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

arXiv: https://arxiv.org/abs/2408.03142 · HTML: https://mlsanity.com/paper/2408.03142/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2024.

## Built on by (most cited first, 4 of 4)

- [Graph Distribution-valued Signals: A Wasserstein Space Perspective](https://mlsanity.com/paper/2509.25802/) (2025)
- [Statistical Testing on Directed Graphs by Surrogate Data Generation](https://mlsanity.com/paper/2606.00758/) (2026)
- [Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering](https://mlsanity.com/paper/2511.16111/) (2025)
- [Filter Learning for Subgraphs: Algebras and Performance Risk Bounds](https://mlsanity.com/paper/2607.21263/) (2026)

## Abstract (arXiv)

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.