Title: A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution

Optimal transport (OT) offers a rigorous framework for mapping between probability distributions. However, despite significant advancements, its application to large-scale datasets continues to pose substantial computational challenges, and the resulting pointwise transport plans are frequently hard to interpret. To address these limitations, we propose Optimal Mixture Transport (OMT), a scalable approach that redefines the transport paradigm by shifting the focus from individual samples to mixtures of subpopulations. This method reformulates the transport problem as a strictly biconvex optimization task that possesses a unique global minimizer.

We provide theoretical assurances regarding the stability of the OMT map, demonstrating that bounded perturbations in the underlying distributions result in correspondingly bounded alterations to the transport plan. By representing subpopulations as exponential-family distributions, OMT effectively decouples computational complexity from the sample size, allowing the cost to scale exclusively with the number of mixture components. We validate the practicality and efficacy of OMT across various synthetic benchmarks and real-world datasets, such as image data and large-scale single-cell RNA sequencing measurements.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC