Related papers: Sparse Regularized Optimal Transport without Curse…
We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…
We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the…
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for…
Entropic optimal transport (EOT) presents an effective and computationally viable alternative to unregularized optimal transport (OT), offering diverse applications for large-scale data analysis. In this work, we derive novel statistical…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…
We give a new proof of the Caffarelli contraction theorem, which states that the Brenier optimal transport map sending the standard Gaussian measure onto a uniformly log-concave probability measure is Lipschitz. The proof combines a recent…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport (OT) and distributionally robust optimization (DRO). In…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. Many formulations impose a global constraint on the transport plan, for instance…
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…
We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsically ill-posed, exhibiting…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
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…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…