Revisiting invariances and introducing priors in Gromov-Wasserstein distances
This addresses the need for more adaptable optimal transport distances in machine learning applications, offering a domain-specific improvement for tasks involving multi-omic data and transfer learning.
The authors tackled the problem that Gromov-Wasserstein distance's invariance to transformations can be too flexible and ignores feature representations, proposing Augmented Gromov-Wasserstein to control rigidity and incorporate feature alignments, resulting in improved performance for tasks like single-cell multi-omic alignment and transfer learning.
Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance property can be too flexible, thus undesirable. Moreover, the Gromov-Wasserstein distance solely considers pairwise sample similarities in input datasets, disregarding the raw feature representations. We propose a new optimal transport-based distance, called Augmented Gromov-Wasserstein, that allows for some control over the level of rigidity to transformations. It also incorporates feature alignments, enabling us to better leverage prior knowledge on the input data for improved performance. We present theoretical insights into the proposed metric. We then demonstrate its usefulness for single-cell multi-omic alignment tasks and a transfer learning scenario in machine learning.