from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	77 the bottom is trained to encode their input (the output of the previous
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	78 layer) and try to reconstruct it from a corrupted version of it. After this
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	79 unsupervised initialization, the stack of denoising auto-encoders can be
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	80 converted into a deep supervised feedforward neural network and fine-tuned by
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	81 stochastic gradient descent.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	82
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	83 Self-taught learning~\citep{RainaR2007} is a paradigm that combines principles
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	84 of semi-supervised and multi-task learning: the learner can exploit examples
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	85 that are unlabeled and/or come from a distribution different from the target
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	86 distribution, e.g., from other classes that those of interest. Whereas
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	87 it has already been shown that deep learners can clearly take advantage of
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	88 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	89 and multi-task learning, not much has been done yet to explore the impact
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	90 of {\em out-of-distribution} examples and of the multi-task setting
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	91 (but see~\citep{CollobertR2008-short}). In particular the {\em relative
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	92 advantage} of deep learning for this settings has not been evaluated.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	93
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	94 In this paper we ask the following questions:
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	95
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	96 %\begin{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	97 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	98 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	99 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	100 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	101
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	102 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	103 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	104 noise, affine transformations, background images) make the resulting
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	105 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	106 the {\em original clean examples}?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	107
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	108 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	109 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	110 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	111
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	112 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	113 Similarly, does the feature learning step in deep learning algorithms benefit more
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	114 training with similar but different classes (i.e. a multi-task learning scenario) than
6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	115 a corresponding shallow and purely supervised architecture?
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	116 %\end{enumerate}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	117
466 6205481bf33f asking the questions Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 464 diff changeset	118 The experimental results presented here provide positive evidence towards all of these questions.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	119
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	120 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	121 \section{Perturbation and Transformation of Character Images}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	122 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	123
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	124 This section describes the different transformations we used to stochastically
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	125 transform source images in order to obtain data. More details can
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	126 be found in this technical report~\citep{ift6266-tr-anonymous}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	127 The code for these transformations (mostly python) is available at
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	128 {\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	129 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	130 amount of deformation or noise introduced.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	131
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	132 There are two main parts in the pipeline. The first one,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	133 from slant to pinch below, performs transformations. The second
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	134 part, from blur to contrast, adds different kinds of noise.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	135
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	136 {\large\bf Transformations}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	137
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	138 \vspace*{2mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	139
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	140 {\bf Slant.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	141 We mimic slant by shifting each row of the image
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	142 proportionnaly to its height: $shift = round(slant \times height)$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	143 The $slant$ coefficient can be negative or positive with equal probability
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	144 and its value is randomly sampled according to the complexity level:
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	145 e $slant \sim U[0,complexity]$, so the
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	146 maximum displacement for the lowest or highest pixel line is of
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	147 $round(complexity \times 32)$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	148 {\bf Thickness.}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	149 Morpholigical operators of dilation and erosion~\citep{Haralick87,Serra82}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	150 are applied. The neighborhood of each pixel is multiplied
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	151 element-wise with a {\em structuring element} matrix.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	152 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	153 matrix, respectively for dilation or erosion. Ten different structural elements with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	154 increasing dimensions (largest is $5\times5$) were used. For each image,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	155 randomly sample the operator type (dilation or erosion) with equal probability and one structural
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	156 element from a subset of the $n$ smallest structuring elements where $n$ is
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	157 $round(10 \times complexity)$ for dilation and $round(6 \times complexity)$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	158 for erosion. A neutral element is always present in the set, and if it is
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	159 chosen no transformation is applied. Erosion allows only the six
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	160 smallest structural elements because when the character is too thin it may
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	161 be completely erased.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	162 {\bf Affine Transformations.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	163 A $2 \times 3$ affine transform matrix (with
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	164 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	165 Each pixel $(x,y)$ of the output image takes the value of the pixel
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	166 nearest to $(ax+by+c,dx+ey+f)$ in the input image. This
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	167 produces scaling, translation, rotation and shearing.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	168 The marginal distributions of $(a,b,c,d,e,f)$ have been tuned by hand to
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	169 forbid important rotations (not to confuse classes) but to give good
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	170 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	171 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	172 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	173 complexity]$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	174 {\bf Local Elastic Deformations.}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	175 This filter induces a "wiggly" effect in the image, following~\citet{SimardSP03},
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	176 which provides more details.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	177 Two "displacements" fields are generated and applied, for horizontal
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	178 and vertical displacements of pixels.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	179 To generate a pixel in either field, first a value between -1 and 1 is
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	180 chosen from a uniform distribution. Then all the pixels, in both fields, are
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	181 multiplied by a constant $\alpha$ which controls the intensity of the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	182 displacements (larger $\alpha$ translates into larger wiggles).
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	183 Each field is convoluted with a Gaussian 2D kernel of
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	184 standard deviation $\sigma$. Visually, this results in a blur.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	185 $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	186 \sqrt[3]{complexity}$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	187 {\bf Pinch.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	188 This GIMP filter is named "Whirl and
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	189 pinch", but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	190 surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}.
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	191 For a square input image, think of drawing a circle of
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	192 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	193 that disk (region inside circle) will have its value recalculated by taking
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	194 the value of another "source" pixel in the original image. The position of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	195 that source pixel is found on the line thats goes through $C$ and $P$, but
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	196 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	197 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	198 d_1$, where $pinch$ is a parameter to the filter.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	199 The actual value is given by bilinear interpolation considering the pixels
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	200 around the (non-integer) source position thus found.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	201 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	202
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	203 \vspace*{1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	204
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	205 {\large\bf Injecting Noise}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	206
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	207 \vspace*{1mm}
483 b9cdb464de5f pointeur a la demo Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 482 diff changeset	208
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	209 {\bf Motion Blur.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	210 This GIMP filter is a ``linear motion blur'' in GIMP
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	211 terminology, with two parameters, $length$ and $angle$. The value of
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	212 a pixel in the final image is the approximately mean value of the $length$ first pixels
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	213 found by moving in the $angle$ direction.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	214 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	215 {\bf Occlusion.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	216 This filter selects a random rectangle from an {\em occluder} character
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	217 images and places it over the original {\em occluded} character
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	218 image. Pixels are combined by taking the max(occluder,occluded),
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	219 closer to black. The corners of the occluder The rectangle corners
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	220 are sampled so that larger complexity gives larger rectangles.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	221 The destination position in the occluded image are also sampled
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	222 according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	223 It has has a probability of not being applied at all of 60\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	224 {\bf Pixel Permutation.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	225 This filter permutes neighbouring pixels. It selects first
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	226 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	227 sequentially exchanged to one other pixel in its $V4$ neighbourhood. Number
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	228 of exchanges to the left, right, top, bottom are equal or does not differ
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	229 from more than 1 if the number of selected pixels is not a multiple of 4.
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	230 It has has a probability of not being applied at all of 80\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	231 {\bf Gaussian Noise.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	232 This filter simply adds, to each pixel of the image independently, a
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	233 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	234 It has has a probability of not being applied at all of 70\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	235 {\bf Background Images.}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	236 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	237 background behind the letter. The background is chosen by first selecting,
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	238 at random, an image from a set of images. Then a 32$\times$32 subregion
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	239 of that image is chosen as the background image (by sampling position
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	240 uniformly while making sure not to cross image borders).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	241 To combine the original letter image and the background image, contrast
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	242 adjustments are made. We first get the maximal values (i.e. maximal
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	243 intensity) for both the original image and the background image, $maximage$
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	244 and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	245 Each background pixel value is multiplied by $\frac{max(maximage -
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	246 contrast, 0)}{maxbg}$ (higher contrast yield darker
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	247 background). The output image pixels are max(background,original).\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	248 {\bf Salt and Pepper Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	249 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	250 The number of selected pixels is $0.2 \times complexity$.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	251 This filter has a probability of not being applied at all of 75\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	252 {\bf Spatially Gaussian Noise.}
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	253 Different regions of the image are spatially smoothed.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	254 The image is convolved with a symmetric Gaussian kernel of
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	255 size and variance choosen uniformly in the ranges $[12,12 + 20 \times
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	256 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	257 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	258 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	259 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	260 averaging centers between the original image and the filtered one. We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	261 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	262 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	263 computed from the following element-wise operation: $\frac{image + filtered
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	264 image \times mask}{mask+1}$.
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	265 This filter has a probability of not being applied at all of 75\%.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	266 {\bf Scratches.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	267 The scratches module places line-like white patches on the image. The
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	268 lines are heavily transformed images of the digit "1" (one), chosen
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	269 at random among five thousands such 1 images. The 1 image is
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	270 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	271 complexity)^2$, using bicubic interpolation,
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	272 Two passes of a greyscale morphological erosion filter
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	273 are applied, reducing the width of the line
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	274 by an amount controlled by $complexity$.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	275 This filter is only applied only 15\% of the time. When it is applied, 50\%
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	276 of the time, only one patch image is generated and applied. In 30\% of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	277 cases, two patches are generated, and otherwise three patches are
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	278 generated. The patch is applied by taking the maximal value on any given
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	279 patch or the original image, for each of the 32x32 pixel locations.\\
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	280 {\bf Color and Contrast Changes.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	281 This filter changes the constrast and may invert the image polarity (white
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	282 on black to black on white). The contrast $C$ is defined here as the
467 e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	283 difference between the maximum and the minimum pixel value of the image.
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	284 Contrast $\sim U[1-0.85 \times complexity,1]$ (so constrast $\geq 0.15$).
e0e57270b2af refs Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 466 diff changeset	285 The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	286 polarity is inverted with $0.5$ probability.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	287
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	288
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	289 \begin{figure}[h]
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	290 \resizebox{.99\textwidth}{!}{\includegraphics{images/example_t.png}}\\
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	291 \caption{Illustration of the pipeline of stochastic
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	292 transformations applied to the image of a lower-case t
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	293 (the upper left image). Each image in the pipeline (going from
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	294 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	295 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	296 (bottom right) is used as training example.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	297 \label{fig:pipeline}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	298 \end{figure}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	299
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	300
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	301 \begin{figure}[h]
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	302 \resizebox{.99\textwidth}{!}{\includegraphics{images/transfo.png}}\\
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	303 \caption{Illustration of each transformation applied alone to the same image
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	304 of an upper-case h (top left). First row (from left to rigth) : original image, slant,
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	305 thickness, affine transformation, local elastic deformation; second row (from left to rigth) :
482 ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	306 pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to rigth) :
ce69aa9204d8 changement au titre et reecriture abstract Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 480 diff changeset	307 background image, salt and pepper noise, spatially Gaussian noise, scratches,
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	308 color and contrast changes.}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	309 \label{fig:transfo}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	310 \end{figure}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	311
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	312
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	313 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	314 \section{Experimental Setup}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	315 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	316
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	317 Whereas much previous work on deep learning algorithms had been performed on
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	318 the MNIST digits classification task~\citep{Hinton06,ranzato-07,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	319 with 60~000 examples, and variants involving 10~000
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	320 examples~\cite{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}, we want
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	321 to focus here on the case of much larger training sets, from 10 times to
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	322 to 1000 times larger. The larger datasets are obtained by first sampling from
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	323 a {\em data source} (NIST characters, scanned machine printed characters, characters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	324 from fonts, or characters from captchas) and then optionally applying some of the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	325 above transformations and/or noise processes.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	326
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	327 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	328 \subsection{Data Sources}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	329 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	330
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	331 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	332 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	333 {\bf NIST.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	334 Our main source of characters is the NIST Special Database 19~\cite{Grother-1995},
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	335 widely used for training and testing character
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	336 recognition systems~\cite{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	337 The dataset is composed with 8????? digits and characters (upper and lower cases), with hand checked classifications,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	338 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	339 corresponding to "0"-"9","A"-"Z" and "a"-"z". The dataset contains 8 series of different complexity.
