Implicitly Adaptive Importance Sampling

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the mismatch between the current proposal and a target distribution. In this work, we present an implicit adaptive importance sampling method that applies to complicated distributions which are not available in closed form. The method iteratively matches the moments of a set of Monte Carlo draws to weighted moments based on importance weights. We apply the method to Bayesian leave-one-out cross-validation and show that it performs better than many existing parametric adaptive importance sampling methods while being computationally inexpensive.