Pseudo-extended Markov chain Monte Carlo
Published in NeurIPS, 2019
Recommended citation: Nemeth, C., Lindsten, F., Filippone, M. and Hensman, J., (2019). "Pseudo-extended Markov chain Monte Carlo." Advances in Neural Information Processing Systems, 32. https://proceedings.neurips.cc/paper/2019/hash/e3ca0449fa2ea7701a7ac53fb719c51a-Abstract.html
Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions. The pseudo-extended method augments the state-space of the posterior using pseudo-samples as auxiliary variables. On the extended space, the modes of the posterior are connected, which allows the MCMC sampler to easily move between well-separated posterior modes. We demonstrate that the pseudo-extended approach delivers improved MCMC sampling over the Hamiltonian Monte Carlo algorithm on multi-modal posteriors, including Boltzmann machines and models with sparsity-inducing priors.