A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915115095293952 |
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| author | Jian, Xingchao Gölz, Martin Ji, Feng Tay, Wee Peng Zoubir, Abdelhak M. |
| author_facet | Jian, Xingchao Gölz, Martin Ji, Feng Tay, Wee Peng Zoubir, Abdelhak M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control Jian, Xingchao Gölz, Martin Ji, Feng Tay, Wee Peng Zoubir, Abdelhak M. Signal Processing 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. |
| title | A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2408.03142 |