Statistical Rates for Entropic Optimal Transport in the Discrete to SubGaussian Regime
Paper proves parametric rates for semi-discrete entropic optimal transport, including barycentric projection and Sinkhorn-EM.
The paper studies statistical rates for entropic optimal transport when one measure has finite support and the other is subGaussian. Empirical dual potentials converge to population counterparts at parametric rates, with no dimension dependence in the leading term. The empirical barycentric projection achieves squared-error rate n^{-1}, improving on the n^{-1/2} rate known for fully subGaussian settings. For a balanced two-component Gaussian mixture, Sinkhorn-EM iterates are sqrt(n)-consistent for any fixed iteration count, up to a sqrt(log n) factor, and simulations support the theory.
- Parametric dual-potential rates have no leading dimension dependence.
- Barycentric projection reaches squared error n to the minus one.
- Sinkhorn-EM is sqrt(n)-consistent up to a sqrt(log n) factor.
From the original article
1 min read at arxiv.orgWe study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian. Our main result establishes parametric convergence rates for the empirical dual potentials to their population counterparts, with no dimension dependence in the leading term.
By Tomas Gonzalez · arxiv.org
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