Hierarchical Implicit Models and Likelihood-Free Variational Inference
This work addresses the problem of scalable inference in flexible implicit models for researchers in machine learning and statistics, representing a novel method for a known bottleneck.
The paper tackles the challenge of using implicit probabilistic models with complex latent structures and large datasets by introducing hierarchical implicit models (HIMs) and likelihood-free variational inference (LFVI), demonstrating applications in ecology, discrete data generation, and text generation.
Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent structure in them, and in performing inferences in such models with large data sets. In this paper, we first introduce hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling, thereby defining models via simulators of data with rich hidden structure. Next, we develop likelihood-free variational inference (LFVI), a scalable variational inference algorithm for HIMs. Key to LFVI is specifying a variational family that is also implicit. This matches the model's flexibility and allows for accurate approximation of the posterior. 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.