Multivariate Stein Factors for a Class of Strongly Log-concave Distributions

Lester Mackey; Jackson Gorham

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arXiv · 1512.07392

Multivariate Stein Factors for a Class of Strongly Log-concave Distributions

Lester Mackey·Jackson Gorham

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Abstract

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 smooth function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions.

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Lester Mackey, Jackson Gorham. 2016-11-23. Multivariate Stein Factors for a Class of Strongly Log-concave Distributions. https://arxiv.org/abs/1512.07392

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