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Minimax estimation of discontinuous optimal transport maps: The semi-discrete case
We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i. i. d.
Optimal transport map estimation in general function spaces
To ensure identifiability, we assume that $T = \nabla \varphi_0$ is the gradient of a convex function, in which case $T$ is known as an \emph{optimal transport map}.
Estimation and Quantization of Expected Persistence Diagrams
To overcome this issue, we propose an algorithm to compute a quantization of the empirical EPD, a measure with small support which is shown to approximate with near-optimal rates a quantization of the theoretical EPD.
A short proof on the rate of convergence of the empirical measure for the Wasserstein distance
We provide a short proof that the Wasserstein distance between the empirical measure of a n-sample and the estimated measure is of order n^-(1/d), if the measure has a lower and upper bounded density on the d-dimensional flat torus.
Statistics Theory Statistics Theory
