A-NICE-MC: Adversarial Training for MCMC

TL;DR

A-NICE-MC introduces a novel adversarial training framework that leverages neural networks and volume-preserving flows to automatically design efficient, domain-specific MCMC proposals, significantly improving sampling efficiency over traditional methods.

Contribution

The paper presents the first automatic framework for designing efficient, domain-specific MCMC proposals using adversarial training and neural network-based kernels.

Findings

Outperforms Hamiltonian Monte Carlo in experiments

Provides strong guarantees of MCMC with neural network expressiveness

Automatically learns problem-specific proposals for faster convergence

Abstract

Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes which can lead to slow convergence, or hand-crafting of problem-specific proposals by an expert. We propose A-NICE-MC, a novel method to train flexible parametric Markov chain kernels to produce samples with desired properties. First, we propose an efficient likelihood-free adversarial training method to train a Markov chain and mimic a given data distribution. Then, we leverage flexible volume preserving flows to obtain parametric kernels for MCMC. Using a bootstrap approach, we show how to train efficient Markov chains to sample from a prescribed posterior distribution by iteratively improving the quality of both the model and the samples. A-NICE-MC provides the first framework to automatically design efficient domain-specific MCMC proposals. Empirical results demonstrate that A-NICE-MC combines the strong guarantees of MCMC with the expressiveness of deep neural networks, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.