Deep and Hierarchical Implicit Models

Implicit probabilistic models are a very flexible class for modeling data. They define a process to simulate observations, and unlike traditional models, they do not require a tractable likelihood function. In this paper, we develop two families of models: hierarchical implicit models and deep implicit models. They combine the idea of implicit densities with hierarchical Bayesian modeling and deep neural networks. The use of implicit models with Bayesian analysis has in general been limited by our ability to perform accurate and scalable inference. We develop a variational inference algorithm for implicit models. Key to our method is specifying a variational family that is also implicit. This matches the model's flexibility and allows for accurate approximation of the posterior. Our method scales up implicit models to sizes previously not possible and opens the door to new modeling designs. We demonstrate diverse applications: a large-scale physical simulator for predator-prey populations in ecology; a Bayesian generative adversarial network for discrete data; and a deep implicit model for text generation.