  Recent work used importance sampling ideas for better variational bounds on
likelihoods. We clarify the applicability of these ideas to pure probabilistic
inference, by showing the resulting Importance Weighted Variational Inference
(IWVI) technique is an instance of augmented variational inference, thus
identifying the looseness in previous work. Experiments confirm IWVI's
practicality for probabilistic inference. As a second contribution, we
investigate inference with elliptical distributions, which improves accuracy in
low dimensions, and convergence in high dimensions.
