论文标题
在对所有离群值的最佳运输中
On making optimal transport robust to all outliers
论文作者
论文摘要
最佳运输（OT）由于其边缘约束而对异常值敏感。基于以下定义，已经提出了异常稳健的OT变体，即离群值是移动昂贵的样本。在本文中，我们表明，考虑到离群值更接近目标度量的情况，该定义受到限制。我们表明，较强的OT较强的OT完全运输这些异常值，导致实践中的表现不佳。为了解决这些异常值，我们建议通过依靠接受对抗性培训的分类器来对其进行分类和目标样本进行分类，以检测它们。如果分类器的预测与其分配的标签不同，则将样本视为异常值。为了减少这些异常值在运输问题中的影响，我们建议将它们从问题中删除，或者通过使用分类器预测来增加移动它们的成本。我们表明，我们成功地检测到这些异常值，并且它们不影响多个实验的运输问题，例如梯度流，生成模型和标签传播。
Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this paper, we show that this definition is restricted by considering the case where outliers are closer to the target measure than clean samples. We show that outlier robust OT fully transports these outliers leading to poor performances in practice. To tackle these outliers, we propose to detect them by relying on a classifier trained with adversarial training to classify source and target samples. A sample is then considered as an outlier if the prediction from the classifier is different from its assigned label. To decrease the influence of these outliers in the transport problem, we propose to either remove them from the problem or to increase the cost of moving them by using the classifier prediction. We show that we successfully detect these outliers and that they do not influence the transport problem on several experiments such as gradient flows, generative models and label propagation.
