Related papers: On the contraction properties of Sinkhorn semigroups

On the contraction properties of Sinkhorn semigroups

URL: http://arxiv.org/abs/2503.09887v1
Date: Wed, 12 Mar 2025 23:05:27 GMT
Title: On the contraction properties of Sinkhorn semigroups
Authors: O. Deniz Akyildiz, Pierre del Moral, Joaquin Miguez,
Abstract summary: We develop a novel semigroup contraction analysis based on Lyapunov techniques to prove the exponential convergence of Sinkhorn equations on weighted Banach spaces.<n>To the best of our knowledge, these are the first results of this type in the literature on entropic transport and the Sinkhorn algorithm.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We develop a novel semigroup contraction analysis based on Lyapunov techniques to prove the exponential convergence of Sinkhorn equations on weighted Banach spaces. This operator-theoretic framework yields exponential decays of Sinkhorn iterates towards Schr\"odinger bridges with respect to general classes of $\phi$-divergences as well as in weighted Banach spaces. To the best of our knowledge, these are the first results of this type in the literature on entropic transport and the Sinkhorn algorithm. We also illustrate the impact of these results in the context of multivariate linear Gaussian models as well as statistical finite mixture models including Gaussian-kernel density estimation of complex data distributions arising in generative models.

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