Weighted-Graph-Based Change Point Detection

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.

RING-CPD: Asymptotic Distribution-free Change-point Detection for Multivariate and Non-Euclidean Data

“…We compare the proposed method to GET and MET on k-MST using the R package gSeg (Chu and Chen, 2019) with k = [ √ n], the method using Bayesiantype statistic based on the shortest Hamiltonian path (Shi, Wu and Rao, 2017) (SWR), the method based on Fréchet means and variances (Dubey and Müller, 2020) (DM). We also compare with three interpoint distance-based methods, the widely used distance-based method E-Divisive (ED) (Matteson and James, 2014) implemented in the R package ecp, and the other two methods proposed recently by Li (2020) and Nie and Nicolae (2021). Li (2020) proposed four statistics and we compare the statistic C 2N that had the satisfactory performance in most of their simulation settings.…”

“…A few nonparametric methods have been proposed, including kernel-based methods (Desobry, Davy and Doncarli, 2005;Li et al, 2015;Garreau and Arlot, 2018;Arlot, Celisse and Harchaoui, 2019;Chang et al, 2019), interpoint distance-based methods (Matteson and James, 2014;Li, 2020) and graph-based methods (Chen and Zhang, 2015;Shi, Wu and Rao, 2017;Zhang and Chen, 2017;Chu and Chen, 2019;Chen, 2019;Song and Chen, 2020;Liu and Chen, 2020;Nie and Nicolae, 2021). However, many existing kernel-based and distancebased methods suffered from the curse of dimensionality for high-dimensional data (Chen and Friedman, 2017), thus losing power for some common types of changes.…”