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changements de Myriam
author Yoshua Bengio <bengioy@iro.umontreal.ca>
date Tue, 01 Jun 2010 13:37:40 -0400
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1 \documentclass{article} % For LaTeX2e
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2 \usepackage{nips10submit_e,times}
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3
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4 \usepackage{amsthm,amsmath,amssymb,bbold,bbm}
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5 \usepackage{algorithm,algorithmic}
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6 \usepackage[utf8]{inputenc}
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7 \usepackage{graphicx,subfigure}
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8 \usepackage[numbers]{natbib}
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9
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10 \title{Deep Self-Taught Learning for Handwritten Character Recognition\\
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11 \emph{Supplementary Material}}
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12
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13 \begin{document}
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14
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15 \maketitle
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16
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17 \section*{Appendix I: Full results}
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18
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19 These tables correspond to Figures 3 and 4 and contain the raw error rates for each model and dataset considered.
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20
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21 \begin{table}[h]
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22 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits +
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23 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training
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24 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture
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25 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07)
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26 and using a validation set to select hyper-parameters and other training choices.
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27 \{SDA,MLP\}0 are trained on NIST,
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28 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07.
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29 The human error rate on digits is a lower bound because it does not count digits that were
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30 recognized as letters. For comparison, the results found in the literature
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31 on NIST digits classification using the same test set are included.}
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32 \label{tab:sda-vs-mlp-vs-humans}
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33 \begin{center}
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34 \begin{tabular}{|l|r|r|r|r|} \hline
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35 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
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36 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline
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37 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline
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38 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline
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39 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline
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40 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline
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41 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline
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42 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline
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43 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline
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44 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline
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45 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline
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46 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline
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47 \end{tabular}
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48 \end{center}
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49 \end{table}
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50
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51 \begin{table}[h]
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52 \caption{Relative change in error rates due to the use of perturbed training data,
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53 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models.
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54 A positive value indicates that training on the perturbed data helped for the
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55 given test set (the first 3 columns on the 62-class tasks and the last one is
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56 on the clean 10-class digits). Clearly, the deep learning models did benefit more
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57 from perturbed training data, even when testing on clean data, whereas the MLP
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58 trained on perturbed data performed worse on the clean digits and about the same
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59 on the clean characters. }
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60 \label{tab:perturbation-effect}
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61 \begin{center}
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62 \begin{tabular}{|l|r|r|r|r|} \hline
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63 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline
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64 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline
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65 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline
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66 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline
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67 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline
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68 \end{tabular}
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69 \end{center}
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70 \end{table}
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71
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72 \begin{table}[h]
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73 \caption{Test error rates and relative change in error rates due to the use of
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74 a multi-task setting, i.e., training on each task in isolation vs training
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75 for all three tasks together, for MLPs vs SDAs. The SDA benefits much
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76 more from the multi-task setting. All experiments on only on the
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77 unperturbed NIST data, using validation error for model selection.
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78 Relative improvement is 1 - single-task error / multi-task error.}
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79 \label{tab:multi-task}
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80 \begin{center}
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81 \begin{tabular}{|l|r|r|r|} \hline
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82 & single-task & multi-task & relative \\
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83 & setting & setting & improvement \\ \hline
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84 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline
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85 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline
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86 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline
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87 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline
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88 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline
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89 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline
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90 \end{tabular}
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91 \end{center}
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92 \end{table}
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93
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94 {\small
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95 \bibliography{strings,ml,aigaion,specials}
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96 %\bibliographystyle{plainnat}
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97 \bibliographystyle{unsrtnat}
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98 %\bibliographystyle{apalike}
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99 }
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100
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101 \end{document}