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人工智能论文:子空间鲁棒WASSERSTEIN距离(Subspace Robust Wasserstein distances)

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dabiao2008 发表于 2019-1-28 11:04:55 | 显示全部楼层 |阅读模式
dabiao2008 2019-1-28 11:04:55 174 0 显示全部楼层
人工智能论文:子空间鲁棒WASSERSTEIN距离(Subspace Robust Wasserstein distances)在高维设置中理解离散测量之间的Wasserstein距离仍然是一个挑战。最近的工作主张采用两步方法来改善鲁棒性并促进最优传输的计算,例如使用随机实线上的投影,或初始量化以减少点数。我们在这项工作中提出了一个新的Wasserstein距离的稳健变体。这个量捕获了这两个度量之间可以实现的最大可能距离,它们在较低的k维子空间上正交投影之后。我们证明了这个距离继承了OT的几个有利的属性,并且计算它可以被铸造为凸的问题。涉及由运输计划引起的位移的二阶矩矩阵的顶部keigenvalues。我们提供了使用熵正则化近似计算这个点的算法,并根据经验说明了这种方法的兴趣。
Making sense of Wasserstein distances between discrete measures inhigh-dimensional settings remains a challenge.Recent work has advocated atwo-step approach to improve robustness and facilitate the computation ofoptimal transport, using for instance projections on random real lines, or apreliminary quantization to reduce the number of points.We propose in thiswork a new robust variant of the Wasserstein distance.This quantity capturesthe maximal possible distance that can be realized between these two measures,after they have been projected orthogonally on a lower k dimensional subspace.We show that this distance inherits several favorably properties of OT, andthat computing it can be cast as a convex probleminvolving the top keigenvalues of the second order moment matrix of the displacements induced by atransport plan.We provide algorithms to approximate the computation of thissaddle point using entropic regularization, and illustrate the interest of thisapproach empirically.人工智能论文:子空间鲁棒WASSERSTEIN距离(Subspace Robust Wasserstein distances) cvB0B8lLz8SSgSI2.jpg
URL地址:https://arxiv.org/abs/1901.08949     ----pdf下载地址:https://arxiv.org/pdf/1901.08949    ----人工智能论文:子空间鲁棒WASSERSTEIN距离(Subspace Robust Wasserstein distances)
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