Previously we covered Variational Autoencoders (VAE) — popular inference tool based on neural networks. In this post we'll consider, a followup work from Torronto by Y. Burda, R. Grosse and R. Salakhutdinov, Importance Weighted Autoencoders (IWAE). The crucial contribution of this work is introduction of a new lower-bound on the marginal log-likelihood $\log p(x)$ which generalizes ELBO, but also allows one to use less accurate approximate posteriors $q(z \mid x, \Lambda)$.
On a dessert we'll discuss another paper, Variational inference for Monte Carlo objectives by A. Mnih and D. Rezende which aims to broaden the applicability of this approach to models where reparametrization trick can not be used (e.g. for discrete variables).