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.
%0 Journal Article
%1 vejdemojohansson2022multiple
%A Vejdemo-Johansson, Mikael
%A Mukherjee, Sayan
%D 2022
%J Foundations of Data Science
%K Persistent_homology false_discovery_rate family-wise_error_rate hypothesis_testing multiple_hypothesis_control
%N 4
%P 667--705
%R 10.3934/fods.2022018
%T Multiple hypothesis testing with persistent homology
%U https://www.aimsciences.org/article/id/63610aba6aa93c5ff77671ee
%V 4
%X 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.
@article{vejdemojohansson2022multiple,
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.},
added-at = {2024-10-02T13:52:45.000+0200},
author = {Vejdemo-Johansson, Mikael and Mukherjee, Sayan},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/20ae02e9e526b5d60bbea08894353c6b7/scadsfct},
doi = {10.3934/fods.2022018},
interhash = {40c05d69eaec8323aed49b085523e14c},
intrahash = {0ae02e9e526b5d60bbea08894353c6b7},
journal = {Foundations of Data Science},
keywords = {Persistent_homology false_discovery_rate family-wise_error_rate hypothesis_testing multiple_hypothesis_control},
number = 4,
pages = {667--705},
timestamp = {2024-10-02T13:52:45.000+0200},
title = {Multiple hypothesis testing with persistent homology},
url = {https://www.aimsciences.org/article/id/63610aba6aa93c5ff77671ee},
volume = 4,
year = 2022
}
