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Related papers: Parametric Stein operators and variance bounds

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We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…

Probability · Mathematics 2020-09-08 Xiao Fang , Yuta Koike

New bounds on the total variation distance between the law of integer valued functionals of possibly non-symmetric and non-homogeneous infinite Rademacher sequences and the Poisson distribution are established. They are based on a…

Probability · Mathematics 2017-07-26 Kai Krokowski

The Straight-Through (ST) estimator is a widely used technique for back-propagating gradients through discrete random variables. However, this effective method lacks theoretical justification. In this paper, we show that ST can be…

Machine Learning · Computer Science 2019-10-08 Pengyu Cheng , Chang Liu , Chunyuan Li , Dinghan Shen , Ricardo Henao , Lawrence Carin

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…

Statistics Theory · Mathematics 2018-07-19 Zhuoran Yang , Krishnakumar Balasubramanian , Han Liu

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

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Numerical Analysis · Mathematics 2018-02-14 Simon Arridge , Kazufumi Ito , Bangti Jin , Chen Zhang

Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is…

Combinatorics · Mathematics 2007-05-23 Jason Fulman

In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…

Probability · Mathematics 2020-01-28 James Thompson

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…

Probability · Mathematics 2013-04-18 Kaspar Stucki , Dominic Schuhmacher

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…

Probability · Mathematics 2009-08-14 Peter Eichelsbacher , Matthias Löwe

We show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with…

Probability · Mathematics 2025-10-01 David Grzybowski , Mark Meckes

Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution…

Machine Learning · Statistics 2021-05-24 Anna Korba , Pierre-Cyril Aubin-Frankowski , Szymon Majewski , Pierre Ablin

The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional…

Statistics Theory · Mathematics 2023-03-13 Adrian Fischer , Robert E. Gaunt , Andrey Sarantsev

We study the convergence of Bernstein type operators leading to two results. The first: The kernel $K_n$ of the Bernstein-Durrmeyer operator at each point $x \in (0, 1)$ $\unicode{x2013}$ that is $K_n(x, t) dt$ $\unicode{x2013}$ once…

Classical Analysis and ODEs · Mathematics 2023-12-05 Mohammed Taariq Mowzer

We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These "Stein factor" bounds deliver control over Wasserstein and related…

Probability · Mathematics 2016-11-24 Lester Mackey , Jackson Gorham

We propose a novel particle-based variational inference method designed to work with multimodal distributions. Our approach, referred to as Branched Stein Variational Gradient Descent (BSVGD), extends the classical Stein Variational…

Machine Learning · Computer Science 2025-07-18 Isaías Bañales , Arturo Jaramillo , Joshué Helí Ricalde-Guerrero

Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…

Robotics · Computer Science 2022-02-10 Fahira Afzal Maken , Fabio Ramos , Lionel Ott

We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…

Methodology · Statistics 2020-03-31 Shota Gugushvili , Frank van der Meulen , Moritz Schauer , Peter Spreij

Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as…

Astrophysics · Physics 2015-05-13 Jason Maron , Mordecai-Mark Mac Low

This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represent densities of particles. The Wasserstein metric is…

Optimization and Control · Mathematics 2020-11-03 Amirhossein Karimi , Tryphon T. Georgiou