Weighted-Graph-Based Change Point Detection

TL;DR

This paper introduces a nonparametric, graph-based method for detecting and localizing change points in data sequences, improving accuracy and power over existing techniques, with theoretical guarantees and real data application.

Contribution

It develops new graph-based test statistics for change point detection that incorporate edge weights, extending to multiple change points with proven theoretical properties.

Findings

Enhanced testing power and localization accuracy in simulations

Accurate control of type I error through analytic approximations

Theoretical guarantees on change point detection and localization

Abstract

We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.