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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.20219 |
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| _version_ | 1866914285827915776 |
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| author | He, Yong Huang, Zizhou Jing, Bingyi Li, Diqing |
| author_facet | He, Yong Huang, Zizhou Jing, Bingyi Li, Diqing |
| contents | In this paper we focus on jointly estimating the edge probabilities for multi-layer networks. We define a novel multi-layer graphon, a ternary function in contrast to the bivariate graphon function in the literature by introducing an additional latent layer position parameter, which is model-free and covers a wide range of multi-layer networks. We develop a computationally efficient two-step neighborhood smoothing algorithm to estimate the edge probabilities of multi-layer networks, which requires little tuning and fully utilize the similarity across both network layers and nodes. Numerical experiments demonstrate the advantages of our method over the existing state-of-the-art ones. A real Worldwide Food Import/Export Network dataset example is analyzed to illustrate the better performance of the proposed method over benchmark methods in terms of link prediction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20219 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Joint Estimation of Edge Probabilities for Multi-layer Networks via Neighborhood Smoothing He, Yong Huang, Zizhou Jing, Bingyi Li, Diqing Methodology In this paper we focus on jointly estimating the edge probabilities for multi-layer networks. We define a novel multi-layer graphon, a ternary function in contrast to the bivariate graphon function in the literature by introducing an additional latent layer position parameter, which is model-free and covers a wide range of multi-layer networks. We develop a computationally efficient two-step neighborhood smoothing algorithm to estimate the edge probabilities of multi-layer networks, which requires little tuning and fully utilize the similarity across both network layers and nodes. Numerical experiments demonstrate the advantages of our method over the existing state-of-the-art ones. A real Worldwide Food Import/Export Network dataset example is analyzed to illustrate the better performance of the proposed method over benchmark methods in terms of link prediction. |
| title | Joint Estimation of Edge Probabilities for Multi-layer Networks via Neighborhood Smoothing |
| topic | Methodology |
| url | https://arxiv.org/abs/2601.20219 |