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comparison writeup/nips2010_submission.tex @ 548:34cb28249de0
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| author | Yoshua Bengio <bengioy@iro.umontreal.ca> |
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| date | Wed, 02 Jun 2010 13:30:35 -0400 |
| parents | 316c7bdad5ad |
| children | ef172f4a322a |
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| 547:316c7bdad5ad | 548:34cb28249de0 |
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| 534 \begin{figure}[ht] | 534 \begin{figure}[ht] |
| 535 \vspace*{-2mm} | 535 \vspace*{-2mm} |
| 536 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}} | 536 \centerline{\resizebox{.99\textwidth}{!}{\includegraphics{images/error_rates_charts.pdf}}} |
| 537 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained | 537 \caption{SDAx are the {\bf deep} models. Error bars indicate a 95\% confidence interval. 0 indicates that the model was trained |
| 538 on NIST, 1 on NISTP, and 2 on P07. Left: overall results | 538 on NIST, 1 on NISTP, and 2 on P07. Left: overall results |
| 539 of all models, on 3 different test sets (NIST, NISTP, P07). | 539 of all models, on NIST and NISTP test sets. |
| 540 Right: error rates on NIST test digits only, along with the previous results from | 540 Right: error rates on NIST test digits only, along with the previous results from |
| 541 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005} | 541 literature~\citep{Granger+al-2007,Cortes+al-2000,Oliveira+al-2002-short,Milgram+al-2005} |
| 542 respectively based on ART, nearest neighbors, MLPs, and SVMs.} | 542 respectively based on ART, nearest neighbors, MLPs, and SVMs.} |
| 543 | 543 |
| 544 \label{fig:error-rates-charts} | 544 \label{fig:error-rates-charts} |
| 592 significant. | 592 significant. |
| 593 The left side of the figure shows the improvement to the clean | 593 The left side of the figure shows the improvement to the clean |
| 594 NIST test set error brought by the use of out-of-distribution examples | 594 NIST test set error brought by the use of out-of-distribution examples |
| 595 (i.e. the perturbed examples examples from NISTP or P07). | 595 (i.e. the perturbed examples examples from NISTP or P07). |
| 596 Relative percent change is measured by taking | 596 Relative percent change is measured by taking |
| 597 100 \% \times (original model's error / perturbed-data model's error - 1). | 597 $100 \% \times$ (original model's error / perturbed-data model's error - 1). |
| 598 The right side of | 598 The right side of |
| 599 Figure~\ref{fig:improvements-charts} shows the relative improvement | 599 Figure~\ref{fig:improvements-charts} shows the relative improvement |
| 600 brought by the use of a multi-task setting, in which the same model is | 600 brought by the use of a multi-task setting, in which the same model is |
| 601 trained for more classes than the target classes of interest (i.e. training | 601 trained for more classes than the target classes of interest (i.e. training |
| 602 with all 62 classes when the target classes are respectively the digits, | 602 with all 62 classes when the target classes are respectively the digits, |
| 603 lower-case, or upper-case characters). Again, whereas the gain from the | 603 lower-case, or upper-case characters). Again, whereas the gain from the |
| 604 multi-task setting is marginal or negative for the MLP, it is substantial | 604 multi-task setting is marginal or negative for the MLP, it is substantial |
| 605 for the SDA. Note that to simplify these multi-task experiments, only the original | 605 for the SDA. Note that to simplify these multi-task experiments, only the original |
| 606 NIST dataset is used. For example, the MLP-digits bar shows the relative | 606 NIST dataset is used. For example, the MLP-digits bar shows the relative |
| 607 percent improvement in MLP error rate on the NIST digits test set | 607 percent improvement in MLP error rate on the NIST digits test set |
| 608 is 100\% $\times$ (1 - single-task | 608 is $100\% \times$ (1 - single-task |
| 609 model's error / multi-task model's error). The single-task model is | 609 model's error / multi-task model's error). The single-task model is |
| 610 trained with only 10 outputs (one per digit), seeing only digit examples, | 610 trained with only 10 outputs (one per digit), seeing only digit examples, |
| 611 whereas the multi-task model is trained with 62 outputs, with all 62 | 611 whereas the multi-task model is trained with 62 outputs, with all 62 |
| 612 character classes as examples. Hence the hidden units are shared across | 612 character classes as examples. Hence the hidden units are shared across |
| 613 all tasks. For the multi-task model, the digit error rate is measured by | 613 all tasks. For the multi-task model, the digit error rate is measured by |