Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling

Stanislav Minsker
Proceedings of the 26th Annual Conference on Learning Theory, PMLR 30:105-121, 2013.

Abstract

We propose a new method for estimating the locations and the value of an absolute maximum (minimum) of a function from the observations contaminated by random noise. Our goal is to solve the problem under minimal regularity and shape constraints. In particular, we do not assume differentiability of a function nor that its maximum is attained at a single point. We provide tight upper and lower bounds for the performance of proposed estimators. Our method is adaptive with respect to the unknown parameters of the problem over a large class of underlying distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v30-Minsker13, title = {Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling}, author = {Minsker, Stanislav}, booktitle = {Proceedings of the 26th Annual Conference on Learning Theory}, pages = {105--121}, year = {2013}, editor = {Shalev-Shwartz, Shai and Steinwart, Ingo}, volume = {30}, series = {Proceedings of Machine Learning Research}, address = {Princeton, NJ, USA}, month = {12--14 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v30/Minsker13.pdf}, url = {https://proceedings.mlr.press/v30/Minsker13.html}, abstract = {We propose a new method for estimating the locations and the value of an absolute maximum (minimum) of a function from the observations contaminated by random noise. Our goal is to solve the problem under minimal regularity and shape constraints. In particular, we do not assume differentiability of a function nor that its maximum is attained at a single point. We provide tight upper and lower bounds for the performance of proposed estimators. Our method is adaptive with respect to the unknown parameters of the problem over a large class of underlying distributions.} }
Endnote
%0 Conference Paper %T Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling %A Stanislav Minsker %B Proceedings of the 26th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2013 %E Shai Shalev-Shwartz %E Ingo Steinwart %F pmlr-v30-Minsker13 %I PMLR %P 105--121 %U https://proceedings.mlr.press/v30/Minsker13.html %V 30 %X We propose a new method for estimating the locations and the value of an absolute maximum (minimum) of a function from the observations contaminated by random noise. Our goal is to solve the problem under minimal regularity and shape constraints. In particular, we do not assume differentiability of a function nor that its maximum is attained at a single point. We provide tight upper and lower bounds for the performance of proposed estimators. Our method is adaptive with respect to the unknown parameters of the problem over a large class of underlying distributions.
RIS
TY - CPAPER TI - Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling AU - Stanislav Minsker BT - Proceedings of the 26th Annual Conference on Learning Theory DA - 2013/06/13 ED - Shai Shalev-Shwartz ED - Ingo Steinwart ID - pmlr-v30-Minsker13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 30 SP - 105 EP - 121 L1 - http://proceedings.mlr.press/v30/Minsker13.pdf UR - https://proceedings.mlr.press/v30/Minsker13.html AB - We propose a new method for estimating the locations and the value of an absolute maximum (minimum) of a function from the observations contaminated by random noise. Our goal is to solve the problem under minimal regularity and shape constraints. In particular, we do not assume differentiability of a function nor that its maximum is attained at a single point. We provide tight upper and lower bounds for the performance of proposed estimators. Our method is adaptive with respect to the unknown parameters of the problem over a large class of underlying distributions. ER -
APA
Minsker, S.. (2013). Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling. Proceedings of the 26th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 30:105-121 Available from https://proceedings.mlr.press/v30/Minsker13.html.

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