Multiple Hypothesis Testing with Persistent Homology

Mikael Vejdemo-Johansson, Sayan Mukherjee

Keywords: multiple hypothesis testing, persistent homology, fwer correction

TL;DR: We describe a way to do one-sample persistent homology hypothesis testing with multiple hypothesis correction.

Abstract:

Multiple hypothesis testing requires a control procedure.
Simply increasing simulations or permutations to meet a Bonferroni-style threshold is prohibitively expensive.
In this paper we propose a null model based approach to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control method that does not suffer from these computational costs.

Previous Submission: Yes