Pseudo-extended Markov chain Monte Carlo
This addresses the issue of computational inefficiency in Bayesian inference for researchers and practitioners dealing with multi-modal posteriors, representing an incremental improvement over existing MCMC methods.
The paper tackles the problem of slow mixing in Markov chain Monte Carlo (MCMC) sampling for multi-modal posterior distributions by introducing the pseudo-extended MCMC method, which augments the state-space with pseudo-samples to connect modes and improve sampling efficiency, demonstrating improved performance over Hamiltonian Monte Carlo on models like Boltzmann machines and those with sparsity-inducing priors.
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.