Skip to main content

MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY

Publication ,  Journal Article
Vejdemo-Johansson, M; Mukherjee, S
Published in: Foundations of Data Science
January 1, 2022

In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational effi- ciency 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.

Duke Scholars

Published In

Foundations of Data Science

DOI

EISSN

2639-8001

Publication Date

January 1, 2022

Volume

4

Issue

4

Start / End Page

667 / 705
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Vejdemo-Johansson, M., & Mukherjee, S. (2022). MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY. Foundations of Data Science, 4(4), 667–705. https://doi.org/10.3934/fods.2022018
Vejdemo-Johansson, M., and S. Mukherjee. “MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY.” Foundations of Data Science 4, no. 4 (January 1, 2022): 667–705. https://doi.org/10.3934/fods.2022018.
Vejdemo-Johansson M, Mukherjee S. MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY. Foundations of Data Science. 2022 Jan 1;4(4):667–705.
Vejdemo-Johansson, M., and S. Mukherjee. “MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY.” Foundations of Data Science, vol. 4, no. 4, Jan. 2022, pp. 667–705. Scopus, doi:10.3934/fods.2022018.
Vejdemo-Johansson M, Mukherjee S. MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY. Foundations of Data Science. 2022 Jan 1;4(4):667–705.

Published In

Foundations of Data Science

DOI

EISSN

2639-8001

Publication Date

January 1, 2022

Volume

4

Issue

4

Start / End Page

667 / 705