Related papers: Optimal transportation for the determinant

In this paper, we investigate Monge-Kantorovich problems for which the absolute continuity of marginals is relaxed. For $X,Y\subseteq\mathbb{R}^{n+1}$ let $(X,\mathcal{B}_X,\mu)$ and $(Y,\mathcal{B}_Y,\nu)$ be two Borel probability spaces,…

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 consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…

We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the…

We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…

This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…

We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton's characteristic functions and conservation of luminous flux, and briefly explain the connection with the…

We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.

We study in this paper optimal mass transport over a strongly connected, directed graph on a given discrete time interval. Differently from previous literature, we do not assume full knowledge of the initial and final goods distribution…

This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…

We consider a multimarginal optimal transport, which includes as a particular case the Wasserstein barycenter problem. In this problem one has to find an optimal coupling between $m$ probability measures, which amounts to finding a tensor…

We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators…

In this paper, we investigate the optimal transport problem when the source is a non-convex polygonal domain in $\mathbb{R}^2$. We show a global $W^{2,1+\epsilon}$ estimate for potentials of optimal transport. Our method applies to a more…

A data driven procedure is developed to compute the optimal map between two conditional probabilities $\rho(x|z_{1},...,z_{L})$ and $\mu(y|z_{1},...,z_{L})$ depending on a set of covariates $z_{i}$. The procedure is tested on synthetic data…

Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…

Let (X,L) be a (semi-) polarized complex projective variety and T a real torus acting holomorphically on X with moment polytope P. Given a probability density g on P we introduce a new type of Monge-Ampere measure on X, defined for singular…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whose discrete Laplace operator converges to the…