2019/07/24 by Leo L. Duan, Duan, Leo L.
Computer Science · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1907.10448
openalex publication_date 2019/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, θ from the posterior distribution and β from the simple multivariate uniform. Specifically, we obtain an approximate estimate of the conditional distribution Π(β| θ) as an infinite mixture of simple location-scale changes; applying the Bayes' theorem, Π(θ|β) 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 theoretic 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.