Robust and efficient change point detection using novel multivariate rank-energy GoF test

Abstract: In this paper, we use and further develop upon a recently proposed multivariate, distribution-free Goodness-of-Fit (GoF) test based on the theory of Optimal Transport (OT) called the Rank Energy (RE) [1], for non-parametric and unsupervised Change Point Detection (CPD) in multivariate time series data. We show that directly using RE leads to high sensitivity to very small changes in distributions (causing high false alarms) and it requires large sample complexity and huge computational cost. To alleviate these drawbacks, we propose a new GoF test statistic called as soft-Rank Energy (sRE) that is based on entropy regularized OT and employ it towards CPD. We discuss the advantages of using sRE over RE and demonstrate that the proposed sRE based CPD outperforms all the existing methods in terms of Area Under the Curve (AUC) and F1-score on real and synthetic data sets.