Sinkhorn iterations converge to a Wasserstein mirror gradient flow (the Sinkhorn flow) as regularization epsilon goes to zero with iterations scaled as 1/epsilon.
[RW23] Cale Rankin and Leonard Wong, Bregman-Wasserstein divergence: geometry and applications , Math arxiv preprint arXiv:2302.05833
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CART impurity criteria are reframed as Bregman divergences from convex functions, unifying node representatives, split rules, and consistency results for exponential-family models.
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Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm
Sinkhorn iterations converge to a Wasserstein mirror gradient flow (the Sinkhorn flow) as regularization epsilon goes to zero with iterations scaled as 1/epsilon.