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About this paper
Mengyu Li, Jun Yu, Tao Li, Cheng Meng
The Spar-Sink algorithm introduces an importance sparsification method for the Sinkhorn algorithm, significantly improving its scalability for entropy-regularized Optimal Transport and Unbalanced Optimal Transport by reducing the per-iteration computational cost from O(n^2) to O(s). This approach yielded hundreds of times speedup and superior accuracy compared to existing methods across synthetic benchmarks and real-world applications like echocardiogram analysis.
Key insights
- Importance sparsification, guided by the structure of optimal transport plans, can dramatically reduce the computational burden of Sinkhorn iterations without compromising accuracy.
- The derived adaptive sampling probabilities allow Spar-Sink to handle more general kernel matrix structures than prior accelerated methods, including those that are sparse and nearly full-rank.
- Theoretical analysis confirms that the Spar-Sink estimators for regularized OT and UOT distances are consistent and maintain the same order of iteration bounds as the classical Sinkhorn algorithm.
Summary by alphaXiv.
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