Network Cross-Validation for Nested Models by Edge-Sampling
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918111285870592 |
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| author | Yang, Bokai Chen, Yuanxing Yang, Yuhong |
| author_facet | Yang, Bokai Chen, Yuanxing Yang, Yuhong |
| contents | In the network literature, a wide range of statistical models has been proposed to exploit structural patterns in the data. Therefore, model selection between different models is a fundamental problem. However, there remains a lack of systematic theoretical understanding for this problem when comparing across different model classes. In this paper, to address this challenging problem, we propose a penalized edge-sampling cross-validation framework for nested network model selection. By incorporating a model complexity penalty into the evaluation process, our method effectively mitigates the overfitting tendency of cross-validation and adapts to varying model structures. This framework supports comparisons among widely used models, including stochastic block models (SBMs), degree-corrected SBMs (DCBMs), and graphon models, providing the first consistency guarantees for model selection across these settings to our knowledge. Empirical evaluations, including both simulated data and the ``Political Books'' network, demonstrate that our method yields stable and accurate performance across various scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14244 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Network Cross-Validation for Nested Models by Edge-Sampling Yang, Bokai Chen, Yuanxing Yang, Yuhong Methodology 62G20(Primary) 62H30, 05C80(Secondary) In the network literature, a wide range of statistical models has been proposed to exploit structural patterns in the data. Therefore, model selection between different models is a fundamental problem. However, there remains a lack of systematic theoretical understanding for this problem when comparing across different model classes. In this paper, to address this challenging problem, we propose a penalized edge-sampling cross-validation framework for nested network model selection. By incorporating a model complexity penalty into the evaluation process, our method effectively mitigates the overfitting tendency of cross-validation and adapts to varying model structures. This framework supports comparisons among widely used models, including stochastic block models (SBMs), degree-corrected SBMs (DCBMs), and graphon models, providing the first consistency guarantees for model selection across these settings to our knowledge. Empirical evaluations, including both simulated data and the ``Political Books'' network, demonstrate that our method yields stable and accurate performance across various scenarios. |
| title | Network Cross-Validation for Nested Models by Edge-Sampling |
| topic | Methodology 62G20(Primary) 62H30, 05C80(Secondary) |
| url | https://arxiv.org/abs/2506.14244 |