Nested Variational Inference
This work addresses the challenge of improving importance sampling efficiency for practitioners in probabilistic modeling and machine learning, though it appears incremental as it builds on existing variational inference and importance sampling frameworks.
The paper tackles the problem of learning proposals for nested importance samplers by developing nested variational inference (NVI), which minimizes KL divergences at each nesting level to improve sample quality, as evidenced by gains in log average weight and effective sample size in experiments on multimodal distributions, hidden Markov models, and hierarchical deep generative models.
We develop nested variational inference (NVI), a family of methods that learn proposals for nested importance samplers by minimizing an forward or reverse KL divergence at each level of nesting. NVI is applicable to many commonly-used importance sampling strategies and provides a mechanism for learning intermediate densities, which can serve as heuristics to guide the sampler. Our experiments apply NVI to (a) sample from a multimodal distribution using a learned annealing path (b) learn heuristics that approximate the likelihood of future observations in a hidden Markov model and (c) to perform amortized inference in hierarchical deep generative models. We observe that optimizing nested objectives leads to improved sample quality in terms of log average weight and effective sample size.