Related papers: Talagrand Concentration Inequalities for Stochasti…
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. Here we focus on differentiable functions on the Euclidean space in presence of a…
A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions…
It is shown that under suitable regularity conditions, differential entropy is a Lipschitz functional on the space of distributions on $n$-dimensional Euclidean space with respect to the quadratic Wasserstein distance. Under similar…
The purpose of this paper is twofold. Firstly, we prove transportation inequalities ${\bf T_2}(C)$ on the space of continuous paths with respect to the uniform metric for the law of the solution to a class of non-linear monotone stochastic…
We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…
This paper investigates the best known bounds on the quadratic Gaussian distortion-rate-perception function with limited common randomness for the Kullback-Leibler divergence-based perception measure, as well as their counterparts for the…
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$Wasserstein…
We obtain hydrodynamic descriptions of a broad class of conserved-mass transport processes on a ring. These processes are governed by chipping, diffusion and coalescence of masses, where microscopic probability weights in their…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
By using a split argument due to [1], the transportation cost inequality is established on the free path space of Markov processes. The general result is applied to stochastic reaction diffusion equations with random initial values.
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
This paper reviews different numerical methods for specific examples of Wasserstein gradient flows: we focus on nonlinear Fokker-Planck equations,but also discuss discretizations of the parabolic-elliptic Keller-Segel model and of the…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the measure satisfies a transport-entropy inequality. We extend some…
Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded observable of the…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
We introduce the optimal transportation interpretation of the Kantorovich norm on thespace of signed Radon measures with finite mass, based on a generalized Wasserstein distancefor measures with different masses.With the formulation and the…