Modeling Non-Uniform Hypergraphs Using Determinantal Point Processes
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| Format: | Preprint |
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2025
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| _version_ | 1866909788939485184 |
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| author | Chen, Yichao Zhang, Jingfei Zhu, Ji |
| author_facet | Chen, Yichao Zhang, Jingfei Zhu, Ji |
| contents | Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a natural representation for these networks, with each hyperedge representing a set of nodes. The majority of existing hypergraph models assume uniform hyperedges (i.e., edges of the same size) or rely on diversity among nodes. In this work, we propose a new hypergraph model based on non-symmetric determinantal point processes. The proposed model naturally accommodates non-uniform hyperedges, has tractable probability mass functions, and accounts for both node similarity and diversity in hyperedges. For model estimation, we maximize the likelihood function under constraints using a computationally efficient projected adaptive gradient descent algorithm. We establish the consistency and asymptotic normality of the estimator. Simulation studies confirm the efficacy of the proposed model, and its utility is further demonstrated through edge predictions on several real-world datasets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12028 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling Non-Uniform Hypergraphs Using Determinantal Point Processes Chen, Yichao Zhang, Jingfei Zhu, Ji Methodology Statistics Theory Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a natural representation for these networks, with each hyperedge representing a set of nodes. The majority of existing hypergraph models assume uniform hyperedges (i.e., edges of the same size) or rely on diversity among nodes. In this work, we propose a new hypergraph model based on non-symmetric determinantal point processes. The proposed model naturally accommodates non-uniform hyperedges, has tractable probability mass functions, and accounts for both node similarity and diversity in hyperedges. For model estimation, we maximize the likelihood function under constraints using a computationally efficient projected adaptive gradient descent algorithm. We establish the consistency and asymptotic normality of the estimator. Simulation studies confirm the efficacy of the proposed model, and its utility is further demonstrated through edge predictions on several real-world datasets. |
| title | Modeling Non-Uniform Hypergraphs Using Determinantal Point Processes |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2509.12028 |