A Generalized Graph Signal Processing Framework for Multiple Hypothesis Testing over Networks
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913874904612864 |
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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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalized Graph Signal Processing Framework for Multiple Hypothesis Testing over Networks Jian, Xingchao Gölz, Martin Ji, Feng Tay, Wee Peng Zoubir, Abdelhak M. Signal Processing Information Theory 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. |
| title | A Generalized Graph Signal Processing Framework for Multiple Hypothesis Testing over Networks |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2506.03496 |