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

TL;DR

This paper introduces a novel multi-layer graphon model and a neighborhood smoothing algorithm for joint estimation of edge probabilities in multi-layer networks, demonstrating improved performance on real data.

Contribution

The paper proposes a new multi-layer graphon model and an efficient neighborhood smoothing method that leverages similarities across layers and nodes for better edge probability estimation.

Findings

Outperforms existing methods in simulations

Achieves better link prediction on real network data

Requires minimal tuning and is computationally efficient

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.