Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport
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by
Shoaib Bin Masud, Boyang Lyu, Shuchin Aeron
2021
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.
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