A-NICE-MC: Adversarial Training for MCMC
This addresses the need for efficient, domain-specific MCMC proposals without expert hand-crafting, offering a novel approach to improve sampling in probabilistic modeling.
The paper tackles the problem of slow convergence in Markov Chain Monte Carlo (MCMC) methods by proposing A-NICE-MC, a framework to automatically train flexible parametric kernels for efficient sampling, which significantly outperforms methods like Hamiltonian Monte Carlo in empirical results.
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.