Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes
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| Format: | Preprint |
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2020
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| _version_ | 1866918376486469632 |
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| author | Agterberg, Joshua Tang, Minh Priebe, Carey |
| author_facet | Agterberg, Joshua Tang, Minh Priebe, Carey |
| contents | Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product graph, which considers as special cases a number of popular network models with low-rank expectations. We then propose a nonparametric two-sample test statistic to conduct this test, assuming only that the networks have independent edges generated from low-rank probability matrices. Our proposed test statistic involves using the maximum mean discrepancy applied to suitably rotated rows of a graph embedding, where the rotation is estimated using optimal transport. We show that our test statistic, appropriately scaled, is consistent for sufficiently dense graphs, and we study its convergence under different sparsity regimes, and our results are demonstrated in numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_09828 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes Agterberg, Joshua Tang, Minh Priebe, Carey Statistics Theory Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product graph, which considers as special cases a number of popular network models with low-rank expectations. We then propose a nonparametric two-sample test statistic to conduct this test, assuming only that the networks have independent edges generated from low-rank probability matrices. Our proposed test statistic involves using the maximum mean discrepancy applied to suitably rotated rows of a graph embedding, where the rotation is estimated using optimal transport. We show that our test statistic, appropriately scaled, is consistent for sufficiently dense graphs, and we study its convergence under different sparsity regimes, and our results are demonstrated in numerical simulations. |
| title | Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2012.09828 |