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

The detection of interesting or anomalous signal behavior using sensor networks plays a key role in many applications. In this work, we model the sensor network as a graph, with each vertex representing a sensor and a signal over time associated with each vertex. The objective is to identify the true state of the signal at each point in the joint spatio-temporal domain. We propose a step-up empirical Bayes multiple hypothesis testing approach to make decisions based on local summary statistics. To this end, we establish consistent estimates of the prior probability of the null hypothesis as well as the probability models under the alternative, which are obtained using a bandlimited generalized graph signal model. Asymptotic control of the false discovery rate is proven. Numerical experiments validate the effectiveness of our approach compared to existing methods.