Generative Bayesian Inference with GANs

TL;DR

This paper introduces Bayesian GANs, a novel method that combines ABC and GANs to directly sample from complex posteriors without explicit likelihoods, demonstrating competitive results on simulated data.

Contribution

The paper develops a Bayesian GAN framework that directly targets posteriors using adversarial training, with post-processing refinements and theoretical convergence guarantees.

Findings

B-GAN can generate iid posterior samples efficiently.

The method shows convergence of the total variation distance to the true posterior.

Experimental results demonstrate competitive performance with recent likelihood-free methods.

Abstract

In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators.