ift6266: writeup/mlj_submission/mlj_submission.tex annotate

annotate writeup/mlj_submission/mlj_submission.tex @ 634:54e8958e963b

bib

author	Yoshua Bengio <bengioy@iro.umontreal.ca>
date	Sat, 19 Mar 2011 22:57:48 -0400
parents	8bd4ff0c5c05
children

rev	line source
587 b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1 \RequirePackage{fix-cm} % from template
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b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	3 %\documentclass{article} % For LaTeX2e
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	4 \documentclass[smallcondensed]{svjour3} % onecolumn (ditto)
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b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	6 \usepackage{times}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	7 \usepackage{wrapfig}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	8 %\usepackage{amsthm} % not to be used with springer tools
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b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	15 \usepackage{natbib} % was [numbers]{natbib}
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b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	23 \title{Deep Self-Taught Learning for Handwritten Character Recognition}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	24 \author{
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	25 Yoshua Bengio \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	26 Frédéric Bastien \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	27 Arnaud Bergeron \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	28 Nicolas Boulanger-Lewandowski \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	29 Thomas Breuel \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	30 Youssouf Chherawala \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	31 Moustapha Cisse \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	32 Myriam Côté \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	33 Dumitru Erhan \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	34 Jeremy Eustache \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	35 Xavier Glorot \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	36 Xavier Muller \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	37 Sylvain Pannetier Lebeuf \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	38 Razvan Pascanu \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	39 Salah Rifai \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	40 Francois Savard \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	41 Guillaume Sicard
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	42 }
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	43 \date{September 30th, submission to MLJ special issue on learning from multi-label data}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	44 \journalname{Machine Learning Journal}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	45 \institute{Frédéric Bastien \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	46 Yoshua Bengio \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	47 Arnaud Bergeron \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	48 Nicolas Boulanger-Lewandowski \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	49 Youssouf Chherawala \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	50 Moustapha Cisse \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	51 Myriam Côté \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	52 Dumitru Erhan \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	53 Jeremy Eustache \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	54 Xavier Glorot \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	55 Xavier Muller \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	56 Sylvain Pannetier-Lebeuf \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	57 Razvan Pascanu \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	58 Salah Rifai \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	59 Francois Savard \and \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	60 Guillaume Sicard \at
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	61 Dept. IRO, Universite de Montreal, C.P. 6128, Montreal, QC, H3C 3J7, Canada\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	62 \email{yoshua.bengio@umontreal.ca}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	63 \and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	64 Thomas Breuel \at
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	65 Department of Computer Science, University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	66 }
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b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	69 \begin{document}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	70
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	71 %\makeanontitle
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	72 \maketitle
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	73
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	74 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	75 \begin{abstract}
591 8bd4ff0c5c05 Correction de merge fsavard parents: 587 diff changeset	76 Recent theoretical and empirical work in statistical machine learning has demonstrated the potential of learning algorithms for deep architectures, i.e., function classes obtained by composing multiple levels of representation. Self-taught learning (exploiting unlabeled examples or examples from other distributions) has already been applied to deep learners, but mostly to show the advantage of unlabeled examples. Here we explore the advantage brought by {\em out-of-distribution examples}. For this purpose we developed a powerful generator of stochastic variations and noise processes for character images, including not only affine transformations but also slant, local elastic deformations, changes in thickness, background images, grey level changes, contrast, occlusion, and various types of noise. The out-of-distribution examples are obtained from these highly distorted images or by including examples of object classes different from those in the target test set. We show that {\em deep learners benefit more from out-of-distribution examples than a corresponding shallow learner}, at least in the area of handwritten character recognition. In fact, we show that they beat previously published results and reach human-level performance on both handwritten digit classification and 62-class handwritten character recognition.
587 b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	77 \end{abstract}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	78 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	79
591 8bd4ff0c5c05 Correction de merge fsavard parents: 587 diff changeset	80 \keywords{self-taught learning \and multi-task learning \and out-of-distribution examples \and deep learning \and handwriting recognition}
587 b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	81
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	82 \section{Introduction}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	83 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	84
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	85 {\bf Deep Learning} has emerged as a promising new area of research in
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	86 statistical machine learning (see \citet{Bengio-2009} for a review).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	87 Learning algorithms for deep architectures are centered on the learning
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	88 of useful representations of data, which are better suited to the task at hand,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	89 and are organized in a hierarchy with multiple levels.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	90 This is in part inspired by observations of the mammalian visual cortex,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	91 which consists of a chain of processing elements, each of which is associated with a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	92 different representation of the raw visual input. In fact,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	93 it was found recently that the features learnt in deep architectures resemble
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	94 those observed in the first two of these stages (in areas V1 and V2
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	95 of visual cortex) \citep{HonglakL2008}, and that they become more and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	96 more invariant to factors of variation (such as camera movement) in
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	97 higher layers~\citep{Goodfellow2009}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	98 Learning a hierarchy of features increases the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	99 ease and practicality of developing representations that are at once
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	100 tailored to specific tasks, yet are able to borrow statistical strength
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	101 from other related tasks (e.g., modeling different kinds of objects). Finally, learning the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	102 feature representation can lead to higher-level (more abstract, more
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	103 general) features that are more robust to unanticipated sources of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	104 variance extant in real data.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	105
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	106 {\bf Self-taught learning}~\citep{RainaR2007} is a paradigm that combines principles
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	107 of semi-supervised and multi-task learning: the learner can exploit examples
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	108 that are unlabeled and possibly come from a distribution different from the target
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	109 distribution, e.g., from other classes than those of interest.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	110 It has already been shown that deep learners can clearly take advantage of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	111 unsupervised learning and unlabeled examples~\citep{Bengio-2009,WestonJ2008-small},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	112 but more needs to be done to explore the impact
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	113 of {\em out-of-distribution} examples and of the {\em multi-task} setting
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	114 (one exception is~\citep{CollobertR2008}, which uses a different kind
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	115 of learning algorithm). In particular the {\em relative
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	116 advantage of deep learning} for these settings has not been evaluated.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	117 The hypothesis discussed in the conclusion is that in the context of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	118 multi-task learning and the availability of out-of-distribution training examples,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	119 a deep hierarchy of features
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	120 may be better able to provide sharing of statistical strength
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	121 between different regions in input space or different tasks, compared to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	122 a shallow learner.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	123
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	124 Whereas a deep architecture can in principle be more powerful than a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	125 shallow one in terms of representation, depth appears to render the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	126 training problem more difficult in terms of optimization and local minima.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	127 It is also only recently that successful algorithms were proposed to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	128 overcome some of these difficulties. All are based on unsupervised
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	129 learning, often in an greedy layer-wise ``unsupervised pre-training''
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	130 stage~\citep{Bengio-2009}. One of these layer initialization techniques,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	131 applied here, is the Denoising
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	132 Auto-encoder~(DA)~\citep{VincentPLarochelleH2008-very-small} (see Figure~\ref{fig:da}),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	133 which
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	134 performed similarly or better than previously proposed Restricted Boltzmann
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	135 Machines in terms of unsupervised extraction of a hierarchy of features
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	136 useful for classification. Each layer is trained to denoise its
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	137 input, creating a layer of features that can be used as input for the next layer.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	138
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	139 %The principle is that each layer starting from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	140 %the bottom is trained to encode its input (the output of the previous
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	141 %layer) and to reconstruct it from a corrupted version. After this
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	142 %unsupervised initialization, the stack of DAs can be
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	143 %converted into a deep supervised feedforward neural network and fine-tuned by
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	144 %stochastic gradient descent.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	145
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	146 %
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	147 In this paper we ask the following questions:
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	148
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	149 %\begin{enumerate}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	150 $\bullet$ %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	151 Do the good results previously obtained with deep architectures on the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	152 MNIST digit images generalize to the setting of a much larger and richer (but similar)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	153 dataset, the NIST special database 19, with 62 classes and around 800k examples?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	154
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	155 $\bullet$ %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	156 To what extent does the perturbation of input images (e.g. adding
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	157 noise, affine transformations, background images) make the resulting
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	158 classifiers better not only on similarly perturbed images but also on
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	159 the {\em original clean examples}? We study this question in the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	160 context of the 62-class and 10-class tasks of the NIST special database 19.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	161
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	162 $\bullet$ %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	163 Do deep architectures {\em benefit {\bf more} from such out-of-distribution}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	164 examples, i.e. do they benefit more from the self-taught learning~\citep{RainaR2007} framework?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	165 We use highly perturbed examples to generate out-of-distribution examples.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	166
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	167 $\bullet$ %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	168 Similarly, does the feature learning step in deep learning algorithms benefit {\bf more}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	169 from training with moderately {\em different classes} (i.e. a multi-task learning scenario) than
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	170 a corresponding shallow and purely supervised architecture?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	171 We train on 62 classes and test on 10 (digits) or 26 (upper case or lower case)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	172 to answer this question.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	173 %\end{enumerate}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	174
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	175 Our experimental results provide positive evidence towards all of these questions,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	176 as well as classifiers that reach human-level performance on 62-class isolated character
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	177 recognition and beat previously published results on the NIST dataset (special database 19).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	178 To achieve these results, we introduce in the next section a sophisticated system
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	179 for stochastically transforming character images and then explain the methodology,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	180 which is based on training with or without these transformed images and testing on
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	181 clean ones. We measure the relative advantage of out-of-distribution examples
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	182 (perturbed or out-of-class)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	183 for a deep learner vs a supervised shallow one.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	184 Code for generating these transformations as well as for the deep learning
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	185 algorithms are made available at {\tt http://hg.assembla.com/ift6266}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	186 We estimate the relative advantage for deep learners of training with
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	187 other classes than those of interest, by comparing learners trained with
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	188 62 classes with learners trained with only a subset (on which they
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	189 are then tested).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	190 The conclusion discusses
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	191 the more general question of why deep learners may benefit so much from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	192 the self-taught learning framework. Since out-of-distribution data
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	193 (perturbed or from other related classes) is very common, this conclusion
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	194 is of practical importance.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	195
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	196 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	197 %\newpage
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	198 \section{Perturbed and Transformed Character Images}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	199 \label{s:perturbations}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	200 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	201
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	202 \begin{wrapfigure}[8]{l}{0.15\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	203 %\begin{minipage}[b]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	204 %\vspace*{-5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	205 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	206 \includegraphics[scale=.4]{Original.png}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	207 {\bf Original}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	208 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	209 \end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	210 %%\vspace{0.7cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	211 %\end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	212 %\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	213 This section describes the different transformations we used to stochastically
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	214 transform $32 \times 32$ source images (such as the one on the left)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	215 in order to obtain data from a larger distribution which
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	216 covers a domain substantially larger than the clean characters distribution from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	217 which we start.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	218 Although character transformations have been used before to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	219 improve character recognizers, this effort is on a large scale both
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	220 in number of classes and in the complexity of the transformations, hence
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	221 in the complexity of the learning task.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	222 The code for these transformations (mostly python) is available at
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	223 {\tt http://hg.assembla.com/ift6266}. All the modules in the pipeline share
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	224 a global control parameter ($0 \le complexity \le 1$) that allows one to modulate the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	225 amount of deformation or noise introduced.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	226 There are two main parts in the pipeline. The first one,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	227 from slant to pinch below, performs transformations. The second
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	228 part, from blur to contrast, adds different kinds of noise.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	229 %\end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	230
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	231 %\vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	232 \subsection{Transformations}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	233 %{\large\bf 2.1 Transformations}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	234 %\vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	235
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	236 \subsubsection*{Thickness}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	237
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	238 %\begin{wrapfigure}[7]{l}{0.15\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	239 \begin{minipage}[b]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	240 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	241 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	242 \vspace*{-5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	243 \includegraphics[scale=.4]{Thick_only.png}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	244 %{\bf Thickness}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	245 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	246 \vspace{.6cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	247 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	248 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	249 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	250 To change character {\bf thickness}, morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	251 are applied. The neighborhood of each pixel is multiplied
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	252 element-wise with a {\em structuring element} matrix.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	253 The pixel value is replaced by the maximum or the minimum of the resulting
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	254 matrix, respectively for dilation or erosion. Ten different structural elements with
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	255 increasing dimensions (largest is $5\times5$) were used. For each image,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	256 randomly sample the operator type (dilation or erosion) with equal probability and one structural
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	257 element from a subset of the $n=round(m \times complexity)$ smallest structuring elements
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	258 where $m=10$ for dilation and $m=6$ for erosion (to avoid completely erasing thin characters).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	259 A neutral element (no transformation)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	260 is always present in the set.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	261 %%\vspace{.4cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	262 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	263
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	264 \vspace{2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	265
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	266 \subsubsection*{Slant}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	267 \vspace*{2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	268
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	269 \begin{minipage}[b]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	270 \centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	271 \includegraphics[scale=.4]{Slant_only.png}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	272 %{\bf Slant}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	273 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	274 \hspace{0.3cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	275 \begin{minipage}[b]{0.83\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	276 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	277 To produce {\bf slant}, each row of the image is shifted
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	278 proportionally to its height: $shift = round(slant \times height)$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	279 $slant \sim U[-complexity,complexity]$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	280 The shift is randomly chosen to be either to the left or to the right.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	281 \vspace{5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	282 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	283 %\vspace*{-4mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	284
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	285 %\newpage
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	286
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	287 \subsubsection*{Affine Transformations}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	288
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	289 \begin{minipage}[b]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	290 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	291 %\begin{wrapfigure}[8]{l}{0.15\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	292 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	293 \includegraphics[scale=.4]{Affine_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	294 \vspace*{6mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	295 %{\small {\bf Affine \mbox{Transformation}}}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	296 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	297 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	298 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	299 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	300 \noindent A $2 \times 3$ {\bf affine transform} matrix (with
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	301 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	302 Output pixel $(x,y)$ takes the value of input pixel
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	303 nearest to $(ax+by+c,dx+ey+f)$,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	304 producing scaling, translation, rotation and shearing.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	305 Marginal distributions of $(a,b,c,d,e,f)$ have been tuned to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	306 forbid large rotations (to avoid confusing classes) but to give good
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	307 variability of the transformation: $a$ and $d$ $\sim U[1-3
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	308 complexity,1+3\,complexity]$, $b$ and $e$ $\sim U[-3 \,complexity,3\,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	309 complexity]$, and $c$ and $f \sim U[-4 \,complexity, 4 \,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	310 complexity]$.\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	311 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	312
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	313 %\vspace*{-4.5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	314 \subsubsection*{Local Elastic Deformations}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	315
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	316 %\begin{minipage}[t]{\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	317 %\begin{wrapfigure}[7]{l}{0.15\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	318 %\hspace*{-8mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	319 \begin{minipage}[b]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	320 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	321 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	322 \vspace*{5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	323 \includegraphics[scale=.4]{Localelasticdistorsions_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	324 %{\bf Local Elastic Deformation}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	325 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	326 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	327 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	328 \hspace{3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	329 \begin{minipage}[b]{0.85\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	330 %%\vspace*{-20mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	331 The {\bf local elastic deformation}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	332 module induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	333 which provides more details.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	334 The intensity of the displacement fields is given by
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	335 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	336 convolved with a Gaussian 2D kernel (resulting in a blur) of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	337 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	338 \vspace{2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	339 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	340
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	341 \vspace*{4mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	342
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	343 \subsubsection*{Pinch}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	344
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	345 \begin{minipage}[b]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	346 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	347 %\begin{wrapfigure}[7]{l}{0.15\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	348 %\vspace*{-5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	349 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	350 \includegraphics[scale=.4]{Pinch_only.png}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	351 \vspace*{15mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	352 %{\bf Pinch}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	353 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	354 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	355 %%\vspace{.6cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	356 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	357 \hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	358 The {\bf pinch} module applies the ``Whirl and pinch'' GIMP filter with whirl set to 0.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	359 A pinch is ``similar to projecting the image onto an elastic
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	360 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	361 For a square input image, draw a radius-$r$ disk
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	362 around its center $C$. Any pixel $P$ belonging to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	363 that disk has its value replaced by
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	364 the value of a ``source'' pixel in the original image,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	365 on the line that goes through $C$ and $P$, but
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	366 at some other distance $d_2$. Define $d_1=distance(P,C)$
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	367 and $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	368 d_1$, where $pinch$ is a parameter of the filter.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	369 The actual value is given by bilinear interpolation considering the pixels
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	370 around the (non-integer) source position thus found.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	371 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	372 %%\vspace{1.5cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	373 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	374
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	375 %\vspace{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	376
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	377 %{\large\bf 2.2 Injecting Noise}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	378 \subsection{Injecting Noise}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	379 %\vspace{2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	380
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	381 \subsubsection*{Motion Blur}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	382
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	383 %%\vspace*{-.2cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	384 \begin{minipage}[t]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	385 \centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	386 \vspace*{0mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	387 \includegraphics[scale=.4]{Motionblur_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	388 %{\bf Motion Blur}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	389 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	390 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	391 %%\vspace*{.5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	392 \vspace*{2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	393 The {\bf motion blur} module is GIMP's ``linear motion blur'', which
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	394 has parameters $length$ and $angle$. The value of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	395 a pixel in the final image is approximately the mean of the first $length$ pixels
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	396 found by moving in the $angle$ direction,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	397 $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	398 %\vspace{5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	399 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	400
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	401 %\vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	402
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	403 \subsubsection*{Occlusion}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	404
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	405 \begin{minipage}[t]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	406 \centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	407 \vspace*{3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	408 \includegraphics[scale=.4]{occlusion_only.png}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	409 %{\bf Occlusion}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	410 %%\vspace{.5cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	411 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	412 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	413 %\vspace*{-18mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	414 The {\bf occlusion} module selects a random rectangle from an {\em occluder} character
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	415 image and places it over the original {\em occluded}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	416 image. Pixels are combined by taking the max(occluder, occluded),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	417 i.e. keeping the lighter ones.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	418 The rectangle corners
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	419 are sampled so that larger complexity gives larger rectangles.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	420 The destination position in the occluded image are also sampled
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	421 according to a normal distribution.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	422 This module is skipped with probability 60\%.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	423 %%\vspace{7mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	424 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	425
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	426 %\vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	427 \subsubsection*{Gaussian Smoothing}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	428
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	429 %\begin{wrapfigure}[8]{l}{0.15\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	430 %\vspace*{-6mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	431 \begin{minipage}[t]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	432 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	433 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	434 \vspace*{6mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	435 \includegraphics[scale=.4]{Bruitgauss_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	436 %{\bf Gaussian Smoothing}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	437 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	438 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	439 %%\vspace{.5cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	440 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	441 \hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	442 With the {\bf Gaussian smoothing} module,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	443 different regions of the image are spatially smoothed.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	444 This is achieved by first convolving
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	445 the image with an isotropic Gaussian kernel of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	446 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	447 complexity]$ and $[2,2 + 6 \times complexity]$. This filtered image is normalized
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	448 between $0$ and $1$. We also create an isotropic weighted averaging window, of the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	449 kernel size, with maximum value at the center. For each image we sample
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	450 uniformly from $3$ to $3 + 10 \times complexity$ pixels that will be
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	451 averaging centers between the original image and the filtered one. We
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	452 initialize to zero a mask matrix of the image size. For each selected pixel
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	453 we add to the mask the averaging window centered on it. The final image is
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	454 computed from the following element-wise operation: $\frac{image + filtered\_image
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	455 \times mask}{mask+1}$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	456 This module is skipped with probability 75\%.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	457 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	458
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	459 %\newpage
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	460
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	461 %\vspace*{-9mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	462 \subsubsection*{Permute Pixels}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	463
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	464 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	465 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	466 \begin{minipage}[t]{0.14\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	467 %\begin{wrapfigure}[7]{l}{
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	468 %\vspace*{-5mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	469 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	470 \vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	471 \includegraphics[scale=.4]{Permutpixel_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	472 %{\small\bf Permute Pixels}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	473 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	474 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	475 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	476 \hspace{3mm}\begin{minipage}[t]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	477 \vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	478 %%\vspace*{-20mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	479 This module {\bf permutes neighbouring pixels}. It first selects a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	480 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	481 of these pixels is then sequentially exchanged with a random pixel
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	482 among its four nearest neighbors (on its left, right, top or bottom).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	483 This module is skipped with probability 80\%.\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	484 %\vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	485 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	486
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	487 %\vspace{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	488
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	489 \subsubsection*{Gaussian Noise}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	490
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	491 \begin{minipage}[t]{0.14\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	492 %\begin{wrapfigure}[7]{l}{
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	493 %%\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	494 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	495 %\hspace*{-3mm}\begin{minipage}[t]{0.18\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	496 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	497 \vspace*{0mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	498 \includegraphics[scale=.4]{Distorsiongauss_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	499 %{\small \bf Gauss. Noise}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	500 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	501 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	502 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	503 \hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	504 \vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	505 %\vspace*{12mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	506 The {\bf Gaussian noise} module simply adds, to each pixel of the image independently, a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	507 noise $\sim Normal(0,(\frac{complexity}{10})^2)$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	508 This module is skipped with probability 70\%.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	509 %%\vspace{1.1cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	510 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	511
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	512 %\vspace*{1.2cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	513
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	514 \subsubsection*{Background Image Addition}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	515
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	516 \begin{minipage}[t]{\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	517 \begin{minipage}[t]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	518 \centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	519 \vspace*{0mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	520 \includegraphics[scale=.4]{background_other_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	521 %{\small \bf Bg Image}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	522 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	523 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	524 \vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	525 Following~\citet{Larochelle-jmlr-2009}, the {\bf background image} module adds a random
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	526 background image behind the letter, from a randomly chosen natural image,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	527 with contrast adjustments depending on $complexity$, to preserve
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	528 more or less of the original character image.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	529 %%\vspace{.8cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	530 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	531 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	532 %%\vspace{-.7cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	533
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	534 \subsubsection*{Salt and Pepper Noise}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	535
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	536 \begin{minipage}[t]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	537 \centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	538 \vspace*{0mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	539 \includegraphics[scale=.4]{Poivresel_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	540 %{\small \bf Salt \& Pepper}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	541 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	542 \hspace{0.3cm}\begin{minipage}[t]{0.83\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	543 \vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	544 The {\bf salt and pepper noise} module adds noise $\sim U[0,1]$ to random subsets of pixels.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	545 The number of selected pixels is $0.2 \times complexity$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	546 This module is skipped with probability 75\%.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	547 %%\vspace{.9cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	548 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	549 %%\vspace{-.7cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	550
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	551 %\vspace{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	552 \subsubsection*{Scratches}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	553
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	554 \begin{minipage}[t]{0.14\textwidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	555 %\begin{wrapfigure}[7]{l}{
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	556 %\begin{minipage}[t]{0.14\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	557 %\centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	558 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	559 \vspace*{4mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	560 %\hspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	561 \includegraphics[scale=.4]{Rature_only.png}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	562 %{\bf Scratches}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	563 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	564 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	565 %\end{wrapfigure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	566 \hspace{0.3cm}\begin{minipage}[t]{0.86\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	567 %%\vspace{.4cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	568 The {\bf scratches} module places line-like white patches on the image. The
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	569 lines are heavily transformed images of the digit ``1'' (one), chosen
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	570 at random among 500 such 1 images,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	571 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	572 complexity)^2$ (in degrees), using bi-cubic interpolation.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	573 Two passes of a grey-scale morphological erosion filter
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	574 are applied, reducing the width of the line
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	575 by an amount controlled by $complexity$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	576 This module is skipped with probability 85\%. The probabilities
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	577 of applying 1, 2, or 3 patches are (50\%,30\%,20\%).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	578 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	579
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	580 %\vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	581
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	582 \subsubsection*{Grey Level and Contrast Changes}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	583
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	584 \begin{minipage}[t]{0.15\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	585 \centering
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	586 \vspace*{0mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	587 \includegraphics[scale=.4]{Contrast_only.png}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	588 %{\bf Grey Level \& Contrast}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	589 \end{minipage}%
