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• W3134700346 abstract "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 $Pi(betamid theta)$ as an infinite mixture of simple location-scale changes; applying the Bayes' theorem, $Pi(thetamidbeta)$ 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." @default.
• W3134700346 created "2021-03-15" @default.
• W3134700346 creator A5049615306 @default.
• W3134700346 date "2019-07-24" @default.
• W3134700346 modified "2023-09-27" @default.
• W3134700346 title "Transport Monte Carlo: High-Accuracy Posterior Approximation via Random Transport" @default.
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• W3134700346 hasPublicationYear "2019" @default.
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