Minimal Unimodal Decompositions on Trees

TL;DR

This paper introduces an efficient algorithm for decomposing a density function on a finite metric tree into a minimal sum of unimodal components, advancing the understanding of unimodal categories in topological data analysis.

Contribution

It provides the first efficient algorithm for minimal unimodal decomposition of tame density functions on finite metric trees, a key problem in topological statistics.

Findings

Algorithm successfully computes minimal unimodal decompositions

Improves computational efficiency over previous methods

Enhances topological analysis of density functions on trees

Abstract

The decomposition of a density function on a domain into a minimal sum of unimodal components is a fundamental problem in statistics, leading to the topological invariant of unimodal category of a density. This paper gives an efficient algorithm for the construction of a minimal unimodal decomposition of a tame density function on a finite metric tree.