Hypothesis testing for topological data analysis

Abstract

Persistence homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for observations that are persistence diagrams are limited. Specifically, there is a need for tests that can assess the strength of evidence against a claim that two samples arise from the same population or process. This expository paper provides an introduction to randomization-style null hypothesis significance tests (NHST) and shows how they can be used with sets of persistence diagrams. The hypothesis test is based on a loss function that comprises pairwise..