Multilayer random dot product graphs: Estimation and online change point detection
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909219982147584 |
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| author | Wang, Fan Li, Wanshan Padilla, Oscar Hernan Madrid Yu, Yi Rinaldo, Alessandro |
| author_facet | Wang, Fan Li, Wanshan Padilla, Oscar Hernan Madrid Yu, Yi Rinaldo, Alessandro |
| contents | We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework. At every time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and latent positions but allow for different connectivity matrices. We propose efficient tensor algorithms under both fixed and random latent position cases to minimize the detection delay while controlling false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimation that is applicable to a wide range of scenarios, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online https://github.com/MountLee/MRDPG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15286 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multilayer random dot product graphs: Estimation and online change point detection Wang, Fan Li, Wanshan Padilla, Oscar Hernan Madrid Yu, Yi Rinaldo, Alessandro Methodology We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework. At every time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and latent positions but allow for different connectivity matrices. We propose efficient tensor algorithms under both fixed and random latent position cases to minimize the detection delay while controlling false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimation that is applicable to a wide range of scenarios, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online https://github.com/MountLee/MRDPG. |
| title | Multilayer random dot product graphs: Estimation and online change point detection |
| topic | Methodology |
| url | https://arxiv.org/abs/2306.15286 |