Mesoscale two-sample testing for networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910050919907328 |
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| author | MacDonald, Peter W. Levina, Elizaveta Zhu, Ji |
| author_facet | MacDonald, Peter W. Levina, Elizaveta Zhu, Ji |
| contents | Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mesoscale two-sample testing for networks MacDonald, Peter W. Levina, Elizaveta Zhu, Ji Methodology Applications Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests. |
| title | Mesoscale two-sample testing for networks |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2410.17046 |