Hamiltonian Adaptive Importance Sampling

Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, instance in the context of Bayesian inference. In IS, samples are simulated from so-called proposal distribution, and choice this key achieving high performance. adaptive IS (AIS) methods, set proposals iteratively improved. AIS relevant timely although many limitations remain yet to be overcome, e.g., curse dimensionality high-dimensional multi-modal problems. Moreover, Hamiltonian (HMC) algorithm has become increasingly popular machine learning statistics. HMC several appealing features such as its exploratory behavior, especially targets, when other methods suffer. paper, we introduce novel importance (HAIS) method. HAIS implements two-step process with parallel chains that cooperate at each iteration. The proposed efficiently adapts population proposals, extracting advantages HMC. can understood particular generic layered family an additional resampling step. achieves significant performance improvement problems w.r.t. state-of-the-art algorithms. We discuss statistical properties show two challenging examples.