On the Capacity Limits of Privileged ERM

Michal Sharoni, Sivan Sabato
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:523-534, 2023.

Abstract

We study the supervised learning paradigm called Learning Using Privileged Information, first suggested by Vapnik and Vashist (2009). In this paradigm, in addition to the examples and labels, additional (privileged) information is provided only for training examples. The goal is to use this information to improve the classification accuracy of the resulting classifier, where this classifier can only use the non-privileged information of new example instances to predict their label. We study the theory of privileged learning with the zero-one loss under the natural Privileged ERM algorithm proposed in Peshyony and Vapnik (2010). We provide a counter example to a claim made in that work regarding the VC dimension of the loss class induced by this problem; We conclude that the claim is incorrect. We then provide a correct VC dimension analysis which gives both lower and upper bounds on the capacity of the Privileged ERM loss class. We further show, via a generalization analysis, that worst-case guarantees for Privileged ERM cannot improve over standard non-privileged ERM, unless the capacity of the privileged information is similar or smaller to that of the non-privileged information. This result points to an important limitation of the Privileged ERM approach. In our closing discussion, we suggest another way in which Privileged ERM might still be helpful, even when the capacity of the privileged information is large.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-sharoni23a, title = {On the Capacity Limits of Privileged ERM}, author = {Sharoni, Michal and Sabato, Sivan}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {523--534}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/sharoni23a/sharoni23a.pdf}, url = {https://proceedings.mlr.press/v206/sharoni23a.html}, abstract = {We study the supervised learning paradigm called Learning Using Privileged Information, first suggested by Vapnik and Vashist (2009). In this paradigm, in addition to the examples and labels, additional (privileged) information is provided only for training examples. The goal is to use this information to improve the classification accuracy of the resulting classifier, where this classifier can only use the non-privileged information of new example instances to predict their label. We study the theory of privileged learning with the zero-one loss under the natural Privileged ERM algorithm proposed in Peshyony and Vapnik (2010). We provide a counter example to a claim made in that work regarding the VC dimension of the loss class induced by this problem; We conclude that the claim is incorrect. We then provide a correct VC dimension analysis which gives both lower and upper bounds on the capacity of the Privileged ERM loss class. We further show, via a generalization analysis, that worst-case guarantees for Privileged ERM cannot improve over standard non-privileged ERM, unless the capacity of the privileged information is similar or smaller to that of the non-privileged information. This result points to an important limitation of the Privileged ERM approach. In our closing discussion, we suggest another way in which Privileged ERM might still be helpful, even when the capacity of the privileged information is large.} }
Endnote
%0 Conference Paper %T On the Capacity Limits of Privileged ERM %A Michal Sharoni %A Sivan Sabato %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-sharoni23a %I PMLR %P 523--534 %U https://proceedings.mlr.press/v206/sharoni23a.html %V 206 %X We study the supervised learning paradigm called Learning Using Privileged Information, first suggested by Vapnik and Vashist (2009). In this paradigm, in addition to the examples and labels, additional (privileged) information is provided only for training examples. The goal is to use this information to improve the classification accuracy of the resulting classifier, where this classifier can only use the non-privileged information of new example instances to predict their label. We study the theory of privileged learning with the zero-one loss under the natural Privileged ERM algorithm proposed in Peshyony and Vapnik (2010). We provide a counter example to a claim made in that work regarding the VC dimension of the loss class induced by this problem; We conclude that the claim is incorrect. We then provide a correct VC dimension analysis which gives both lower and upper bounds on the capacity of the Privileged ERM loss class. We further show, via a generalization analysis, that worst-case guarantees for Privileged ERM cannot improve over standard non-privileged ERM, unless the capacity of the privileged information is similar or smaller to that of the non-privileged information. This result points to an important limitation of the Privileged ERM approach. In our closing discussion, we suggest another way in which Privileged ERM might still be helpful, even when the capacity of the privileged information is large.
APA
Sharoni, M. & Sabato, S.. (2023). On the Capacity Limits of Privileged ERM. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:523-534 Available from https://proceedings.mlr.press/v206/sharoni23a.html.

Related Material