Related papers: Entropic and displacement interpolation: a computa…
The Optimal Transport (OT) problem investigates a transport map that connects two distributions while minimizing a given cost function. Finding such a transport map has diverse applications in machine learning, such as generative modeling…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…
Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can…
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…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the…
We consider optimal transport problems where the cost for transporting a given probability measure $\mu_0$ to another one $\mu_1$ consists of two parts: the first one measures the transportation from $\mu_0$ to an intermediate (pivot)…
We discuss a connection (and a proper place in this framework) of the unforced and deterministically forced Burgers equation for local velocity fields of certain flows, with probabilistic solutions of the so-called Schr\"{o}dinger…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
Regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model…
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 investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…