Parallel Adaptive Importance Sampling

Standard MCMC algorithms can be easily parallelised, simply by executing many independent chains across a cluster. However, since a priori we do not have much information about the target distribution, each chain does not start in equilibrium, and as such must be "burned-in". Since it takes each chain the same amount of time to burn-in, this process takes the same amount of time no matter how many processors are used. This motivates a method which allows communication across the chains, allowing for better mixing properties. In this talk, we will introduce the Parallel Adaptive Importance Sampling (PAIS) algorithm, which incorporates sophisticated MCMC proposals and optimal transport resampling methods from particle filtering in order to construct a proposal regime which incorporates information from the previous state of chain from all processors, leading to better mixing properties. We will also present some recent advances in speeding up PAIS by using transport maps to simplify the posterior distribution.