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comparison writeup/nips2010_submission.tex @ 491:19eab4daf212
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| author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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| date | Mon, 31 May 2010 22:15:44 -0400 |
| parents | d6cf4912abb0 ee9836baade3 |
| children | a194ce5a4249 |
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| 609 %\bibliographystyle{plainnat} | 609 %\bibliographystyle{plainnat} |
| 610 \bibliographystyle{unsrtnat} | 610 \bibliographystyle{unsrtnat} |
| 611 %\bibliographystyle{apalike} | 611 %\bibliographystyle{apalike} |
| 612 } | 612 } |
| 613 | 613 |
| 614 \newpage | |
| 615 | |
| 616 \centerline{APPENDIX FOR {\bf Deep Self-Taught Learning for Handwritten Character Recognition}} | |
| 617 | |
| 618 \vspace*{1cm} | |
| 619 | |
| 620 \begin{table}[h] | |
| 621 \caption{Overall comparison of error rates ($\pm$ std.err.) on 62 character classes (10 digits + | |
| 622 26 lower + 26 upper), except for last columns -- digits only, between deep architecture with pre-training | |
| 623 (SDA=Stacked Denoising Autoencoder) and ordinary shallow architecture | |
| 624 (MLP=Multi-Layer Perceptron). The models shown are all trained using perturbed data (NISTP or P07) | |
| 625 and using a validation set to select hyper-parameters and other training choices. | |
| 626 \{SDA,MLP\}0 are trained on NIST, | |
| 627 \{SDA,MLP\}1 are trained on NISTP, and \{SDA,MLP\}2 are trained on P07. | |
| 628 The human error rate on digits is a lower bound because it does not count digits that were | |
| 629 recognized as letters. For comparison, the results found in the literature | |
| 630 on NIST digits classification using the same test set are included.} | |
| 631 \label{tab:sda-vs-mlp-vs-humans} | |
| 632 \begin{center} | |
| 633 \begin{tabular}{|l|r|r|r|r|} \hline | |
| 634 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 635 Humans& 18.2\% $\pm$.1\% & 39.4\%$\pm$.1\% & 46.9\%$\pm$.1\% & $1.4\%$ \\ \hline | |
| 636 SDA0 & 23.7\% $\pm$.14\% & 65.2\%$\pm$.34\% & 97.45\%$\pm$.06\% & 2.7\% $\pm$.14\%\\ \hline | |
| 637 SDA1 & 17.1\% $\pm$.13\% & 29.7\%$\pm$.3\% & 29.7\%$\pm$.3\% & 1.4\% $\pm$.1\%\\ \hline | |
| 638 SDA2 & 18.7\% $\pm$.13\% & 33.6\%$\pm$.3\% & 39.9\%$\pm$.17\% & 1.7\% $\pm$.1\%\\ \hline | |
| 639 MLP0 & 24.2\% $\pm$.15\% & 68.8\%$\pm$.33\% & 78.70\%$\pm$.14\% & 3.45\% $\pm$.15\% \\ \hline | |
| 640 MLP1 & 23.0\% $\pm$.15\% & 41.8\%$\pm$.35\% & 90.4\%$\pm$.1\% & 3.85\% $\pm$.16\% \\ \hline | |
| 641 MLP2 & 24.3\% $\pm$.15\% & 46.0\%$\pm$.35\% & 54.7\%$\pm$.17\% & 4.85\% $\pm$.18\% \\ \hline | |
| 642 \citep{Granger+al-2007} & & & & 4.95\% $\pm$.18\% \\ \hline | |
| 643 \citep{Cortes+al-2000} & & & & 3.71\% $\pm$.16\% \\ \hline | |
| 644 \citep{Oliveira+al-2002} & & & & 2.4\% $\pm$.13\% \\ \hline | |
| 645 \citep{Milgram+al-2005} & & & & 2.1\% $\pm$.12\% \\ \hline | |
| 646 \end{tabular} | |
| 647 \end{center} | |
| 648 \end{table} | |
| 649 | |
| 650 \begin{table}[h] | |
| 651 \caption{Relative change in error rates due to the use of perturbed training data, | |
| 652 either using NISTP, for the MLP1/SDA1 models, or using P07, for the MLP2/SDA2 models. | |
| 653 A positive value indicates that training on the perturbed data helped for the | |
| 654 given test set (the first 3 columns on the 62-class tasks and the last one is | |
| 655 on the clean 10-class digits). Clearly, the deep learning models did benefit more | |
| 656 from perturbed training data, even when testing on clean data, whereas the MLP | |
| 657 trained on perturbed data performed worse on the clean digits and about the same | |
| 658 on the clean characters. } | |
| 659 \label{tab:perturbation-effect} | |
| 660 \begin{center} | |
| 661 \begin{tabular}{|l|r|r|r|r|} \hline | |
| 662 & NIST test & NISTP test & P07 test & NIST test digits \\ \hline | |
| 663 SDA0/SDA1-1 & 38\% & 84\% & 228\% & 93\% \\ \hline | |
| 664 SDA0/SDA2-1 & 27\% & 94\% & 144\% & 59\% \\ \hline | |
| 665 MLP0/MLP1-1 & 5.2\% & 65\% & -13\% & -10\% \\ \hline | |
| 666 MLP0/MLP2-1 & -0.4\% & 49\% & 44\% & -29\% \\ \hline | |
| 667 \end{tabular} | |
| 668 \end{center} | |
| 669 \end{table} | |
| 670 | |
| 671 \begin{table}[h] | |
| 672 \caption{Test error rates and relative change in error rates due to the use of | |
| 673 a multi-task setting, i.e., training on each task in isolation vs training | |
| 674 for all three tasks together, for MLPs vs SDAs. The SDA benefits much | |
| 675 more from the multi-task setting. All experiments on only on the | |
| 676 unperturbed NIST data, using validation error for model selection. | |
| 677 Relative improvement is 1 - single-task error / multi-task error.} | |
| 678 \label{tab:multi-task} | |
| 679 \begin{center} | |
| 680 \begin{tabular}{|l|r|r|r|} \hline | |
| 681 & single-task & multi-task & relative \\ | |
| 682 & setting & setting & improvement \\ \hline | |
| 683 MLP-digits & 3.77\% & 3.99\% & 5.6\% \\ \hline | |
| 684 MLP-lower & 17.4\% & 16.8\% & -4.1\% \\ \hline | |
| 685 MLP-upper & 7.84\% & 7.54\% & -3.6\% \\ \hline | |
| 686 SDA-digits & 2.6\% & 3.56\% & 27\% \\ \hline | |
| 687 SDA-lower & 12.3\% & 14.4\% & 15\% \\ \hline | |
| 688 SDA-upper & 5.93\% & 6.78\% & 13\% \\ \hline | |
| 689 \end{tabular} | |
| 690 \end{center} | |
| 691 \end{table} | |
| 692 | |
| 693 | 614 |
| 694 \end{document} | 615 \end{document} |