Change-point detection in dynamic networks via graphon estimation

TL;DR

This paper introduces a model-free, graphon-based method for detecting change-points in dynamic networks, demonstrating superior accuracy and robustness through theoretical guarantees and numerical experiments.

Contribution

It develops a novel graphon estimation technique and a change-point detection algorithm that outperform existing methods, especially in large networks.

Findings

Faster convergence rate in large networks.

Robust detection across various dynamic network types.

Superior performance over existing methods.

Abstract

We propose a general approach for change-point detection in dynamic networks. The proposed method is model-free and covers a wide range of dynamic networks. The key idea behind our approach is to effectively utilize the network structure in designing change-point detection algorithms. This is done via an initial step of graphon estimation, where we propose a modified neighborhood smoothing~(MNBS) algorithm for estimating the link probability matrices of a dynamic network. Based on the initial graphon estimation, we then develop a screening and thresholding algorithm for multiple change-point detection in dynamic networks. The convergence rate and consistency for the change-point detection procedure are derived as well as those for MNBS. When the number of nodes is large~(e.g., exceeds the number of temporal points), our approach yields a faster convergence rate in detecting change-points comparing with an algorithm that simply employs averaged information of the dynamic network across time. Numerical experiments demonstrate robust performance of the proposed algorithm for change-point detection under various types of dynamic networks, and superior performance over existing methods is observed. A real data example is provided to illustrate the effectiveness and practical impact of the procedure.