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We derive finite-particle rates for the regularized Stein variational gradient descent (R-SVGD) algorithm introduced by He et al. (2024) that corrects the constant-order bias of the SVGD by applying a resolvent-type preconditioner to the…

Machine Learning · Statistics 2026-05-19 Ye He , Krishnakumar Balasubramanian , Sayan Banerjee , Promit Ghosal

New bounds for the $k$-th order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature.…

Probability · Mathematics 2017-03-21 Robert E. Gaunt

The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…

Machine Learning · Computer Science 2021-02-16 Jung Hun Oh , Maryam Pouryahya , Aditi Iyer , Aditya P. Apte , Allen Tannenbaum , Joseph O. Deasy

We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic…

Probability · Mathematics 2020-05-12 Thomas Bonis

This paper uses the generator approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. Until now, the standard way to invoke Stein's method for this problem was to use the…

Probability · Mathematics 2022-02-15 Anton Braverman

We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization.…

Analysis of PDEs · Mathematics 2018-11-07 Jianfeng Lu , Yulong Lu , James Nolen

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this…

Data Analysis, Statistics and Probability · Physics 2023-01-19 Caroline Chaux , Laurent Duval , Amel Benazza-Benyahia , Jean-Christophe Pesquet

Kernel Stein discrepancy (KSD) is a widely used kernel-based measure of discrepancy between probability measures. It is often employed in the scenario where a user has a collection of samples from a candidate probability measure and wishes…

Statistics Theory · Mathematics 2025-02-13 George Wynne , Mikołaj Kasprzak , Andrew B. Duncan

In this paper, the Milstein method is used to approximate invariant measures of stochastic differential equations with commutative noise. The decay rate of the transition probability kernel generated by the Milstein method to the unique…

Numerical Analysis · Mathematics 2019-01-28 Lihui Weng , Wei Liu

Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is…

Robotics · Computer Science 2021-07-13 Alexander Lambert , Byron Boots

In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…

Probability · Mathematics 2017-10-25 Alberto Chiarini , Alessandra Cipriani , Giovanni Conforti

Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of…

Statistics Theory · Mathematics 2021-09-14 Liam Hodgkinson , Robert Salomone , Fred Roosta

Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…

Machine Learning · Computer Science 2021-03-19 Francesco D'Angelo , Vincent Fortuin

Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…

Probability · Mathematics 2018-07-30 Laure Coutin , Laurent Decreusefond

We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random $N$-vectors. We achieve this by deducing a specific integral representation for the Hessian matrix of a solution…

Probability · Mathematics 2015-09-15 Ben Berckmoes , Bob Lowen , Jan Van Casteren

In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…

Probability · Mathematics 2010-04-06 Gesine Reinert , Adrian Röllin

Providing theoretical guarantees for parameter estimation in exponential random graph models is a largely open problem. While maximum likelihood estimation has theoretical guarantees in principle, verifying the assumptions for these…

Statistics Theory · Mathematics 2026-03-26 Adrian Fischer , Gesine Reinert , Wenkai Xu

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the…

Statistics Theory · Mathematics 2014-07-08 Bert van Es , Peter Spreij

In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…

Numerical Analysis · Mathematics 2020-12-30 Kaipeng Wang , Andrew Christlieb , Yan Jiang , Mengping Zhang

We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test…

Probability · Mathematics 2020-09-22 Xiao Fang , Yuta Koike