Multiple testing with persistent homology

Mikael Vejdemo-Johansson; Sayan Mukherjee

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arXiv · 1812.06491

Multiple testing with persistent homology

Mikael Vejdemo-Johansson·Sayan Mukherjee

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Abstract

In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the observation that one can empirically simulate a null distribution that is universal across many hypothesis testing applications involving persistence homology. Our observation suggests that one can simulate the null distribution efficiently based on a small number of summaries of the collected data and use this null in the same way that p-value tables were used in classical statistics. To illustrate the efficiency and utility of the null distribution we provide procedures for rejecting acyclicity with both control of the Family-Wise Error Rate (FWER) and the False Discovery Rate (FDR). We will argue that the empirical null we propose is very general conditional on a few summaries of the data based on simulations and limit theorems for persistent homology for point processes.

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BibTeX RIS

Mikael Vejdemo-Johansson, Sayan Mukherjee. 2018-12-16. Multiple testing with persistent homology. https://arxiv.org/abs/1812.06491

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