Pseudo-extended Markov chain Monte Carlo

Nemeth, Christopher and Lindsten, Fredrik and Filippone, Maurizio and Hensman, James (2019) Pseudo-extended Markov chain Monte Carlo. In: Thirty-third Conference on Neural Information Processing Systems, 2019-12-08 - 2019-12-14, Vancouver Convention Center.

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Abstract

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 seudoextended 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.