Stochastic adaptation of importance sampler

摘要

Improving efficiency of importance sampler is at the center of research inMonte Carlo methods. While adaptive approach is usually difficult within theMarkov Chain Monte Carlo framework, the counterpart in importance sampling canbe justified and validated easily. We propose an iterative adaptation methodfor learning the proposal distribution of an importance sampler based onstochastic approximation. The stochastic approximation method can recruitgeneral iterative optimization techniques like the minorization-maximizationalgorithm. The effectiveness of the approach in optimizing the Kullbackdivergence between the proposal distribution and the target is demonstratedusing several simple examples.