  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.
