Sampling by divergence minimization

Abstract

We introduce a Markov Chain Monte Carlo (MCMC) method that is designed to sample from target distributions with irregular geometry using an adaptive scheme. In cases where targets exhibit non-Gaussian behavior, we propose that adaptation should be regional rather than global. Our algorithm minimizes the information projection component of the Kullback–Leibler (KL) divergence between the proposal and target distributions to encourage proposals that are distributed similarly to the regional geometry of the target. Unlike traditional adaptive MCMC, this procedure rapidly adapts to the geometry of the target’s current position as it explores the surrounding space without the need for many preexisting samples. The divergence minimization algorithms are tested on target distributions with irregularly shaped modes and we provide results demonstrating the effectiveness of our methods.

Keywords:

• Adaptive MCMC
• KL divergence
• Markov Chain Monte Carlo
• Sampling

Acknowledgements

We thank the anonymous referee for very helpful comments which have improved our paper and helped emphasize its position in the broader adaptive MCMC literature.

Disclosure statement

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Code availability statement

The implementations of the algorithms discussed here along with all code used to generate examples can be accessed at https://github.com/AmeerD/Scout-MCMC.

Notes

1 https://github.com/AmeerD/Scout-MCMC