Reviews: Tensor Monte Carlo: Particle Methods for the GPU era

Summary: The authors describe an improved objective function for variational inference. In the spirit of the Importance Weighted Autoencoder they use multiple samples from the approximating distribution to obtain a tighter bound on the log marginal probability. The key insight of the paper is that they can use all combinations (across subsets of parameters) of samples drawn from the approximating distribution to compute marginal probability estimator. Naively this would require computation that scales exponentially in the number of subsets. The authors reduce this complexity by exploiting dependency structures in the generative model.