Keywords: Variational Inference, Nested Importance Sampling, Bayesian Inference, Monte Carlo Methods
TL;DR: Variational Inference Framework based on Nested Importance Sampling
Abstract: We develop nested variational inference (NVI), a family of methods that learn proposals for nested importance samplers by minimizing an inclusive or exclusive KL divergence at each level of nesting. NVI is applicable to many commonly-used importance sampling strategies and additionally provides a mechanism for learning intermediate densities, which can serve as heuristics to guide the sampler. Our experiments apply NVI to learn samplers targeting (a) an unnormalized density using annealing and (b) the posterior of a hidden Markov model. We observe improved sample quality in terms of log average weight and effective sample size.