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	340 The fourth series, $hsf_4$, experimentally recognized to be the most difficult one is recommended
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	341 by NIST as testing set and is used in our work and some previous work~\cite{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002,Milgram+al-2005}
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	342 for that purpose. We randomly split the remainder into a training set and a validation set for
480 150203d2b5c3 added number of train test and valid for NIST Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 479 diff changeset	343 model selection. The sizes of these data sets are: 651668 for training, 80000 for validation,
150203d2b5c3 added number of train test and valid for NIST Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 479 diff changeset	344 and 82587 for testing.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	345 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	346 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	347 useful to estimate the effect of a multi-task setting.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	348 Note that the distribution of the classes in the NIST training and test sets differs
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	349 substantially, with relatively many more digits in the test set, and uniform distribution
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	350 of letters in the test set, not in the training set (more like the natural distribution
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	351 of letters in text).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	352
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	353 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	354 {\bf Fonts.}
479 6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	355 In order to have a good variety of sources we downloaded an important number of free fonts from: {\tt http://anonymous.url.net}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	356 %real adress {\tt http://cg.scs.carleton.ca/~luc/freefonts.html}
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	357 in addition to Windows 7's, this adds up to a total of $9817$ different fonts that we can choose uniformly.
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	358 The ttf file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	359 directly as input to our models.
6593e67381a3 Added transformation figure Xavier Glorot <glorotxa@iro.umontreal.ca> parents: 476 diff changeset	360
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	361 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	362 {\bf Captchas.}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	363 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	364 generating characters of the same format as the NIST dataset. This software is based on
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	365 a random character class generator and various kinds of tranformations similar to those described in the previous sections.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	366 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	367 Transformations (slant, distorsions, rotation, translation) are applied to each randomly generated character with a complexity
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	368 depending on the value of the complexity parameter provided by the user of the data source. Two levels of complexity are
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	369 allowed and can be controlled via an easy to use facade class.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	370
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	371 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	372 {\bf OCR data.}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	373 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	374 characters (from various documents and books) where included as an
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	375 additional source. This set is part of a larger corpus being collected by the Image Understanding
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	376 Pattern Recognition Research group lead by Thomas Breuel at University of Kaiserslautern
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	377 ({\tt http://www.iupr.com}), and which will be publically released.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	378 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	379
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	380 \vspace*{-1mm}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	381 \subsection{Data Sets}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	382 \vspace*{-1mm}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	383
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	384 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	385 from one of the 62 character classes.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	386 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	387
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	388 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	389 {\bf NIST.} This is the raw NIST special database 19.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	390
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	391 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	392 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	393 and sending them through the above transformation pipeline.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	394 For each new exemple to generate, a source is selected with probability $10\%$ from the fonts,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	395 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	396 order given above, and for each of them we sample uniformly a complexity in the range $[0,0.7]$.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	397
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	398 %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	399 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same sources proportion)
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	400 except that we only apply
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	401 transformations from slant to pinch. Therefore, the character is
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	402 transformed but no additionnal noise is added to the image, giving images
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	403 closer to the NIST dataset.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	404 %\end{itemize}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	405
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	406 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	407 \subsection{Models and their Hyperparameters}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	408 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	409
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	410 All hyper-parameters are selected based on performance on the NISTP validation set.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	411
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	412 {\bf Multi-Layer Perceptrons (MLP).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	413 Whereas previous work had compared deep architectures to both shallow MLPs and
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	414 SVMs, we only compared to MLPs here because of the very large datasets used.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	415 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	416 exponentials) on the output layer for estimating P(class \| image).
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	417 The hyper-parameters are the following: number of hidden units, taken in
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	418 $\{300,500,800,1000,1500\}$. The optimization procedure is as follows. Training
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	419 examples are presented in minibatches of size 20. A constant learning
474 bcf024e6ab23 fits now, but still now graphics Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 472 diff changeset	420 rate is chosen in $10^{-3},0.01, 0.025, 0.075, 0.1, 0.5\}$
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	421 through preliminary experiments, and 0.1 was selected.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	422
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	423 {\bf Stacked Denoising Auto-Encoders (SDAE).}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	424 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	425 can be used to initialize the weights of each layer of a deep MLP (with many hidden
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	426 layers)~\citep{Hinton06,ranzato-07,Bengio-nips-2006}
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	427 enabling better generalization, apparently setting parameters in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	428 basin of attraction of supervised gradient descent yielding better
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	429 generalization~\citep{Erhan+al-2010}. It is hypothesized that the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	430 advantage brought by this procedure stems from a better prior,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	431 on the one hand taking advantage of the link between the input
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	432 distribution $P(x)$ and the conditional distribution of interest
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	433 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	434 taking advantage of the expressive power and bias implicit in the
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	435 deep architecture (whereby complex concepts are expressed as
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	436 compositions of simpler ones through a deep hierarchy).
