The sample complexity of level set approximation

François Bachoc (1) , Tommaso R Cesari (2) , Sébastien Gerchinovitz (3, 1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TSE-R - Toulouse School of Economics
3 IRT Saint Exupéry - Institut de Recherche Technologique

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 Hölder functions, and we investigate how such rates improve when additional smoothness or other structural assumptions hold true.

Domains: Statistics [math.ST]; Machine Learning [stat.ML]

François Bachoc, Tommaso R Cesari, Sébastien Gerchinovitz. The sample complexity of level set approximation. 2020. ⟨hal-02976018v1⟩