Concentration bounds for intrinsic dimension estimation using Gaussian kernels

TL;DR

This paper establishes finite-sample concentration bounds for intrinsic dimension estimation with Gaussian kernels, detailing how sample size, bandwidth, and data regularity affect accuracy, and introduces a heuristic for bandwidth selection.

Contribution

It provides explicit finite-sample bounds for Gaussian kernel-based dimension estimation and proposes a practical bandwidth selection heuristic.

Findings

Explicit finite-sample concentration bounds derived

Bandwidth selection heuristic proposed and validated

Bounds depend on sample size, bandwidth, and data regularity

Abstract

We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters, characterizing precisely how regularity conditions influence statistical performance. We also propose a bandwidth selection heuristic using derivative information, supported by numerical experiments.