Unlocking Versatile Scalability: Custom Algorithms for Enhanced Optimal Transport

The Significance of Optimal Transport Methods in Machine Learning

Optimal transport (OT) methods have long been limited in their relevance to machine learning due to computational costs and rigidity in modeling. Recent developments have addressed these limitations through entropic regularization and low-rank solvers, as well as unbalanced variants of OT. The goal is to merge these developments to create scalable and versatile solvers.

Addressing Computational and Modeling Limitations

The computational outlook for OT methods has been improved with entropic regularization, while more recent low-rank solvers hold the promise of scaling OT further. Additionally, the rigidity of mass conservation has been eased with unbalanced variants of OT.

Merging Developments for Scalable and Versatile Solvers

The goal of this paper is to merge low-rank and unbalanced variants of OT to create scalable and versatile solvers. Custom algorithms have been proposed to implement these extensions for the linear OT problem and its fused-Gromov-Wasserstein generalization, showing practical relevance to challenging spatial transcriptomics matching problems. These algorithms are implemented in the ott-jax toolbox.

By merging these developments, the aim is to achieve the promise of solvers that are both scalable and versatile, making them relevant to a wide range of machine learning applications.

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