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

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Stanislav Minsker
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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.

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