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

arXiv: https://arxiv.org/abs/1907.10448 · HTML: https://mlsanity.com/paper/1907.10448/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Discretely Indexed Flows](https://mlsanity.com/paper/2204.01361/) (2022)

## Abstract (arXiv)

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 Pi(βmid θ) as an infinite mixture of simple location-scale changes; applying the Bayes' theorem, Pi(θmidβ) 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.