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We detail an approach to develop Stein's method for bounding integral metrics on probability measures defined on a Riemannian manifold $\mathbf M$. Our approach exploits the relationship between the generator of a diffusion on $\mathbf M$…

Probability · Mathematics 2023-04-28 Huiling Le , Alexander Lewis , Karthik Bharath , Christopher Fallaize

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

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…

Probability · Mathematics 2013-04-05 Christophe Ley , Yvik Swan

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

Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity…

Machine Learning · Statistics 2026-01-30 Fabian Bleile , Sarah Lumpp , Mathias Drton

Out-of-distribution detection methods are often either data-centric, detecting deviations from the training input distribution irrespective of their effect on a trained model, or model-centric, relying on classifier outputs without explicit…

Machine Learning · Computer Science 2026-02-10 Michał Kozyra , Gesine Reinert

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…

Probability · Mathematics 2018-03-09 Thomas A. Courtade , Max Fathi , Ashwin Pananjady

Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works focused on studying kernel choices to…

Methodology · Statistics 2022-06-02 Wenkai Xu

Distributional approximation is a fundamental problem in machine learning with numerous applications across all fields of science and engineering and beyond. The key challenge in most approximation methods is the need to tackle the…

Statistics Theory · Mathematics 2024-09-19 Xiaoda Qu , Xiran Fan , Baba C. Vemuri

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

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

Kernel Stein discrepancies (KSDs) are widely used for goodness-of-fit testing, but standard KSDs can be insensitive to higher-order dependence features such as tail dependence. We introduce the Copula-Stein Discrepancy (CSD), which defines…

Machine Learning · Statistics 2026-01-13 Agnideep Aich , Ashit Baran Aich

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

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

When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…

Statistics Theory · Mathematics 2022-10-07 Alessandro Barp , Francois-Xavier Briol , Andrew B. Duncan , Mark Girolami , Lester Mackey

We develop connections between Stein's approximation method, logarithmic Sobolev and transport inequalities by introducing a new class of functional inequalities involving the relative entropy, the Stein kernel, the relative Fisher…

Probability · Mathematics 2014-07-24 Michel Ledoux , Ivan Nourdin , Giovanni Peccati

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

Combinatorial black-box optimization in high-dimensional settings demands a careful trade-off between exploiting promising regions of the search space and preserving sufficient exploration to identify multiple optima. Although…

Artificial Intelligence · Computer Science 2026-04-20 Thomas Landais , Olivier Goudet , Adrien Goëffon , Frédéric Saubion , Sylvain Lamprier

We investigate stability of invariant measures of diffusion processes with respect to $L^p$ distances on the coefficients, under an assumption of log-concavity. The method is a variant of a technique introduced by Crippa and De Lellis to…

Probability · Mathematics 2020-10-28 Max Fathi , Dan Mikulincer

This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population…

Methodology · Statistics 2012-03-22 Ann Cohen Brandwein , William E. Strawderman