  Adaptive importance sampling (AIS) methods provide a useful alternative to
Markov Chain Monte Carlo (MCMC) algorithms for performing inference of
intractable distributions. Population Monte Carlo (PMC) algorithms constitute a
family of AIS approaches which adapt the proposal distributions iteratively to
improve the approximation of the target distribution. Recent work in this area
primarily focuses on ameliorating the proposal adaptation procedure for
high-dimensional applications. However, most of the AIS algorithms use simple
proposal distributions for sampling, which might be inadequate in exploring
target distributions with intricate geometries. In this work, we construct
expressive proposal distributions in the AIS framework using normalizing flow,
an appealing approach for modeling complex distributions. We use an iterative
parameter update rule to enhance the approximation of the target distribution.
Numerical experiments show that in high-dimensional settings, the proposed
algorithm offers significantly improved performance compared to the existing
techniques.
