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.

翻译：最优传输（OT）通过计算样本间有意义的对齐来比较概率分布。协同最优传输（COOT）进一步扩展了这一比较，同时推断特征间的对齐。尽管该方法能够实现更优的对齐效果，并推广了OT与Gromov-Wasserstein距离，但我们的理论结果表明，它对真实数据中普遍存在的异常值敏感。这促使我们提出非平衡COOT，并理论证明了其对所比较数据中噪声的鲁棒性。据我们所知，这是不可比空间中OT方法的首个此类结果。基于这一理论发现，我们提供了实证证据，证明该方法在具有挑战性的异质域自适应任务中（包括类别比例变化场景）以及单细胞测量数据样本与特征同步对齐问题中的鲁棒性。