Unbalanced CO-Optimal Transport
This work addresses robustness issues in optimal transport methods for incomparable spaces, offering incremental improvements for applications in domain adaptation and bioinformatics.
The paper tackles the sensitivity of CO-optimal transport (COOT) to outliers in real-world data by proposing unbalanced COOT, which provably shows robustness to noise and empirically demonstrates this in tasks like heterogeneous domain adaptation and single-cell alignment.
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.