Related papers: Statistical optimal transport
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field…
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
We analyze several optimal transportation problems between de-terminantal point processes. We show how to estimate some of the distances between distributions of DPP they induce. We then apply these results to evaluate the accuracy of a new…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter…
We discuss methods of Optimal Transportation Theory and its relations to problems in quantum mechanics. This essentially means that the cost function is some Hamiltonian $H(q,p)$ on a phase space (symplectic manifold), and the marginal…
We introduce a stochastic optimal transport for the Langevin dynamics with positive mass and study its zero--mass limit. The new aspect of this paper is that we only fix the initial and terminal probability distributions of the positions of…
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…
We review some known facts in the transport theory of mesoscopic systems, including counting statistics, and discuss its relation with the mathematical treatment of open systems.
We present a framework for performing regression when both covariate and response are probability distributions on a compact interval $\Omega\subset\mathbb{R}$. Our regression model is based on the theory of optimal transportation and links…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
This is an expository paper describing how duality theory for Hessian manifolds provides a natural setting for optimal transport. We explain how this can be used to solve Monge-Amp\`ere equations and survey recent results along these lines…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems,…