相关论文: Learning Elastic Costs to Shape Monge Displacement…
Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which…
Within the field of optimal transport (OT), the choice of ground cost is crucial to ensuring that the optimality of a transport map corresponds to usefulness in real-world applications. It is therefore desirable to use known information to…
Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…
Consider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on the real line, and suppose the cost of matching two points satisfies the Monge condition. We introduce a notion of locally…
In this paper, we study the regularity of optimal mappings in Monge's mass transfer problem. Using the approximation to Monge's cost function given by the Euclidean distance c(x,y)=dist(x,y) through the costs…
Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network based optimal transport map solver has gained great attention in…
The relationship between demand and prices of a set of products can be modeled as a linear mapping from logarithmic price changes to logarithmic changes in demand. We consider the problem of estimating the coefficient matrix of this…
A remarkable connection between optimal design and Monge transport was initiated in the years 1997 in the context of the minimal elastic compliance problem and where the euclidean metric cost was naturally involved. In this paper we present…
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y -- x|. The selected plan at the limit is, among those which are optimal for the non-penalized problem,…
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost $c(x,y)=\|x-y\|$ in dimension $d>1$. We develop a comprehensive variational convergence framework that entails…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
We propose deep learning methods for classical Monge's optimal mass transportation problems, where where the distribution constraint is treated as penalty terms defined by the maximum mean discrepancy in the theory of Hilbert space…
We consider an optimal transport problem between laws of random probability measures: given a base cost function, we build the associated OT cost between probability measures that in turn we use to define the OT cost between probability…
Monotone gradient functions play a central role in solving the Monge formulation of the optimal transport (OT) problem, which arises in modern applications ranging from fluid dynamics to robot swarm control. When the transport cost is the…
We provide a solution to the problem of optimal transport by Brownian martingales in general dimensions whenever the transport cost satisfies certain subharmonic properties in the target variable, as well as a stochastic version of the…