The sample complexity of level set approximation
Statistics Theory
2021-02-24 v2 Machine Learning
Statistics Theory
Abstract
We study the problem of approximating the level set of an unknown function by sequentially querying its values. We introduce a family of algorithms called Bisect and Approximate through which we reduce the level set approximation problem to a local function approximation problem. We then show how this approach leads to rate-optimal sample complexity guarantees for H{\"o}lder functions, and we investigate how such rates improve when additional smoothness or other structural assumptions hold true.
Cite
@article{arxiv.2010.13405,
title = {The sample complexity of level set approximation},
author = {François Bachoc and Tommaso Cesari and Sébastien Gerchinovitz},
journal= {arXiv preprint arXiv:2010.13405},
year = {2021}
}