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	590 \hspace{3mm}\begin{minipage}[t]{0.85\linewidth}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	591 \vspace*{1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	592 The {\bf grey level and contrast} module changes the contrast by changing grey levels, and may invert the image polarity (white
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	593 to black and black to white). The contrast is $C \sim U[1-0.85 \times complexity,1]$
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	594 so the image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	595 polarity is inverted with probability 50\%.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	596 %%\vspace{.7cm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	597 \end{minipage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	598 %\vspace{2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	599
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	600
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	601 \iffalse
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	602 \begin{figure}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	603 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{example_t.png}}}\\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	604 \caption{Illustration of the pipeline of stochastic
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	605 transformations applied to the image of a lower-case \emph{t}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	606 (the upper left image). Each image in the pipeline (going from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	607 left to right, first top line, then bottom line) shows the result
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	608 of applying one of the modules in the pipeline. The last image
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	609 (bottom right) is used as training example.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	610 \label{fig:pipeline}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	611 \end{figure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	612 \fi
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	613
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	614 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	615 \section{Experimental Setup}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	616 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	617
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	618 Much previous work on deep learning had been performed on
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	619 the MNIST digits task~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006,Salakhutdinov+Hinton-2009},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	620 with 60~000 examples, and variants involving 10~000
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	621 examples~\citep{Larochelle-jmlr-toappear-2008,VincentPLarochelleH2008}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	622 The focus here is on much larger training sets, from 10 times to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	623 to 1000 times larger, and 62 classes.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	624
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	625 The first step in constructing the larger datasets (called NISTP and P07) is to sample from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	626 a {\em data source}: {\bf NIST} (NIST database 19), {\bf Fonts}, {\bf Captchas},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	627 and {\bf OCR data} (scanned machine printed characters). Once a character
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	628 is sampled from one of these sources (chosen randomly), the second step is to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	629 apply a pipeline of transformations and/or noise processes described in section \ref{s:perturbations}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	630
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	631 To provide a baseline of error rate comparison we also estimate human performance
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	632 on both the 62-class task and the 10-class digits task.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	633 We compare the best Multi-Layer Perceptrons (MLP) against
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	634 the best Stacked Denoising Auto-encoders (SDA), when
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	635 both models' hyper-parameters are selected to minimize the validation set error.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	636 We also provide a comparison against a precise estimate
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	637 of human performance obtained via Amazon's Mechanical Turk (AMT)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	638 service (http://mturk.com).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	639 AMT users are paid small amounts
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	640 of money to perform tasks for which human intelligence is required.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	641 Mechanical Turk has been used extensively in natural language processing and vision.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	642 %processing \citep{SnowEtAl2008} and vision
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	643 %\citep{SorokinAndForsyth2008,whitehill09}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	644 AMT users were presented
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	645 with 10 character images (from a test set) and asked to choose 10 corresponding ASCII
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	646 characters. They were forced to choose a single character class (either among the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	647 62 or 10 character classes) for each image.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	648 80 subjects classified 2500 images per (dataset,task) pair.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	649 Different humans labelers sometimes provided a different label for the same
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	650 example, and we were able to estimate the error variance due to this effect
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	651 because each image was classified by 3 different persons.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	652 The average error of humans on the 62-class task NIST test set
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	653 is 18.2\%, with a standard error of 0.1\%.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	654
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	655 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	656 \subsection{Data Sources}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	657 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	658
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	659 %\begin{itemize}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	660 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	661 {\bf NIST.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	662 Our main source of characters is the NIST Special Database 19~\citep{Grother-1995},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	663 widely used for training and testing character
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	664 recognition systems~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	665 The dataset is composed of 814255 digits and characters (upper and lower cases), with hand checked classifications,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	666 extracted from handwritten sample forms of 3600 writers. The characters are labelled by one of the 62 classes
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	667 corresponding to ``0''-``9'',``A''-``Z'' and ``a''-``z''. The dataset contains 8 parts (partitions) of varying complexity.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	668 The fourth partition (called $hsf_4$, 82587 examples),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	669 experimentally recognized to be the most difficult one, is the one recommended
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	670 by NIST as a testing set and is used in our work as well as some previous work~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	671 for that purpose. We randomly split the remainder (731668 examples) into a training set and a validation set for
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	672 model selection.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	673 The performances reported by previous work on that dataset mostly use only the digits.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	674 Here we use all the classes both in the training and testing phase. This is especially
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	675 useful to estimate the effect of a multi-task setting.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	676 The distribution of the classes in the NIST training and test sets differs
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	677 substantially, with relatively many more digits in the test set, and a more uniform distribution
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	678 of letters in the test set (whereas in the training set they are distributed
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	679 more like in natural text).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	680 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	681
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	682 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	683 {\bf Fonts.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	684 In order to have a good variety of sources we downloaded an important number of free fonts from:
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	685 {\tt http://cg.scs.carleton.ca/\textasciitilde luc/freefonts.html}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	686 % TODO: pointless to anonymize, it's not pointing to our work
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	687 Including the operating system's (Windows 7) fonts, there is a total of $9817$ different fonts that we can choose uniformly from.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	688 The chosen {\tt ttf} file is either used as input of the Captcha generator (see next item) or, by producing a corresponding image,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	689 directly as input to our models.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	690 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	691
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	692 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	693 {\bf Captchas.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	694 The Captcha data source is an adaptation of the \emph{pycaptcha} library (a python based captcha generator library) for
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	695 generating characters of the same format as the NIST dataset. This software is based on
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	696 a random character class generator and various kinds of transformations similar to those described in the previous sections.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	697 In order to increase the variability of the data generated, many different fonts are used for generating the characters.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	698 Transformations (slant, distortions, rotation, translation) are applied to each randomly generated character with a complexity
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	699 depending on the value of the complexity parameter provided by the user of the data source.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	700 %Two levels of complexity are allowed and can be controlled via an easy to use facade class. %TODO: what's a facade class?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	701 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	702
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	703 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	704 {\bf OCR data.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	705 A large set (2 million) of scanned, OCRed and manually verified machine-printed
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	706 characters where included as an
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	707 additional source. This set is part of a larger corpus being collected by the Image Understanding
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	708 Pattern Recognition Research group led by Thomas Breuel at University of Kaiserslautern
