Likelihood Almost Free Inference Networks

Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since the ELBO requires variational likelihood evaluations of the latent variables. In this paper, we propose a novel framework to enrich the variational family based on an alternative lower bound, by introducing auxiliary random variables to the variational distribution only. While offering a much richer family of complex variational distributions, the resulting inference network is likelihood almost free in the sense that only the latent variables require evaluations from simple likelihoods and samples from all the auxiliary variables are sufficient for maximum likelihood inference. We show that the proposed approach is essentially optimizing a probabilistic mixture of ELBOs, thus enriching modeling capacity and enhancing robustness. It outperforms state-of-the-art methods in our experiments on several density estimation tasks.