Related papers: Optimal Transport between Gaussian Stationary Proc…
We present a definition of stochastic Hamiltonian process on finite graph via its corresponding density dynamics in Wasserstein manifold. We demonstrate the existence of stochastic Hamiltonian process in many classical discrete problems,…
We propose a transfer principle to study the adapted 2-Wasserstein distance between stochastic processes. First, we obtain an explicit formula for the distance between real-valued mean-square continuous Gaussian processes by introducing the…
In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the…
We investigate barycenters of Gaussian process laws in adapted Wasserstein space. The adapted Wasserstein distance refines classical optimal transport by enforcing compatibility of transport plans with the temporal flow of information, and…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. In many "mesoscopic" transport processes,…
We study the Braunstein-Kimble setup for teleportation of quantum state of a single mode of optical field. We assume that the sender and receiver share a two-mode Gaussian state and we identify optimum local Gaussian operations that…
Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.
In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying…
This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We propose a novel fused Gromov-Wasserstein alignment method to jointly learn the Hawkes processes in different event spaces, and align their event types. Given two Hawkes processes, we use fused Gromov-Wasserstein discrepancy to measure…