论文标题
不平衡的合作运输
Unbalanced CO-Optimal Transport
论文作者
论文摘要
最佳传输（OT）通过计算样品之间有意义的对齐方式比较概率分布。合作运输（COOT）也通过推断特征之间的对齐方式进一步进行了比较。尽管这种方法会导致更好的对齐方式并概括了OT和Gromov-Wasserstein距离，但我们提供了一个理论上的结果，表明它对现实世界中无处不在的离群值敏感。这促使我们提出了不平衡的COOT，我们可以证明其在比较数据集中对噪声的稳健性。据我们所知，这是无与伦比空间中OT方法的第一个结果。在此结果中，我们为这种鲁棒性提供了这种鲁棒性的经验证据，这些鲁棒性是在有或不带有不同比例的类别以及同时对齐的样本和在单细胞测量范围内的样本和特征的具有挑战性的任务。
Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a theoretical result showing that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise in the compared datasets. To the best of our knowledge, this is the first such result for OT methods in incomparable spaces. With this result in hand, we provide empirical evidence of this robustness for the challenging tasks of heterogeneous domain adaptation with and without varying proportions of classes and simultaneous alignment of samples and features across single-cell measurements.
