Complexity-Based Approach to Calibration with Checking Rules

Dean P. Foster, Alexander Rakhlin, Karthik Sridharan, Ambuj Tewari
Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:293-314, 2011.

Abstract

We consider the problem of forecasting a sequence of outcomes from an unknown source. The quality of the forecaster is measured by a family of checking rules. We prove upper bounds on the value of the associated game, thus certifying the existence of a calibrated strategy for the forecaster. We show that complexity of the family of checking rules can be captured by the notion of a sequential cover introduced in (Rakhlin et al., 2010a). Various natural assumptions on the class of checking rules are considered, including finiteness of Vapnik-Chervonenkis and Littlestone’s dimensions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v19-foster11a, title = {Complexity-Based Approach to Calibration with Checking Rules}, author = {Foster, Dean P. and Rakhlin, Alexander and Sridharan, Karthik and Tewari, Ambuj}, booktitle = {Proceedings of the 24th Annual Conference on Learning Theory}, pages = {293--314}, 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/foster11a/foster11a.pdf}, url = {https://proceedings.mlr.press/v19/foster11a.html}, abstract = {We consider the problem of forecasting a sequence of outcomes from an unknown source. The quality of the forecaster is measured by a family of checking rules. We prove upper bounds on the value of the associated game, thus certifying the existence of a calibrated strategy for the forecaster. We show that complexity of the family of checking rules can be captured by the notion of a sequential cover introduced in (Rakhlin et al., 2010a). Various natural assumptions on the class of checking rules are considered, including finiteness of Vapnik-Chervonenkis and Littlestone’s dimensions.} }
Endnote
%0 Conference Paper %T Complexity-Based Approach to Calibration with Checking Rules %A Dean P. Foster %A Alexander Rakhlin %A Karthik Sridharan %A Ambuj Tewari %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-foster11a %I PMLR %P 293--314 %U https://proceedings.mlr.press/v19/foster11a.html %V 19 %X We consider the problem of forecasting a sequence of outcomes from an unknown source. The quality of the forecaster is measured by a family of checking rules. We prove upper bounds on the value of the associated game, thus certifying the existence of a calibrated strategy for the forecaster. We show that complexity of the family of checking rules can be captured by the notion of a sequential cover introduced in (Rakhlin et al., 2010a). Various natural assumptions on the class of checking rules are considered, including finiteness of Vapnik-Chervonenkis and Littlestone’s dimensions.
RIS
TY - CPAPER TI - Complexity-Based Approach to Calibration with Checking Rules AU - Dean P. Foster AU - Alexander Rakhlin AU - Karthik Sridharan AU - Ambuj Tewari 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-foster11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 19 SP - 293 EP - 314 L1 - http://proceedings.mlr.press/v19/foster11a/foster11a.pdf UR - https://proceedings.mlr.press/v19/foster11a.html AB - We consider the problem of forecasting a sequence of outcomes from an unknown source. The quality of the forecaster is measured by a family of checking rules. We prove upper bounds on the value of the associated game, thus certifying the existence of a calibrated strategy for the forecaster. We show that complexity of the family of checking rules can be captured by the notion of a sequential cover introduced in (Rakhlin et al., 2010a). Various natural assumptions on the class of checking rules are considered, including finiteness of Vapnik-Chervonenkis and Littlestone’s dimensions. ER -
APA
Foster, D.P., Rakhlin, A., Sridharan, K. & Tewari, A.. (2011). Complexity-Based Approach to Calibration with Checking Rules. Proceedings of the 24th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 19:293-314 Available from https://proceedings.mlr.press/v19/foster11a.html.

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