EMS Coreset: An Efficient Expectation-Maximization Algorithm for Sinkhorn Coreset

2026-08-17

AI Summary

This study addresses the computational intensity and poor scalability of optimal transport-based coreset selection by proposing a Scalable Sinkhorn Coreset method. By introducing non-uniform weights to enable closed-form updates for entropy-regularized optimal transport couplings, this approach generalizes k-means to soft assignment centroids. We theoretically establish the algorithm’s asymptotic consistency and Lipschitz stability. Empirical evaluations on both synthetic and real-world datasets demonstrate superior approximation quality compared to existing baselines. Furthermore, the proposed method achieves significantly reduced runtime in large-scale scenarios, effectively reconciling theoretical guarantees with computational efficiency.

Abstract

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.

Problem

• Coreset
• Optimal Transport
• Scalability
• Sinkhorn

Innovation

• Sinkhorn Coreset
• Closed-form Updates
• Non-uniform Weights
• Entropic Regularization
• Asymptotic Consistency