The paper derives convergence rates for two optimal transport map estimators that relax compact-support, convexity and sub-exponential tail assumptions, including a sieve estimator that drops strong convexity.
For the multivariate case, where the OT maps are functions between two Rd spaces, we define the OT maps to be the composition of these three cases: for z = (z1, · · ·, zd)⊤ ∈ Rd,
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Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions
The paper derives convergence rates for two optimal transport map estimators that relax compact-support, convexity and sub-exponential tail assumptions, including a sieve estimator that drops strong convexity.