提出高效生成最优传输核心集的新方法，显著提速且保持精度。
EMS Coreset: An Efficient Expectation-Maximization Algorithm for Sinkhorn Coreset
- 通过非均匀权重实现熵正则化运输耦合的闭式更新，提升效率。
- 在真实与合成数据上比传统方法更快，大尺度下优势更明显。
- 理论保证稳定性和一致性，适合大规模数据处理场景。
核心集可将大规模数据压缩为小而具代表性的子集以提升下游学习效率。然而，基于最优传输（OT）的选择通常需要大量计算运输计划，限制了可扩展性。本文提出一种可扩展的Sinkhorn核心集方法，通过允许非均匀核心集权重，实现了熵正则化OT耦合的闭式更新，生成的中心点通过软分配推广了k-means算法。我们建立了所选测度的渐近一致性及对数据扰动的Lipschitz稳定性，提供精度和鲁棒性保障。在合成与真实世界基准测试中，该方法在保持或提升近似质量的同时，相比Wasserstein和标准Sinkhorn基线显著降低运行时间，尤其在大规模场景下表现突出。
原文摘要 · Abstract (English)
Coresets distill large datasets into small, representative subsets for efficient downstream learning. Yet Optimal Transport (OT)-based selection typically requires intensive computation of transport plans, limiting scalability. We introduce a scalable Sinkhorn coreset method that permits closed-form updates of the entropically regularized OT coupling by allowing non-uniform coreset weights. This produces centroids that generalize k-means via soft assignments. We establish asymptotic consistency of the selected measure and Lipschitz stability to data perturbations, providing accuracy and robustness guarantees. Across synthetic and real-world benchmarks, the proposed method achieves competitive or improved approximation quality while substantially reducing runtime compared to Wasserstein- and standard Sinkhorn-based coreset selection, especially at large scale.
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