Transport Monte Carlo: High-Accuracy Posterior Approximation via Random Transport

• 成果类型: Article
• 署名作者: Duan, Leo L.
• 署名单位: State University System of Florida; University of Florida
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2003201
• 发表日期: 2023
• 页码: 1659-1670
• 关键词: flow; mcmc

摘要

In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a joint distribution (random transport plan) between two random variables, theta from the posterior distribution and beta from the simple multivariate uniform. Specifically, we obtain an approximate estimate of the conditional distribution Pi(beta vertical bar theta) as an infinite mixture of simple location-scale changes; applying the Bayes' theorem, Pi(theta vertical bar beta) can be sampled as one of the reversed transforms from the uniform, with the weight proportional to the posterior density/mass function. This produces independent random samples with high approximation accuracy, as well as nice theoretical guarantees. Our method shows compelling advantages in performance and accuracy, compared to the state-of-the-art Markov chain Monte Carlo and approximations such as variational Bayes and normalizing flow. We illustrate this approach via several challenging applications, such as sampling from multi-modal distribution, estimating sparse signals in high dimension, and soft-thresholding of a graph with a prior on the degrees. Supplementary materials for this article, including the source code and additional comparison with popular alternative algorithms are available on the journal website.