Establishes explicit finite-sample bias and variance bounds for regularized OT costs that improve prior entropic results, deliver the first quantitative bounds for L^p regularization, and yield an n^{-2/(d+4)} rate for quadratic regularization with quadratic cost.
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A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
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Finite-sample bounds for regularized optimal transport
Establishes explicit finite-sample bias and variance bounds for regularized OT costs that improve prior entropic results, deliver the first quantitative bounds for L^p regularization, and yield an n^{-2/(d+4)} rate for quadratic regularization with quadratic cost.
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Statistical Estimation of Monge Transport Maps via Brenier Potentials
A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.