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.

翻译：在本文中,我们根据最佳运输理论,将最近提出的用于分配相似性统计测试的多变级级能源距离扩大至柔性级能源距离。不同之处在于,这反过来又使我们能够将级能源扩大到一个亚空间强级能源距离,即所谓的预测软兰克能源距离,可以通过优化施蒂费尔方块进行计算。我们通过实验发现,使用预测的软级能源,可以通过投射到一个适当选定的低维次空间,将检测力与假警报相权衡。我们还展示了在多变时间序列数据中进行不受监督的变化点探测的拟议测试的效用。所有代码都可以在实验部分提供的链接上公开查阅。