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arXiv · 2601.20219

Joint Estimation of Edge Probabilities for Multi-layer Networks via Neighborhood Smoothing

Yong He·Zizhou Huang·Bingyi Jing·Diqing Li
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Abstract

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.

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Yong He, Zizhou Huang, Bingyi Jing, Diqing Li. 2026-01-28. Joint Estimation of Edge Probabilities for Multi-layer Networks via Neighborhood Smoothing. https://arxiv.org/abs/2601.20219

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