OMT 解决了大规模数据上最优传输计算昂贵且结果难解释的痛点，做分布对齐、数据融合或生物信息学的团队可以直接用这个框架来获得稳定且可解释的传输计划。
最优传输（OT）在分布映射中提供了理论框架，但计算成本高且结果难以解释。新提出的最优混合传输（OMT）将传输对象从单个样本转向子总体混合，并将问题转化为严格双凸优化，保证唯一全局最小值。OMT 在理论上证明传输映射的稳定性，即底层分布的有限扰动导致传输计划的有限变化。通过将子总体建模为指数族分布，OMT 的计算复杂度仅与混合成分数量相关，而非样本量。在图像数据和单细胞 RNA 测序等大规模真实数据集上，OMT 展示了有效性和实用性。
A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution
Optimal transport (OT) provides a principled framework for mapping between probability distributions. Despite extensive progress, applying OT to large-scale data remains computationally demanding, and the resulting pointwise transport plans are often difficult to interpret. We introduce Optimal Mixture Transport (OMT), a scalable framework that shifts the transport paradigm from individual samples to mixtures of subpopulations, reformulating the transport problem as a strictly biconvex optimization with a unique global minimizer. We further establish theoretical guarantees on the stability of the OMT map, showing that bounded perturbations of the underlying distributions lead to bounded changes in the transport plan. By formulating subpopulations as exponential-family distributions, OMT decouples computational complexity from the sample size, scaling solely with the number of mixture components. We demonstrate the effectiveness and practicality of OMT on a wide range of synthetic benchmarks and real-world datasets, including image data and large-scale single-cell RNA sequencing measurements.