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Related papers: An algebra of Stein operators

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We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent result of Gaunt, Mijoule and Swan \cite{gms18}. This…

Probability · Mathematics 2020-09-28 Robert E. Gaunt , Guillaume Mijoule , Yvik Swan

In this paper, we extend Stein's method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the…

Probability · Mathematics 2018-04-18 Robert E. Gaunt

Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric…

Probability · Mathematics 2013-05-23 Christophe Ley , Yvik Swan

The first essential ingredient to build up Stein's method for a continuous target distribution is to identify a so-called \textit{Stein operator}, namely a linear differential operator with polynomial coefficients. In this paper, we…

Probability · Mathematics 2022-01-11 Ehsan Azmoodeh , Dario Gasbarra , Robert E. Gaunt

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Probability · Mathematics 2023-04-27 Guillaume Mijoule , Martin Raič , Gesine Reinert , Yvik Swan

We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…

Probability · Mathematics 2016-03-28 Christophe Ley , Gesine Reinert , Yvik Swan

In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators…

Probability · Mathematics 2016-05-10 N. S. Upadhye , V. Cekanavicius , P. Vellaisamy

We introduce a density-power weighted variant for the Stein operator, called the $\gamma$-Stein operator. This is a novel class of operators derived from the $\gamma$-divergence, designed to build robust inference methods for unnormalized…

Machine Learning · Statistics 2026-05-26 Shinto Eguchi

In this paper we present a general framework for Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterisations, among which we highlight score-Stein operators and kernel Stein…

Probability · Mathematics 2019-11-14 Guillaume Mijoule , Gesine Reinert , Yvik Swan

In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…

Probability · Mathematics 2023-07-06 Benjamin Arras , Ehsan Azmoodeh , Guillaume Poly , Yvik Swan

In this paper, we make a novel connection between Stein's method and noncommutative algebra by viewing polynomial Stein operators (Stein operators with polynomial coefficients) as elements of the first Weyl algebra. Through this connection…

Probability · Mathematics 2025-04-30 Ehsan Azmoodeh , Dario Gasbarra , Robert E. Gaunt

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common…

Machine Learning · Statistics 2024-04-16 Jiaxin Shi , Yuhao Zhou , Jessica Hwang , Michalis K. Titsias , Lester Mackey

We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…

Probability · Mathematics 2023-11-03 Gilles Germain , Yvik Swan

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…

Probability · Mathematics 2017-05-30 Robert E. Gaunt

Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…

Probability · Mathematics 2014-04-01 Robert E. Gaunt

Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…

Statistics Theory · Mathematics 2024-12-05 Bruno Ebner , Adrian Fischer , Robert E. Gaunt , Babette Picker , Yvik Swan

In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…

Probability · Mathematics 2022-01-06 Kalyan Barman , N. S. Upadhye

Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's…

Machine Learning · Statistics 2018-06-11 Jiaxin Shi , Shengyang Sun , Jun Zhu

We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic,…

Probability · Mathematics 2024-12-03 Mario Díaz , Arturo Jaramillo

In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wide family of Stein-Covariance identities which we put to use…

Probability · Mathematics 2018-12-27 Marie Ernst , Gesine Reinert , Yvik Swan
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