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Related papers: An algebra of Stein operators

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Let $W$ be a random variable with mean zero and variance $\sigma^2$. The distribution of a variate $W^*$, satisfying $EWf(W)=\sigma ^2 Ef'(W^*)$ for smooth functions $f$, exists uniquely and defines the zero bias transformation on the…

Probability · Mathematics 2007-05-23 Larry Goldstein , Gesine Reinert

In many fields, data appears in the form of direction (unit vector) and usual statistical procedures are not applicable to such directional data. In this study, we propose non-parametric goodness-of-fit testing procedures for general…

Methodology · Statistics 2020-02-18 Wenkai Xu , Takeru Matsuda

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

Probability · Mathematics 2024-11-06 Dominic Schuhmacher , Leoni Carla Wirth

Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…

Probability · Mathematics 2013-01-03 Larry Goldstein , Gesine Reinert

This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…

Statistics Theory · Mathematics 2026-01-19 Robert E. Gaunt , Frédéric Ouimet , Donald Richards

Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds…

Machine Learning · Statistics 2018-11-14 Jackson Gorham , Andrew B. Duncan , Sebastian J. Vollmer , Lester Mackey

The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…

Methodology · Statistics 2026-03-02 Shaochen Wang , Christian H. Weiß

Reliable robotic manipulation requires control policies that can accurately represent and adapt to uncertainty arising from contact-rich interactions. Modern data-driven methods mitigate uncertainty through large-scale training and…

We present a de Bruijn type approximation for quantifying the content of m smooth numbers, derived from samples obtained through a probability measure over the set of integers less than or equal to n, with point mass function at k inversely…

Probability · Mathematics 2025-03-04 Arturo Jaramillo , Xiaochuan Yang

We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable…

funct-an · Mathematics 2008-02-03 J. F. van Diejen

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…

Probability · Mathematics 2025-10-28 Paul Mansanarez , Guillaume Poly , Yvik Swan

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally…

Machine Learning · Statistics 2017-11-15 Qiang Liu

Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary,…

Probability · Mathematics 2014-10-29 John Pike , Haining Ren

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…

Machine Learning · Statistics 2021-07-22 Shijing Si , Chris. J. Oates , Andrew B. Duncan , Lawrence Carin , François-Xavier Briol

In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate approximate samples from posteriors efficiently. Based on the…

Numerical Analysis · Mathematics 2026-02-09 Junxiong Jia , Peijun Li , Deyu Meng

In this article we examine the densities of a product and a ratio of two real positive definite matrix-variate random variables $X_1$ and $X_2$, which are statistically independently distributed, and we consider the density of the product…

Classical Analysis and ODEs · Mathematics 2013-03-19 A. M. Mathai , H. J. Haubold

This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…

Statistics Theory · Mathematics 2024-04-24 Xiucai Ding , Yun Li , Fan Yang

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Probability · Mathematics 2007-05-23 Mathew D. Penrose , J. E. Yukich

Stein Variational Gradient Descent (SVGD) is a highly efficient method to sample from an unnormalized probability distribution. However, the SVGD update relies on gradients of the log-density, which may not always be available. Existing…

Machine Learning · Computer Science 2026-03-13 Cornelius V. Braun , Robert T. Lange , Marc Toussaint

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL)…

Machine Learning · Statistics 2022-04-26 Jiaxin Shi , Chang Liu , Lester Mackey