Bounds on Individual Risk for Log-loss Predictors

Peter D. Grünwald, Wojciech Kotłowski
Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:813-816, 2011.

Abstract

In sequential prediction with log-loss as well as density estimationwith risk measured by KL divergence, one is often interested in the expected instantaneous loss, or, equivalently, the individual risk at a given fixed sample size $n$. For Bayesianprediction and estimation methods, it is often easy to obtain bounds on the cumulative risk. Such results are based on bounding the individual sequence regret, a technique that is very well known in the COLT community. Motivated by the easiness of proofs for the cumulative risk, our open problem is to use the results on cumulative risk to prove corresponding individual-risk bounds.

Cite this Paper

BibTeX
@InProceedings{pmlr-v19-grunwald11b, title = {Bounds on Individual Risk for Log-loss Predictors}, author = {Grünwald, Peter D. and Kotłowski, Wojciech}, booktitle = {Proceedings of the 24th Annual Conference on Learning Theory}, pages = {813--816}, 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/grunwald11b/grunwald11b.pdf}, url = {https://proceedings.mlr.press/v19/grunwald11b.html}, abstract = {In sequential prediction with log-loss as well as density estimationwith risk measured by KL divergence, one is often interested in the expected instantaneous loss, or, equivalently, the individual risk at a given fixed sample size $n$. For Bayesianprediction and estimation methods, it is often easy to obtain bounds on the cumulative risk. Such results are based on bounding the individual sequence regret, a technique that is very well known in the COLT community. Motivated by the easiness of proofs for the cumulative risk, our open problem is to use the results on cumulative risk to prove corresponding individual-risk bounds.} }
Endnote
%0 Conference Paper %T Bounds on Individual Risk for Log-loss Predictors %A Peter D. Grünwald %A Wojciech Kotłowski %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-grunwald11b %I PMLR %P 813--816 %U https://proceedings.mlr.press/v19/grunwald11b.html %V 19 %X In sequential prediction with log-loss as well as density estimationwith risk measured by KL divergence, one is often interested in the expected instantaneous loss, or, equivalently, the individual risk at a given fixed sample size $n$. For Bayesianprediction and estimation methods, it is often easy to obtain bounds on the cumulative risk. Such results are based on bounding the individual sequence regret, a technique that is very well known in the COLT community. Motivated by the easiness of proofs for the cumulative risk, our open problem is to use the results on cumulative risk to prove corresponding individual-risk bounds.
RIS
TY - CPAPER TI - Bounds on Individual Risk for Log-loss Predictors AU - Peter D. Grünwald AU - Wojciech Kotłowski 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-grunwald11b PB - PMLR DP - Proceedings of Machine Learning Research VL - 19 SP - 813 EP - 816 L1 - http://proceedings.mlr.press/v19/grunwald11b/grunwald11b.pdf UR - https://proceedings.mlr.press/v19/grunwald11b.html AB - In sequential prediction with log-loss as well as density estimationwith risk measured by KL divergence, one is often interested in the expected instantaneous loss, or, equivalently, the individual risk at a given fixed sample size $n$. For Bayesianprediction and estimation methods, it is often easy to obtain bounds on the cumulative risk. Such results are based on bounding the individual sequence regret, a technique that is very well known in the COLT community. Motivated by the easiness of proofs for the cumulative risk, our open problem is to use the results on cumulative risk to prove corresponding individual-risk bounds. ER -
APA
Grünwald, P.D. & Kotłowski, W.. (2011). Bounds on Individual Risk for Log-loss Predictors. Proceedings of the 24th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 19:813-816 Available from https://proceedings.mlr.press/v19/grunwald11b.html.

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