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

2025-04-06

IEEE International Conference on Acoustics, Speech, and Signal Processing

AI Summary

This paper addresses the multiple hypothesis testing (MHT) problem on the joint domain of graphs and measure spaces, aiming to assign p-values to each spatiotemporal sampling point and achieve globally coordinated decision-making. To overcome the limitation of conventional methods—reliance on homogeneous priors and alternative distributions—we propose a generalized graph signal modeling framework that, for the first time, unifies inhomogeneous priors and heterogeneous alternatives as graph signals defined over the joint domain. Integrating graph signal processing, nonparametric Bayesian inference, and spatiotemporal statistical modeling, we develop a p-value aggregation and calibration method grounded in graph Fourier transform. Theoretically, our approach guarantees false discovery rate (FDR) control while maximizing statistical power. Experiments on synthetic and real-world sensor network data demonstrate an average 18.7% improvement in recall under FDR constraints, alongside strong scalability and practical applicability.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Extend MHT to joint graph-measure space domains
• Model inhomogeneous null-alternative distributions via graph signals
• Develop powerful detection using joint domain information

Innovation

• Extends two-groups model for inhomogeneous data
• Uses generalized graph signal for modeling
• Enhances detection via joint domain information