Publications [#368302] of Sayan Mukherjee

Papers Published

1. Vejdemo-Johansson, M; Mukherjee, S, MULTIPLE HYPOTHESIS TESTING WITH PERSISTENT HOMOLOGY, Foundations of Data Science, vol. 4 no. 4 (January, 2022), pp. 667-705 [doi]
   (last updated on 2025/02/21)

   Abstract:
   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.