相关论文: An improved central limit theorem and fast converg…

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of…

We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport…

We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated optimal…

We address the problem of proving a Central Limit Theorem for the empirical optimal transport cost, $\sqrt{n}\{\mathcal{T}_c(P_n,Q)-\mathcal{W}_c(P,Q)\}$, in the semi discrete case, i.e when the distribution $P$ is finitely supported. We…

We investigate the convergence rate of the optimal entropic cost $v_\varepsilon$ to the optimal transport cost as the noise parameter $\varepsilon \downarrow 0$. We show that for a large class of cost functions $c$ on $\mathbb{R}^d\times…

We prove a Central Limit Theorem for the empirical optimal transport cost, $\sqrt{\frac{nm}{n+m}}\{\mathcal{T}_c(P_n,Q_m)-\mathcal{T}_c(P,Q)\}$, in the semi discrete case, i.e when the distribution $P$ is supported in $N$ points, but…

For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…

Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…

We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…

Consider the Monge-Kantorovich problem of transporting densities $\rho_0$ to $\rho_1$ on $\mathbb{R}^d$ with a strictly convex cost function. A popular relaxation of the problem is the one-parameter family called the entropic cost problem.…

The empirical optimal transport (OT) cost between two probability measures from random data is a fundamental quantity in transport based data analysis. In this work, we derive novel guarantees for its convergence rate when the involved…

For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…

This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…

In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…

We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects…

We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter $\varepsilon$ tends to $0$. We establish lower and upper bounds on the difference…

We study the convergence of the transport plans $\gamma_\epsilon$ towards $\gamma_0$ as well as the cost of the entropy-regularized optimal transport $(c,\gamma_\epsilon)$ towards $(c,\gamma_0)$ as the regularization parameter $\epsilon$…

We study the small-regularisation limit of the entropic optimal transport problem on the line with distance cost. While convergence of entropic minimizers is well understood in the discrete setting and in the case where the cost is…