Variational approximation for importance sampling

We propose an importance sampling algorithm with proposal distribution obtained from variational approximation. This method combines the strength of both importance sampling and variational method. On one hand, this method avoids the bias from variational method. On the other hand, variational approximation provides a way to design the proposal distribution for the importance sampling algorithm. Theoretical justification of the proposed method is provided. Numerical results show that using variational approximation as the proposal can improve the performance of importance sampling and sequential importance sampling.