Related papers: Multi-marginal optimal transport and probabilistic…
We shall present a measure theoretical approach for which together with the Kantorovich duality provide an efficient tool to study the optimal transport problem. Specifically, we study the support of optimal plans where the cost function…
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…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…
We study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
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…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum…
We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of…
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees. Leveraging an entropic version of Brenier's theorem, we show that our…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
In this paper we extend the duality theory of the multi-marginal optimal transport problem for cost functions depending on a decreasing function of the distance (not necessarily bounded). This class of cost functions appears in the context…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…