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/}
}