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	437 Here we chose to use the Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	438 Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	439 these deep hierarchies of features, as it is very simple to train and
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	440 teach (see tutorial and code there: {\tt http://deeplearning.net/tutorial}),
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	441 provides immediate and efficient inference, and yielded results
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	442 comparable or better than RBMs in series of experiments
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	443 \citep{VincentPLarochelleH2008}. During training of a Denoising
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	444 Auto-Encoder, it is presented with a stochastically corrupted version
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	445 of the input and trained to reconstruct the uncorrupted input,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	446 forcing the hidden units to represent the leading regularities in
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	447 the data. Once it is trained, its hidden units activations can
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	448 be used as inputs for training a second one, etc.
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	449 After this unsupervised pre-training stage, the parameters
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	450 are used to initialize a deep MLP, which is fine-tuned by
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	451 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	452 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	453 amount of corruption noise (we used the masking noise process, whereby a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	454 fixed proportion of the input values, randomly selected, are zeroed), and a
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	455 separate learning rate for the unsupervised pre-training stage (selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	456 from the same above set). The fraction of inputs corrupted was selected
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	457 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	458 of hidden layers but it was fixed to 3 based on previous work with
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	459 stacked denoising auto-encoders on MNIST~\citep{VincentPLarochelleH2008}.
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	460
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	461 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	462 \section{Experimental Results}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	463
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	464 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	465 \subsection{SDA vs MLP vs Humans}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	466 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	467
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	468 We compare here the best MLP (according to validation set error) that we found against
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	469 the best SDA (again according to validation set error), along with a precise estimate
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	470 of human performance obtained via Amazon's Mechanical Turk (AMT)
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	471 service\footnote{http://mturk.com}. AMT users are paid small amounts
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	472 of money to perform tasks for which human intelligence is required.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	473 Mechanical Turk has been used extensively in natural language
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	474 processing \citep{SnowEtAl2008} and vision
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	475 \citep{SorokinAndForsyth2008,whitehill09}. AMT users where presented
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	476 with 10 character images and asked to type 10 corresponding ascii
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	477 characters. They were forced to make a hard choice among the
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	478 62 or 10 character classes (all classes or digits only).
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	479 Three users classified each image, allowing
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	480 to estimate inter-human variability (shown as +/- in parenthesis below).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	481
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	482 Figure~\ref{fig:error-rates-charts} summarizes the results obtained.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	483 More detailed results and tables can be found in the appendix.
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	484
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	485 \begin{table}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	486 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	487 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	488 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	489 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	490 and using a validation set to select hyper-parameters and other training choices.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	491 \{SDA,MLP\}0 are trained on NIST,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	492 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	493 The human error rate on digits is a lower bound because it does not count digits that were
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	494 recognized as letters. For comparison, the results found in the literature
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	495 on NIST digits classification using the same test set are included.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	496 \label{tab:sda-vs-mlp-vs-humans}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	497 \begin{center}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	498 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	499 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	500 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	501 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	502 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	503 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	504 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	505 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	506 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	507 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	508 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	509 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	510 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	511 \end{tabular}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	512 \end{center}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	513 \end{table}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	514
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	515 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	516 \resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}\\
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	517 \caption{Charts corresponding to table \ref{tab:sda-vs-mlp-vs-humans}. Left: overall results; error bars indicate a 95\% confidence interval. Right: error rates on NIST test digits only, with results from litterature. }
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	518 \label{fig:error-rates-charts}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	519 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	520
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	521 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	522 \subsection{Perturbed Training Data More Helpful for SDAE}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	523 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	524
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	525 \begin{table}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	526 \caption{Relative change in error rates due to the use of perturbed training data,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	527 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	528 A positive value indicates that training on the perturbed data helped for the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	529 given test set (the first 3 columns on the 62-class tasks and the last one is
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	530 on the clean 10-class digits). Clearly, the deep learning models did benefit more
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	531 from perturbed training data, even when testing on clean data, whereas the MLP
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	532 trained on perturbed data performed worse on the clean digits and about the same
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	533 on the clean characters. }
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	534 \label{tab:perturbation-effect}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	535 \begin{center}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	536 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	537 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	538 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	539 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	540 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	541 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	542 \end{tabular}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	543 \end{center}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	544 \end{table}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	545
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	546 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	547 \subsection{Multi-Task Learning Effects}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	548 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	549
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	550 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	551 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	552 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	553 recognizing upper case characters (knowing that the input is one), and
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	554 recognizing lower case characters (knowing that the input is one). We
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	555 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	556 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	557 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	558 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	559 (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	560 shallow learner.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	561
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	562 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	563 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	564 fine-tuned on NIST.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	565
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	566 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	567 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	568 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	569 On the other hand the SDA benefitted from the multi-task setting, with relative
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	570 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	571 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	572
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	573 \begin{table}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	574 \caption{Test error rates and relative change in error rates due to the use of
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	575 a multi-task setting, i.e., training on each task in isolation vs training
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	576 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	577 more from the multi-task setting. All experiments on only on the
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	578 unperturbed NIST data, using validation error for model selection.
