Related papers: General Divergence Regularized Optimal Transport: …
We propose to tackle the problem of understanding the effect of regularization in Sinkhorn algotihms. In the case of Gaussian distributions we provide a closed form for the regularized optimal transport which enables to provide a better…
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…
This work proposes new estimators for discrete optimal transport plans that enjoy Gaussian limits centered at the true solution. This behavior stands in stark contrast with the performance of existing estimators, including those based on…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions. The wide adoption of OT into existing data analysis and…
Grogan et al [11,12] have recently proposed a solution to colour transfer by minimising the Euclidean distance L2 between two probability density functions capturing the colour distributions of two images (palette and target). It was shown…
We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the…
Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…
Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
In recent years, the use of entropy-regularized optimal transport with $L^p$-type entropies has become increasingly popular. In this setting, the solutions are sparse, in the sense that the support of the regularized optimal coupling,…
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…
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…
We introduce the Sinkhorn treatment effect, an entropic optimal transport measure of divergence between counterfactual distributions. Unlike classical quantities such as the average treatment effect, this measure captures differences across…
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 analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regularization penalizes transport couplings by the squared $L^2$…