Safe importance sampling based on partial posteriors and neural variational approximations

In this work, we present two novel importance sampling (IS) methods, which can be considered safe in the sense that they avoid catastrophic scenarios where the IS estimators could have infinite variance. This is obtained by using a population of proposal densities where each one is wider than the posterior distribution. In fact, we consider partial posterior distributions (i.e., considering a smaller number of data) as proposal densities. Neuronal variational approximations are also discussed. The experimental results show the benefits of the proposed schemes.