Related papers: Stein's method for Fr\'echet approximation: a regu…
We study the approximation of a (finite) continuous-time Markov chain by a Markov chain on a reduced state space, and we provide formal error bounds for the approximated transient distributions in the Wasserstein distance. These bounds…
We propose probabilistic representations for inverse Stein operators (i.e. solutions to Stein equations) under general conditions; in particular we deduce new simple expressions for the Stein kernel. These representations allow to deduce…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…
We prove a bound for the Wasserstein distance between vectors of smooth complex random variables and complex Gaussians in the framework of complex Markov diffusion generators. For the special case of chaotic eigenfunctions, this bound can…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen…
This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…
Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often…
We give some rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales with differences having finite variances. For the Kolmogorov distances, we present some exact Berry-Esseen bounds for martingales,…
We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to…
In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…
Convergence rate to the stationary distribution for continuous-time Markov processes can be studied using Lyapunov functions. Recent work by the author provided explicit rates of convergence in special case of a reflected jump-diffusion on…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
Let $S_{n}$ be a sum of independent identically distribution random variables with finite first moment and $h_{M}$ be a call function defined by $g_{M}(x)=\max\{x-M,0\}$ for $x\in\mathbb{R}$, $M>0$. In this paper, we assume the random…
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two…