Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport

TL;DR

This paper introduces a differentiable, subspace-robust multivariate rank test based on entropy-regularized optimal transport, enabling improved distributional similarity testing and change point detection in multivariate data.

Contribution

It extends multivariate rank energy distance to a differentiable, subspace-robust form using optimal transport, facilitating flexible and efficient statistical testing.

Findings

Projected soft rank energy balances detection power and false alarms.

The method effectively detects change points in multivariate time series.

Code implementation is publicly available for reproducibility.

Abstract

In this paper, we extend the recently proposed multivariate rank energy distance, based on the theory of optimal transport, for statistical testing of distributional similarity, to soft rank energy distance. Being differentiable, this in turn allows us to extend the rank energy to a subspace robust rank energy distance, dubbed Projected soft-Rank Energy distance, which can be computed via optimization over the Stiefel manifold. We show via experiments that using projected soft rank energy one can trade-off the detection power vs the false alarm via projections onto an appropriately selected low dimensional subspace. We also show the utility of the proposed tests on unsupervised change point detection in multivariate time series data. All codes are publicly available at the link provided in the experiment section.