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

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