Outlier-Robust Optimal Transport
Outlier-Robust Optimal Transport
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发表时间：
2020-12
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通讯作者：
Debarghya Mukherjee;Aritra Guha;J. Solomon;Yuekai Sun;M. Yurochkin
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作者：
Debarghya Mukherjee;Aritra Guha;J. Solomon;Yuekai Sun;M. Yurochkin
最佳传输（OT）提供了一种测量分布之间距离的方法，这取决于样本空间的几何形状。鉴于近年来求解OT问题的进展，OT距离被广泛地用作最小距离估计中的损失函数。尽管它的流行和优势，然而，OT是极其敏感的异常值。一个单独的对抗性异常点可以任意地增加OT距离。为了解决这个问题，在这项工作中，我们提出了一个异常稳健的OT公式。我们的公式是凸的，但第一眼就很难缩放。我们推导了一个基于代价截断的\emph{等价}公式，该公式易于纳入正则化OT的现代随机算法中。我们演示了我们的模型在模拟中应用于Huber污染模型下的均值估计以及在实际数据上的离群值检测。
Optimal transport (OT) provides a way of measuring distances between distributions that depends on the geometry of the sample space. In light of recent advances in solving the OT problem, OT distances are widely used as loss functions in minimum distance estimation. Despite its prevalence and advantages, however, OT is extremely sensitive to outliers. A single adversarially-picked outlier can increase OT distance arbitrarily. To address this issue, in this work we propose an outlier-robust OT formulation. Our formulation is convex but challenging to scale at a first glance. We proceed by deriving an \emph{equivalent} formulation based on cost truncation that is easy to incorporate into modern stochastic algorithms for regularized OT. We demonstrate our model applied to mean estimation under the Huber contamination model in simulation as well as outlier detection on real data.