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	709 ({\tt http://www.iupr.com}), and which will be publicly released.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	710 %TODO: let's hope that Thomas is not a reviewer! :) Seriously though, maybe we should anonymize this
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	711 %\end{itemize}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	712
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	713 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	714 \subsection{Data Sets}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	715 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	716
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	717 All data sets contain 32$\times$32 grey-level images (values in $[0,1]$) associated with a label
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	718 from one of the 62 character classes.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	719 %\begin{itemize}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	720 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	721
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	722 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	723 {\bf NIST.} This is the raw NIST special database 19~\citep{Grother-1995}. It has
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	724 \{651668 / 80000 / 82587\} \{training / validation / test\} examples.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	725 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	726
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	727 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	728 {\bf P07.} This dataset is obtained by taking raw characters from all four of the above sources
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	729 and sending them through the transformation pipeline described in section \ref{s:perturbations}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	730 For each new example to generate, a data source is selected with probability $10\%$ from the fonts,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	731 $25\%$ from the captchas, $25\%$ from the OCR data and $40\%$ from NIST. We apply all the transformations in the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	732 order given above, and for each of them we sample uniformly a \emph{complexity} in the range $[0,0.7]$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	733 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	734 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	735
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	736 %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	737 {\bf NISTP.} This one is equivalent to P07 (complexity parameter of $0.7$ with the same proportions of data sources)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	738 except that we only apply
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	739 transformations from slant to pinch. Therefore, the character is
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	740 transformed but no additional noise is added to the image, giving images
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	741 closer to the NIST dataset.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	742 It has \{81920000 / 80000 / 20000\} \{training / validation / test\} examples.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	743 %\end{itemize}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	744
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	745 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	746 \subsection{Models and their Hyperparameters}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	747 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	748
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	749 The experiments are performed using MLPs (with a single
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	750 hidden layer) and SDAs.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	751 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	752
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	753 {\bf Multi-Layer Perceptrons (MLP).}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	754 Whereas previous work had compared deep architectures to both shallow MLPs and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	755 SVMs, we only compared to MLPs here because of the very large datasets used
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	756 (making the use of SVMs computationally challenging because of their quadratic
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	757 scaling behavior). Preliminary experiments on training SVMs (libSVM) with subsets of the training
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	758 set allowing the program to fit in memory yielded substantially worse results
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	759 than those obtained with MLPs. For training on nearly a billion examples
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	760 (with the perturbed data), the MLPs and SDA are much more convenient than
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	761 classifiers based on kernel methods.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	762 The MLP has a single hidden layer with $\tanh$ activation functions, and softmax (normalized
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	763 exponentials) on the output layer for estimating $P(class \| image)$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	764 The number of hidden units is taken in $\{300,500,800,1000,1500\}$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	765 Training examples are presented in minibatches of size 20. A constant learning
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	766 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	767 %through preliminary experiments (measuring performance on a validation set),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	768 %and $0.1$ (which was found to work best) was then selected for optimizing on
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	769 %the whole training sets.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	770 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	771
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	772
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	773 {\bf Stacked Denoising Auto-Encoders (SDA).}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	774 Various auto-encoder variants and Restricted Boltzmann Machines (RBMs)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	775 can be used to initialize the weights of each layer of a deep MLP (with many hidden
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	776 layers)~\citep{Hinton06,ranzato-07-small,Bengio-nips-2006},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	777 apparently setting parameters in the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	778 basin of attraction of supervised gradient descent yielding better
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	779 generalization~\citep{Erhan+al-2010}. This initial {\em unsupervised
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	780 pre-training phase} uses all of the training images but not the training labels.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	781 Each layer is trained in turn to produce a new representation of its input
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	782 (starting from the raw pixels).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	783 It is hypothesized that the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	784 advantage brought by this procedure stems from a better prior,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	785 on the one hand taking advantage of the link between the input
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	786 distribution $P(x)$ and the conditional distribution of interest
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	787 $P(y\|x)$ (like in semi-supervised learning), and on the other hand
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	788 taking advantage of the expressive power and bias implicit in the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	789 deep architecture (whereby complex concepts are expressed as
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	790 compositions of simpler ones through a deep hierarchy).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	791
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	792 \begin{figure}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	793 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	794 \centerline{\resizebox{0.8\textwidth}{!}{\includegraphics{denoising_autoencoder_small.pdf}}}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	795 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	796 \caption{Illustration of the computations and training criterion for the denoising
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	797 auto-encoder used to pre-train each layer of the deep architecture. Input $x$ of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	798 the layer (i.e. raw input or output of previous layer)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	799 s corrupted into $\tilde{x}$ and encoded into code $y$ by the encoder $f_\theta(\cdot)$.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	800 The decoder $g_{\theta'}(\cdot)$ maps $y$ to reconstruction $z$, which
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	801 is compared to the uncorrupted input $x$ through the loss function
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	802 $L_H(x,z)$, whose expected value is approximately minimized during training
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	803 by tuning $\theta$ and $\theta'$.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	804 \label{fig:da}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	805 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	806 \end{figure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	807
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	808 Here we chose to use the Denoising
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	809 Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	810 these deep hierarchies of features, as it is simple to train and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	811 explain (see Figure~\ref{fig:da}, as well as
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	812 tutorial and code there: {\tt http://deeplearning.net/tutorial}),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	813 provides efficient inference, and yielded results
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	814 comparable or better than RBMs in series of experiments
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	815 \citep{VincentPLarochelleH2008}. During training, a Denoising
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	816 Auto-encoder is presented with a stochastically corrupted version
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	817 of the input and trained to reconstruct the uncorrupted input,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	818 forcing the hidden units to represent the leading regularities in
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	819 the data. Here we use the random binary masking corruption
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	820 (which sets to 0 a random subset of the inputs).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	821 Once it is trained, in a purely unsupervised way,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	822 its hidden units' activations can
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	823 be used as inputs for training a second one, etc.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	824 After this unsupervised pre-training stage, the parameters
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	825 are used to initialize a deep MLP, which is fine-tuned by
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	826 the same standard procedure used to train them (see previous section).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	827 The SDA hyper-parameters are the same as for the MLP, with the addition of the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	828 amount of corruption noise (we used the masking noise process, whereby a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	829 fixed proportion of the input values, randomly selected, are zeroed), and a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	830 separate learning rate for the unsupervised pre-training stage (selected
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	831 from the same above set). The fraction of inputs corrupted was selected
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	832 among $\{10\%, 20\%, 50\%\}$. Another hyper-parameter is the number
