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- W4289367630 abstract "We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the empirical regularized transport plan itself asymptotically follows a Gaussian law. The theory includes the Boltzmann-Shannon entropy regularization and hence a limit law for the widely applied Sinkhorn divergence. Our approach is based on an application of the implicit function theorem to necessary and sufficient optimality conditions for the regularized transport problem. The asymptotic results are investigated in Monte Carlo simulations. We further discuss computational and statistical applications, e.g. confidence bands for colocalization analysis of protein interaction networks based on regularized optimal transport." @default.
- W4289367630 created "2022-08-02" @default.
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- W4289367630 date "2018-10-23" @default.
- W4289367630 modified "2023-09-29" @default.
- W4289367630 title "Empirical Regularized Optimal Transport: Statistical Theory and Applications" @default.
- W4289367630 doi "https://doi.org/10.48550/arxiv.1810.09880" @default.
- W4289367630 hasPublicationYear "2018" @default.
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