A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control

TL;DR

This paper introduces a graph signal processing approach to multiple hypothesis testing in sensor networks, enabling accurate false discovery rate control by leveraging the joint spatio-temporal structure of data.

Contribution

It proposes a novel method that models p-value distributions and hypotheses as bandlimited graph signals, providing consistent estimates and asymptotic FDR control.

Findings

Effective FDR control demonstrated in simulations

Outperforms existing multiple testing methods

Accurate estimation of local false discovery rates

Abstract

We consider a multiple hypothesis testing problem in a sensor network over the joint spatio-temporal domain. The sensor network is modeled as a graph, with each vertex representing a sensor and a signal over time associated with each vertex. We assume a hypothesis test and an associated $p$-value for every sample point in the joint spatio-temporal domain. Our goal is to determine which points have true alternative. By parameterizing the unknown $p$-value distribution under the alternative and the prior probabilities of hypotheses being null with a bandlimited generalized graph signal, we can obtain consistent estimates for them. Consequently, we also obtain an estimate of the local false discovery rates (lfdr). We prove that by using a step-up procedure on the estimated lfdr, we can achieve asymptotic false discovery rate control at a pre-determined level. Numerical experiments validate the effectiveness of our approach compared to existing methods.