A Generalized Graph Signal Processing Framework for Multiple Hypothesis Testing over Networks

TL;DR

This paper introduces a flexible graph signal processing framework for multiple hypothesis testing over networks, enhancing detection power by modeling inhomogeneity across the joint domain of graph and measure space.

Contribution

It extends the traditional two-groups model to incorporate inhomogeneous priors and distributions using generalized graph signals, enabling more effective hypothesis testing over complex domains.

Findings

Improved detection power over traditional methods

Effective modeling of inhomogeneity in hypothesis testing

Framework applicable to sensor networks and similar domains

Abstract

We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make decisions for all hypotheses simultaneously, using all available $p$-values. In practice, this problem resembles the detection problem over a sensor network during a period of time. To solve this problem, we extend the traditional two-groups model such that the prior probability of the null hypothesis and the alternative distribution of $p$-values can be inhomogeneous over the joint domain. We model the inhomogeneity via a generalized graph signal. This more flexible statistical model yields a more powerful detection strategy by leveraging the information from the joint domain.