Topological density estimation

TL;DR

Topological density estimation (TDE) is a novel method that infers the multimodal structure of a density function to improve bandwidth selection in kernel density estimation, offering better performance and runtime.

Contribution

This paper introduces TDE, a new approach leveraging topological inference for improved bandwidth selection in kernel density estimation.

Findings

TDE outperforms competing methods on highly multimodal densities.

TDE provides useful auxiliary information about density structure.

TDE can assess its own suitability for specific data.

Abstract

We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We show that TDE has performance and runtime advantages over competing methods of kernel density estimation for highly multimodal probability density functions. We also show that TDE yields useful auxiliary information, that it can determine its own suitability for use, and we explain its performance.