Efficient nonparametric importance sampling for Bayesian learning

Monte Carlo methods, such as importance sampling, have become a major tool in Bayesian inference. However, in order to produce an accurate estimate, the sampling distribution is required to be close to the target distribution. Several adaptive importance sampling algorithms, proposed over the last few years, attempt to learn a good sampling distribution automatically, but their performance is often unsatisfactory. In addition, a theoretical analysis, which takes into account the computational cost of the sampling algorithms, is still lacking. In this paper, we present a first attempt at such analysis, and we propose some modifications to existing adaptive importance sampling algorithms, which produce significantly more accurate estimates.