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In this paper, we extend the recently proposed multivariate rank energydistance, based on the theory of optimal transport, for statistical testing ofdistributional similarity, to soft rank energy distance. Being differentiable,this in turn allows us to extend the rank energy to a subspace robust rankenergy distance, dubbed Projected soft-Rank Energy distance, which can becomputed via optimization over the Stiefel manifold. We show via experimentsthat using projected soft rank energy one can trade-off the detection power vsthe false alarm via projections onto an appropriately selected low dimensionalsubspace. We also show the utility of the proposed tests on unsupervised changepoint detection in multivariate time series data. All codes are publiclyavailable at the link provided in the experiment section.

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