Variational Inference using Implicit Distributions
This work addresses the need for better theoretical understanding and practical algorithms in variational inference for researchers in machine learning, though it is incremental as it builds on existing methods.
The paper tackles the problem of unifying and extending variational inference methods using implicit distributions, providing a review of existing algorithms and a framework for developing new ones based on prior-contrastive and joint-contrastive approaches.
Generative adversarial networks (GANs) have given us a great tool to fit implicit generative models to data. Implicit distributions are ones we can sample from easily, and take derivatives of samples with respect to model parameters. These models are highly expressive and we argue they can prove just as useful for variational inference (VI) as they are for generative modelling. Several papers have proposed GAN-like algorithms for inference, however, connections to the theory of VI are not always well understood. This paper provides a unifying review of existing algorithms establishing connections between variational autoencoders, adversarially learned inference, operator VI, GAN-based image reconstruction, and more. Secondly, the paper provides a framework for building new algorithms: depending on the way the variational bound is expressed we introduce prior-contrastive and joint-contrastive methods, and show practical inference algorithms based on either density ratio estimation or denoising.