Related papers: A regularized transportation cost stemming from en…
We study the potential functions that determine the optimal density for $\varepsilon$-entropically regularized optimal transport, the so-called Schr\"odinger potentials, and their convergence to the counterparts in classical optimal…
Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures $\mu$ on $\R^d$ which can be expressed as the moment measures of suitable convex functions $u$, i.e. are of the form $(\nabla u)\_\\#e^{- u}$ for…
We provide non-asymptotic bounds and asymptotic limits for convex transport costs between the distribution of partial sums of independent and identically distributed square integrable and centered random variables and the normal…
Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
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…
This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean $\ell_2$-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn--Knopp algorithm, Accelerated Gradient…
In this paper, we formulate the problem of inferring a Finite Mixture Model from discrete data as an optimal transport problem with entropic regularization of parameter $\lambda\geq 0$. Our method unifies hard and soft clustering, the…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a…
The question of which costs admit unique optimizers in the Monge-Kantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known…
We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $\epsilon$-regularity result for optimal transport maps…
This paper deals with a variant of the optimal transportation problem. Given f $\in$ L 1 (R d , [0, 1]) and a cost function c $\in$ C(R d x R d) of the form c(x, y) = k(y -- x), we minimise $\int$ c d$\gamma$ among transport plans $\gamma$…
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…
We develop an $\e$-regularity theory at the boundary for a general class of Monge-Amp\`ere type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H\"older densities supported on $C^2$…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…