Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling
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
Text
Minsker. "Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling." Annual Conference on Computational Learning Theory, 2013.Markdown
[Minsker. "Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling." Annual Conference on Computational Learning Theory, 2013.](https://mlanthology.org/colt/2013/minsker2013colt-estimation/)BibTeX
@inproceedings{minsker2013colt-estimation,
title = {{Estimation of Extreme Values and Associated Level Sets of a Regression Function via Selective Sampling}},
author = {Minsker, Stanislav},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2013},
pages = {105-121},
url = {https://mlanthology.org/colt/2013/minsker2013colt-estimation/}
}