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

arXiv: https://arxiv.org/abs/2103.08811 · HTML: https://mlsanity.com/paper/2103.08811/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 16 Mar 2021.

## Builds on (most cited first, 6 of 6)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation](https://mlsanity.com/paper/1909.08733/) (2019)
- [Two-sample Test using Projected Wasserstein Distance](https://mlsanity.com/paper/2010.11970/) (2020)
- [Optimal Transport Based Change Point Detection and Time Series Segment Clustering](https://mlsanity.com/paper/1911.01325/) (2019)
- [On Matched Filtering for Statistical Change Point Detection](https://mlsanity.com/paper/2006.05539/) (2020)

## Abstract (arXiv)

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.