Oracle inequalities for computationally budgeted model selection

Alekh Agarwal, John C. Duchi, Peter L. Bartlett, Clement Levrard
Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:69-86, 2011.

Abstract

We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we argue that any practical model selection procedure must not only trade off estimation and approximation error, but also the effects of the computational effort required to compute empirical minimizers for different function classes. We provide a framework for analyzing such problems, and we give algorithms for model selection under a computational budget. These algorithms satisfy oracle inequalities that show that the risk of the selected model is not much worse than if we had devoted all of our computational budget to the best function class.

Cite this Paper

BibTeX
@InProceedings{pmlr-v19-agarwal11a, title = {Oracle inequalities for computationally budgeted model selection}, author = {Agarwal, Alekh and Duchi, John C. and Bartlett, Peter L. and Levrard, Clement}, booktitle = {Proceedings of the 24th Annual Conference on Learning Theory}, pages = {69--86}, year = {2011}, editor = {Kakade, Sham M. and von Luxburg, Ulrike}, volume = {19}, series = {Proceedings of Machine Learning Research}, address = {Budapest, Hungary}, month = {09--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v19/agarwal11a/agarwal11a.pdf}, url = {https://proceedings.mlr.press/v19/agarwal11a.html}, abstract = {We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we argue that any practical model selection procedure must not only trade off estimation and approximation error, but also the effects of the computational effort required to compute empirical minimizers for different function classes. We provide a framework for analyzing such problems, and we give algorithms for model selection under a computational budget. These algorithms satisfy oracle inequalities that show that the risk of the selected model is not much worse than if we had devoted all of our computational budget to the best function class.} }
Endnote
%0 Conference Paper %T Oracle inequalities for computationally budgeted model selection %A Alekh Agarwal %A John C. Duchi %A Peter L. Bartlett %A Clement Levrard %B Proceedings of the 24th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2011 %E Sham M. Kakade %E Ulrike von Luxburg %F pmlr-v19-agarwal11a %I PMLR %P 69--86 %U https://proceedings.mlr.press/v19/agarwal11a.html %V 19 %X We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we argue that any practical model selection procedure must not only trade off estimation and approximation error, but also the effects of the computational effort required to compute empirical minimizers for different function classes. We provide a framework for analyzing such problems, and we give algorithms for model selection under a computational budget. These algorithms satisfy oracle inequalities that show that the risk of the selected model is not much worse than if we had devoted all of our computational budget to the best function class.
RIS
TY - CPAPER TI - Oracle inequalities for computationally budgeted model selection AU - Alekh Agarwal AU - John C. Duchi AU - Peter L. Bartlett AU - Clement Levrard BT - Proceedings of the 24th Annual Conference on Learning Theory DA - 2011/12/21 ED - Sham M. Kakade ED - Ulrike von Luxburg ID - pmlr-v19-agarwal11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 19 SP - 69 EP - 86 L1 - http://proceedings.mlr.press/v19/agarwal11a/agarwal11a.pdf UR - https://proceedings.mlr.press/v19/agarwal11a.html AB - We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we argue that any practical model selection procedure must not only trade off estimation and approximation error, but also the effects of the computational effort required to compute empirical minimizers for different function classes. We provide a framework for analyzing such problems, and we give algorithms for model selection under a computational budget. These algorithms satisfy oracle inequalities that show that the risk of the selected model is not much worse than if we had devoted all of our computational budget to the best function class. ER -
APA
Agarwal, A., Duchi, J.C., Bartlett, P.L. & Levrard, C.. (2011). Oracle inequalities for computationally budgeted model selection. Proceedings of the 24th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 19:69-86 Available from https://proceedings.mlr.press/v19/agarwal11a.html.

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