Connection Probabilities Estimation in Multi-layer Networks via Iterative Neighborhood Smoothing

TL;DR

This paper introduces MICE, an iterative method for estimating connection probabilities in multi-layer networks, improving accuracy and efficiency through joint neighborhood refinement, with proven consistency and superior performance in simulations and real data.

Contribution

The paper presents a novel iterative framework for connection probability estimation in multi-layer networks, combining layer and node neighborhood information with theoretical guarantees.

Findings

MICE achieves higher estimation accuracy than existing methods.

Theoretical analysis confirms the estimator's consistency and optimal convergence rate.

Empirical results demonstrate MICE's effectiveness in real-world network data.

Abstract

Understanding the structural mechanisms of multi-layer networks is essential for analyzing complex systems characterized by multiple interacting layers. This work studies the problem of estimating connection probabilities in multi-layer networks and introduces a new Multi-layer Iterative Connection Probability Estimation (MICE) method. The proposed approach employs an iterative framework that jointly refines inter-layer and intra-layer similarity sets by dynamically updating distance metrics derived from current probability estimates. By leveraging both layer-level and node-level neighborhood information, MICE improves estimation accuracy while preserving computational efficiency. Theoretical analysis establishes the consistency of the estimator and shows that, under mild regularity conditions, the proposed method achieves an optimal convergence rate comparable to that of an oracle estimator. Extensive simulation studies across diverse graphon structures demonstrate the superior performance of MICE relative to existing methods. Empirical evaluations using brain network data from patients with Attention-Deficit/Hyperactivity Disorder (ADHD) and global food and agricultural trade network data further illustrate the robustness and effectiveness of the method in link prediction tasks. Overall, this work provides a theoretically grounded and practically scalable framework for probabilistic modeling and inference in multi-layer network systems.