相关论文: Transportation Distance and the Central Limit Theo…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
We give an overview of various results and methods related to information-theoretic distances of R\'enyi type in the light of their applications to the central limit theorem (CLT). The first part (Sections 1-9) is devoted to the total…
We consider some repulsive multimarginal optimal transportation problems which include, as a particular case, the Coulomb cost. We prove a regularity property of the minimizers (optimal transportation plan) from which we deduce existence…
We study the Monge and Kantorovich transportation problems on $\mathbb{R}^{\infty}$ within the class of exchangeable measures. With the help of the de Finetti decomposition theorem the problem is reduced to an unconstrained optimal…
Fix probability densities $f$ and $g$ on open sets $X \subset \mathbf{R}^m$ and $Y \subset \mathbf{R}^n$ with $m\ge n\ge1$. Consider transporting $f$ onto $g$ so as to minimize the cost $-s(x,y)$. We give a non-degeneracy condition (a) on…
Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When…
We consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are…
In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is…
We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an application, we determine optimal solutions of both the primal…
We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…
We prove that $c$-cyclically monotone transport plans $\pi$ optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
Motivated by a recent work of Benoist and Quint and extending results from the PhD thesis of the third author, we obtain limit theorems for products of independent and identically distributed elements of GLd (R), such as the…
Some classical mass transportation problems are investigated in a finitely additive setting. Let $\Omega=\prod_{i=1}^n\Omega_i$ and $\mathcal{A}=\otimes_{i=1}^n\mathcal{A}_i$, where $(\Omega_i,\mathcal{A}_i,\mu_i)$ is a ($\sigma$-additive)…
We prove the central limit theorem (CLT) for a sequence of independent zero-mean random variables $\xi_j$, perturbed by predictable multiplicative factors $\lambda_j$ with values in intervals $[\underline\lambda_j,\overline\lambda_j]$. It…
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…
The paper proves transportation inequalities for probability measures on spheres for the Wasserstein metrics with respect to cost functions that are powers of the geodesic distance. Let $\mu$ be a probability measure on the sphere ${\bf…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
We introduce the Constrained Least-cost Tour (CLT) problem: given an undirected graph with weight and cost functions on the edges, minimise the total cost of a tour rooted at a start vertex such that the total weight lies within a given…