Likelihood-based Inference for Random Networks with Changepoints

TL;DR

This paper introduces a likelihood-based approach for detecting changepoints in evolving undirected networks, providing theoretical guarantees and practical methods for identifying shifts in network structure over time.

Contribution

It develops a novel likelihood-based framework for changepoint detection in affine preferential attachment networks, including hypothesis testing, estimation, and extensions to multiple changepoints.

Findings

Proposes a consistent estimator for a single changepoint.

Extends methodology to multiple changepoints with efficient algorithms.

Demonstrates effectiveness through simulations and Twitter network data.

Abstract

Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying data-generative mechanism itself is invariant with time. Such observation leads to the study of changepoints or sudden shifts in the distributional structure of the evolving network. In this paper, we propose a likelihood-based methodology to detect changepoints in undirected, affine preferential attachment networks, and establish a hypothesis testing framework to detect a single changepoint, together with a consistent estimator for the changepoint. Such results require establishing consistency and asymptotic normality of the MLE under the changepoint regime, which suffers from long range dependence. The methodology is then extended to the multiple changepoint setting via both a sliding window method and a more computationally efficient score statistic. We also compare the proposed methodology with previously developed non-parametric estimators of the changepoint via simulation, and the methods developed herein are applied to modeling the popularity of a topic in a Twitter network over time.