arXiv research

New optimal transport method handles mass creation and destruction.

New algorithm detects anomalies by forcing samples to displace mass in low-density regions.

Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.

We use mass-transportation as a tool to compare surfaces (2-manifolds). In particular, we determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be inv…

We extend Sobolev transport to unbalanced measures on graphs.

Using McCann's transportation map, we establish a transport inequality on compact manifolds with positive Ricci curvature. This inequality contains the sharp spectral comparison estimates.

New framework for optimal transport with jumps over intermediate spaces.

New algorithms solve partial optimal transport problems for applications like PU learning.

Gradient flow solves optimal mass transport for covariance matrices.

Study mass transport in low-diffusivity using Lagrangian coordinates.

In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that th…

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using th…

Given a transportation cost $c: M \times\bar M \to\mathbf{R}$, optimal maps minimize the total cost of moving masses from $M$ to $\bar M$. We find a pseudo-metric and a calibration form on $M\times\bar M$ such that the graph of an optimal map is a calibrated maximal submanifold. We define the mass of space-like current…

New forms of multi-marginal POT problem derived for computational efficiency.

We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Ampère type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this evolution equation to the stationary solution of the optimal transport problem. We …

A simple model for unbalanced optimal transport captures key features.

A new method for transporting unbalanced measures on graphs efficiently.

In this paper we give a new proof of a theorem by Alexandrov on the Gauss curvature prescription of Euclidean convex sets. This proof is based on the duality theory of convex sets and on optimal mass transport. A noteworthy property of this proof is that it does not rely neither on the theory of convex polyhedra nor on…

USD algorithm transports distributions with or without mass conservation.

Study group actions in metric spaces, proving convergence of lens spaces.

A new method for averaging probability distributions based on optimal weak mass transport.

We present a constructive approach to surface comparison realizable by a polynomial-time algorithm. We determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solut…

A framework models order book dynamics using point processes and mass transport.

Sharp inequalities in nonnegative Ricci curvature spaces using mass transport.

Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution. A possible way of dealing with this problem is to use an ensemble of GANs, wher…

New method for comparing different mass measures on tree structures using entropy partial transport.

Solves probabilistic Lambert problem connecting astrodynamics with optimal mass transport.

Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that is difficult to solve and slowly converging. Motivated from techniques in the reg…

The Gilbert-Steiner problem is a mass transportation problem, where the cost of the transportation depends on the network used to move the mass and it is proportional to a certain power of the "flow". In this paper, we introduce a new formulation of the problem, which turns it into the minimization of a convex function…

We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to define an evolution of metrics on non-smooth metric measure spaces with Ricci curvature bounded from below.

This paper is concerned with the study of the Monge optimal transport problem in sub-Riemannian manifolds where the cost is given by the square of the sub-Riemannian distance. Our aim is to extend previous results on existence and uniqueness of optimal transport maps to cases of sub-Riemannian structures which admit ma…

On compact manifolds which are not simply connected, we prove the existence of "fake" solutions to the optimal transportion problem. These maps preserve volume and arise as the exponential of a closed 1 form, hence appear geometrically like optimal transport maps. The set of such solutions forms a manifold with dimensi…

Optimizes angular velocity transfers for rigid bodies under deadline constraints.

MF-PID uses interacting samples to efficiently transport probability mass.

Optimal transport with path constraints for distributions of different masses.

Sharp Sobolev inequalities proved on manifolds with non-negative Ricci curvature.

The paper proves $L^p$-Sobolev inequalities for minimal submanifolds.

The paper reviews advances in estimating and understanding optimal transport maps.

New methods estimate transport-growth pairs in unbalanced optimal transport.

Geometric analysis on diffeomorphism groups for fluid dynamics and information geometry.

Efficient federated algorithm for calculating transportation barycenter.

In his book on Convex Polyhedra (section 7.2), A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data. The first goal of this paper is to give a variational solution to the problem of existence and uniqueness of a closed convex hypersu…

The aim of this paper is to prove isoperimetric inequalities on submanifolds of the Euclidean space using mass transportation methods. We obtain a sharp ?weighted isoperimetric inequality? and a nonsharp classical inequality similar to the one obtained by J. Michael and L. Simon. The proof relies on the description of …

Let M be a compact Riemannian manifold and let $μ$,d be the associated measure and distance on M. Robert McCann obtained, generalizing results for the Euclidean case by Yann Brenier, the polar factorization of Borel maps S : M -> M pushing forward $μ$ to a measure $ν$: each S factors uniquely a.e. into the composition …

Paper proposes a new approach to optimal transport for vector and matrix densities.

New method designs fairer transport plans with uncertainty.

A new method for efficient optimal partial transport in 1D.

Proposes m-POT to improve m-OT's misspecified mappings issue.