Related papers: Multivariate Stein Factors for a Class of Strongly…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we obtain a characterizing non-local Stein operator which boils…
We provide the first finite-particle convergence rate for Stein variational gradient descent (SVGD), a popular algorithm for approximating a probability distribution with a collection of particles. Specifically, whenever the target…
The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in…
We consider contractivity for diffusion semigroups w.r.t. Kantorovich ($L^1$ Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown…
L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes…
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…
Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the…
We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…
In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the…
We establish existence of Stein kernels for probability measures on $\mathbb{R}^d$ satisfying a Poincar\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…
Let $(W,H,\mu)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t(x))$ is a diffusion process satisfying the stochastic differential equation with diffusion and drift coefficients $\sigma: \R^n\to \R^n\otimes \R^d$, $b: \R^n\to…
We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our discrepancy is expressed in terms of the ratio of reverse…
We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$. Applications include a sharp mixing time bound for the bases-exchange walk…
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…