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	833 of hidden layers but it was fixed to 3 based on previous work with
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	834 SDAs on MNIST~\citep{VincentPLarochelleH2008}. The size of the hidden
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	835 layers was kept constant across hidden layers, and the best results
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	836 were obtained with the largest values that we could experiment
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	837 with given our patience, with 1000 hidden units.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	838
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	839 %\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	840
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	841 \begin{figure}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	842 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	843 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{error_rates_charts.pdf}}}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	844 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	845 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	846 on NIST, 1 on NISTP, and 2 on P07. Left: overall results
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	847 of all models, on NIST and NISTP test sets.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	848 Right: error rates on NIST test digits only, along with the previous results from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	849 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	850 respectively based on ART, nearest neighbors, MLPs, and SVMs.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	851 \label{fig:error-rates-charts}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	852 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	853 \end{figure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	854
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	855
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	856 \begin{figure}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	857 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	858 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{improvements_charts.pdf}}}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	859 %\vspace*{-3mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	860 \caption{Relative improvement in error rate due to self-taught learning.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	861 Left: Improvement (or loss, when negative)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	862 induced by out-of-distribution examples (perturbed data).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	863 Right: Improvement (or loss, when negative) induced by multi-task
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	864 learning (training on all classes and testing only on either digits,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	865 upper case, or lower-case). The deep learner (SDA) benefits more from
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	866 both self-taught learning scenarios, compared to the shallow MLP.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	867 \label{fig:improvements-charts}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	868 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	869 \end{figure}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	870
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	871 \section{Experimental Results}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	872 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	873
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	874 %%\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	875 %\subsection{SDA vs MLP vs Humans}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	876 %%\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	877 The models are either trained on NIST (MLP0 and SDA0),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	878 NISTP (MLP1 and SDA1), or P07 (MLP2 and SDA2), and tested
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	879 on either NIST, NISTP or P07, either on the 62-class task
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	880 or on the 10-digits task. Training (including about half
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	881 for unsupervised pre-training, for DAs) on the larger
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	882 datasets takes around one day on a GPU-285.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	883 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	884 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	885 SDA2), along with the previous results on the digits NIST special database
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	886 19 test set from the literature, respectively based on ARTMAP neural
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	887 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	888 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	889 ~\citep{Milgram+al-2005}. More detailed and complete numerical results
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	890 (figures and tables, including standard errors on the error rates) can be
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	891 found in Appendix.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	892 The deep learner not only outperformed the shallow ones and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	893 previously published performance (in a statistically and qualitatively
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	894 significant way) but when trained with perturbed data
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	895 reaches human performance on both the 62-class task
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	896 and the 10-class (digits) task.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	897 17\% error (SDA1) or 18\% error (humans) may seem large but a large
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	898 majority of the errors from humans and from SDA1 are from out-of-context
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	899 confusions (e.g. a vertical bar can be a ``1'', an ``l'' or an ``L'', and a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	900 ``c'' and a ``C'' are often indistinguishible).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	901
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	902 In addition, as shown in the left of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	903 Figure~\ref{fig:improvements-charts}, the relative improvement in error
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	904 rate brought by self-taught learning is greater for the SDA, and these
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	905 differences with the MLP are statistically and qualitatively
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	906 significant.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	907 The left side of the figure shows the improvement to the clean
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	908 NIST test set error brought by the use of out-of-distribution examples
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	909 (i.e. the perturbed examples examples from NISTP or P07).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	910 Relative percent change is measured by taking
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	911 $100 \% \times$ (original model's error / perturbed-data model's error - 1).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	912 The right side of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	913 Figure~\ref{fig:improvements-charts} shows the relative improvement
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	914 brought by the use of a multi-task setting, in which the same model is
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	915 trained for more classes than the target classes of interest (i.e. training
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	916 with all 62 classes when the target classes are respectively the digits,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	917 lower-case, or upper-case characters). Again, whereas the gain from the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	918 multi-task setting is marginal or negative for the MLP, it is substantial
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	919 for the SDA. Note that to simplify these multi-task experiments, only the original
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	920 NIST dataset is used. For example, the MLP-digits bar shows the relative
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	921 percent improvement in MLP error rate on the NIST digits test set
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	922 is $100\% \times$ (single-task
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	923 model's error / multi-task model's error - 1). The single-task model is
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	924 trained with only 10 outputs (one per digit), seeing only digit examples,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	925 whereas the multi-task model is trained with 62 outputs, with all 62
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	926 character classes as examples. Hence the hidden units are shared across
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	927 all tasks. For the multi-task model, the digit error rate is measured by
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	928 comparing the correct digit class with the output class associated with the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	929 maximum conditional probability among only the digit classes outputs. The
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	930 setting is similar for the other two target classes (lower case characters
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	931 and upper case characters).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	932 %%\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	933 %\subsection{Perturbed Training Data More Helpful for SDA}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	934 %%\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	935
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	936 %%\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	937 %\subsection{Multi-Task Learning Effects}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	938 %%\vspace*{-1mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	939
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	940 \iffalse
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	941 As previously seen, the SDA is better able to benefit from the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	942 transformations applied to the data than the MLP. In this experiment we
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	943 define three tasks: recognizing digits (knowing that the input is a digit),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	944 recognizing upper case characters (knowing that the input is one), and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	945 recognizing lower case characters (knowing that the input is one). We
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	946 consider the digit classification task as the target task and we want to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	947 evaluate whether training with the other tasks can help or hurt, and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	948 whether the effect is different for MLPs versus SDAs. The goal is to find
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	949 out if deep learning can benefit more (or less) from multiple related tasks
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	950 (i.e. the multi-task setting) compared to a corresponding purely supervised
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	951 shallow learner.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	952
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	953 We use a single hidden layer MLP with 1000 hidden units, and a SDA
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	954 with 3 hidden layers (1000 hidden units per layer), pre-trained and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	955 fine-tuned on NIST.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	956
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	957 Our results show that the MLP benefits marginally from the multi-task setting
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	958 in the case of digits (5\% relative improvement) but is actually hurt in the case
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	959 of characters (respectively 3\% and 4\% worse for lower and upper class characters).
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	960 On the other hand the SDA benefited from the multi-task setting, with relative
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	961 error rate improvements of 27\%, 15\% and 13\% respectively for digits,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	962 lower and upper case characters, as shown in Table~\ref{tab:multi-task}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	963 \fi
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	964
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	965
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	966 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	967 \section{Conclusions and Discussion}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	968 %\vspace*{-2mm}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	969
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	970 We have found that the self-taught learning framework is more beneficial
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	971 to a deep learner than to a traditional shallow and purely
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	972 supervised learner. More precisely,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	973 the answers are positive for all the questions asked in the introduction.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	974 %\begin{itemize}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	975
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	976 $\bullet$ %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	977 {\bf Do the good results previously obtained with deep architectures on the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	978 MNIST digits generalize to a much larger and richer (but similar)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	979 dataset, the NIST special database 19, with 62 classes and around 800k examples}?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	980 Yes, the SDA {\em systematically outperformed the MLP and all the previously
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	981 published results on this dataset} (the ones that we are aware of), {\em in fact reaching human-level
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	982 performance} at around 17\% error on the 62-class task and 1.4\% on the digits,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	983 and beating previously published results on the same data.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	984
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	985 $\bullet$ %\item
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	986 {\bf To what extent do self-taught learning scenarios help deep learners,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	987 and do they help them more than shallow supervised ones}?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	988 We found that distorted training examples not only made the resulting
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	989 classifier better on similarly perturbed images but also on
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	990 the {\em original clean examples}, and more importantly and more novel,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	991 that deep architectures benefit more from such {\em out-of-distribution}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	992 examples. MLPs were helped by perturbed training examples when tested on perturbed input
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	993 images (65\% relative improvement on NISTP)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	994 but only marginally helped (5\% relative improvement on all classes)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	995 or even hurt (10\% relative loss on digits)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	996 with respect to clean examples . On the other hand, the deep SDAs
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	997 were significantly boosted by these out-of-distribution examples.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	998 Similarly, whereas the improvement due to the multi-task setting was marginal or
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	999 negative for the MLP (from +5.6\% to -3.6\% relative change),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1000 it was quite significant for the SDA (from +13\% to +27\% relative change),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1001 which may be explained by the arguments below.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1002 %\end{itemize}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1003
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1004 In the original self-taught learning framework~\citep{RainaR2007}, the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1005 out-of-sample examples were used as a source of unsupervised data, and
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1006 experiments showed its positive effects in a \emph{limited labeled data}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1007 scenario. However, many of the results by \citet{RainaR2007} (who used a
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1008 shallow, sparse coding approach) suggest that the {\em relative gain of self-taught
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1009 learning vs ordinary supervised learning} diminishes as the number of labeled examples increases.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1010 We note instead that, for deep
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1011 architectures, our experiments show that such a positive effect is accomplished
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1012 even in a scenario with a \emph{large number of labeled examples},
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1013 i.e., here, the relative gain of self-taught learning is probably preserved
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1014 in the asymptotic regime.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1015
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1016 {\bf Why would deep learners benefit more from the self-taught learning framework}?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1017 The key idea is that the lower layers of the predictor compute a hierarchy
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1018 of features that can be shared across tasks or across variants of the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1019 input distribution. A theoretical analysis of generalization improvements
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1020 due to sharing of intermediate features across tasks already points
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1021 towards that explanation~\cite{baxter95a}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1022 Intermediate features that can be used in different
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1023 contexts can be estimated in a way that allows to share statistical
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1024 strength. Features extracted through many levels are more likely to
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1025 be more abstract (as the experiments in~\citet{Goodfellow2009} suggest),
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1026 increasing the likelihood that they would be useful for a larger array
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1027 of tasks and input conditions.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1028 Therefore, we hypothesize that both depth and unsupervised
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1029 pre-training play a part in explaining the advantages observed here, and future
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1030 experiments could attempt at teasing apart these factors.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1031 And why would deep learners benefit from the self-taught learning
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1032 scenarios even when the number of labeled examples is very large?
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1033 We hypothesize that this is related to the hypotheses studied
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1034 in~\citet{Erhan+al-2010}. Whereas in~\citet{Erhan+al-2010}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1035 it was found that online learning on a huge dataset did not make the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1036 advantage of the deep learning bias vanish, a similar phenomenon
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1037 may be happening here. We hypothesize that unsupervised pre-training
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1038 of a deep hierarchy with self-taught learning initializes the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1039 model in the basin of attraction of supervised gradient descent
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1040 that corresponds to better generalization. Furthermore, such good
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1041 basins of attraction are not discovered by pure supervised learning
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1042 (with or without self-taught settings), and more labeled examples
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1043 does not allow the model to go from the poorer basins of attraction discovered
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1044 by the purely supervised shallow models to the kind of better basins associated
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1045 with deep learning and self-taught learning.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1046
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1047 A Flash demo of the recognizer (where both the MLP and the SDA can be compared)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1048 can be executed on-line at {\tt http://deep.host22.com}.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1049
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1050
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1051 \section*{Appendix I: Detailed Numerical Results}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1052
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1053 These tables correspond to Figures 2 and 3 and contain the raw error rates for each model and dataset considered.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1054 They also contain additional data such as test errors on P07 and standard errors.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1055
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1056 \begin{table}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1057 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1058 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1059 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1060 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1061 and using a validation set to select hyper-parameters and other training choices.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1062 \{SDA,MLP\}0 are trained on NIST,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1063 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1064 The human error rate on digits is a lower bound because it does not count digits that were
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1065 recognized as letters. For comparison, the results found in the literature
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1066 on NIST digits classification using the same test set are included.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1067 \label{tab:sda-vs-mlp-vs-humans}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1068 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1069 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1070 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1071 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1072 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1073 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1074 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1075 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1076 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1077 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1078 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1079 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1080 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1081 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1082 \end{tabular}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1083 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1084 \end{table}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1085
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1086 \begin{table}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1087 \caption{Relative change in error rates due to the use of perturbed training data,
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1088 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1089 A positive value indicates that training on the perturbed data helped for the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1090 given test set (the first 3 columns on the 62-class tasks and the last one is
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1091 on the clean 10-class digits). Clearly, the deep learning models did benefit more
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1092 from perturbed training data, even when testing on clean data, whereas the MLP
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1093 trained on perturbed data performed worse on the clean digits and about the same
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1094 on the clean characters. }
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1095 \label{tab:perturbation-effect}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1096 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1097 \begin{tabular}{\|l\|r\|r\|r\|r\|} \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1098 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1099 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1100 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1101 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1102 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1103 \end{tabular}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1104 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1105 \end{table}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1106
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1107 \begin{table}[ht]
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1108 \caption{Test error rates and relative change in error rates due to the use of
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1109 a multi-task setting, i.e., training on each task in isolation vs training
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1110 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1111 more from the multi-task setting. All experiments on only on the
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1112 unperturbed NIST data, using validation error for model selection.
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1113 Relative improvement is 1 - single-task error / multi-task error.}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1114 \label{tab:multi-task}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1115 \begin{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1116 \begin{tabular}{\|l\|r\|r\|r\|} \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1117 & single-task & multi-task & relative \\
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1118 & setting & setting & improvement \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1119 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1120 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1121 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1122 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1123 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1124 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1125 \end{tabular}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1126 \end{center}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1127 \end{table}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1128
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1129 %\afterpage{\clearpage}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1130 \clearpage
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1131 {
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1132 \bibliographystyle{spbasic} % basic style, author-year citations
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1133 \bibliography{strings,strings-short,strings-shorter,ift6266_ml,specials,aigaion-shorter}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1134 %\bibliographystyle{plainnat}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1135 %\bibliographystyle{unsrtnat}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1136 %\bibliographystyle{apalike}
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1137 }
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1138
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1139
b1be957dd1be Added mlj_submission to group every file needed for that. fsavard parents: diff changeset	1140 \end{document}

Mercurial > ift6266

annotate writeup/mlj_submission/mlj_submission.tex @ 634:54e8958e963b