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	579 Relative improvement is 1 - single-task error / multi-task error.}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	580 \label{tab:multi-task}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	581 \begin{center}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	582 \begin{tabular}{\|l\|r\|r\|r\|} \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	583 & single-task & multi-task & relative \\
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	584 & setting & setting & improvement \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	585 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	586 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	587 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	588 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	589 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	590 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	591 \end{tabular}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	592 \end{center}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	593 \end{table}
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	594
475 ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	595
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	596 \begin{figure}[h]
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	597 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	598 \caption{Charts corresponding to tables \ref{tab:perturbation-effect} (left) and \ref{tab:multi-task} (right).}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	599 \label{fig:improvements-charts}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	600 \end{figure}
ead3085c1c66 Added charts to nips2010_submission.tex fsavard parents: 469 diff changeset	601
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	602 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	603 \section{Conclusions}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	604 \vspace*{-1mm}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	605
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	606 The conclusions are positive for all the questions asked in the introduction.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	607 %\begin{itemize}
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	608 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	609 Do the good results previously obtained with deep architectures on the
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	610 MNIST digits generalize to the setting of a much larger and richer (but similar)
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	611 dataset, the NIST special database 19, with 62 classes and around 800k examples?
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	612 Yes, the SDA systematically outperformed the MLP, in fact reaching human-level
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	613 performance.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	614
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	615 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	616 To what extent does the perturbation of input images (e.g. adding
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	617 noise, affine transformations, background images) make the resulting
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	618 classifier better not only on similarly perturbed images but also on
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	619 the {\em original clean examples}? Do deep architectures benefit more from such {\em out-of-distribution}
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	620 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	621 MLPs were helped by perturbed training examples when tested on perturbed input images,
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	622 but only marginally helped wrt clean examples. On the other hand, the deep SDAs
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	623 were very significantly boosted by these out-of-distribution examples.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	624
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	625 $\bullet$ %\item
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	626 Similarly, does the feature learning step in deep learning algorithms benefit more
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	627 training with similar but different classes (i.e. a multi-task learning scenario) than
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	628 a corresponding shallow and purely supervised architecture?
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	629 Whereas the improvement due to the multi-task setting was marginal or
2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	630 negative for the MLP, it was very significant for the SDA.
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	631 %\end{itemize}
472 2dd6e8962df1 conclusion Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 469 diff changeset	632
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	633 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	634 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	635
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	636
9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	637 {\small
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	638 \bibliography{strings,ml,aigaion,specials}
469 d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	639 %\bibliographystyle{plainnat}
d02d288257bf redone bib style Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 467 diff changeset	640 \bibliographystyle{unsrtnat}
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	641 %\bibliographystyle{apalike}
484 9a757d565e46 reduction de taille Yoshua Bengio <bengioy@iro.umontreal.ca> parents: 483 diff changeset	642 }
464 24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	643
24f4a8b53fcc nips2010_submission.tex Yoshua Bengio <bengioy@iro.umontreal.ca> parents: diff changeset	644 \end{document}

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