Related papers: Generalized Talagrand Inequality for Sinkhorn Dist…
We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an…
We introduce an inequality which may be viewed as a generalization of both the Brascamp-Lieb inequality and its reverse (Barthe's inequality), and prove its information-theoretic (i.e.\ entropic) formulation. This result leads to a unified…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note,…
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.…
We exhibit a surprising relationship between elliptic gradient systems of PDEs, multi-marginal Monge-Kantorovich optimal transport problem, and multivariable Hardy-Littlewood inequalities. We show that the notion of an orientable elliptic…
The optimal mass transportation was introduced by Monge some 200 years ago and is, today, the source of large number of results in analysis, geometry and convexity. Here I investigate a new, surprising link between optimal transformations…
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix…
Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical method based on Sinkhorn's algorithm for the entropic…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly…
For displacement convex functionals in the probability space equip\-ped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type \L oja\-sie\-wicz inequalities. \chg{We also discuss the more…
We study the problem of estimating a function $T$ given independent samples from a distribution $P$ and from the pushforward distribution $T_\sharp P$. This setting is motivated by applications in the sciences, where $T$ represents the…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…
Let $G$ be a countable discrete group with an orthogonal representation $\alpha$ on a real Hilbert space $H$. We prove $L_p$ Poincar\'e inequalities for the group measure space $L_\infty(\Omega_H,\gamma)\rtimes G$, where both the group…
In this paper we study two basic facts of optimal transportation on Wiener space W. Our first aim is to answer to the Monge Problem on the Wiener space endowed with the Sobolev type norm (k,gamma) to the power of p (cases p = 1 and p > 1…
This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…
Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric…