Generative Bayesian Inference with GANs
Yuexi Wang, Veronika Ročková
TL;DR
The paper tackles likelihood-free Bayesian inference for simulator-based models by uniting ABC with generative adversarial networks to learn implicit samplers of the posterior π(θ|X). The authors propose B-GAN, a conditional Wasserstein GAN that matches the ABC reference table to approximate the joint π(X,θ) and thereby draws iid posterior samples from π(θ|X0) with minimal extra cost after training. They augment B-GAN with two refinements—a two-step sequential proposal strategy and an adversarial variational Bayes objective—to improve locality around the observed data and tighten posterior approximations. Theoretical results establish finite-sample bounds on the total variation distance between the true and approximate posteriors, and empirical studies across LV, Boom-and-Bust, and SIR/common cold data demonstrate competitive or superior performance relative to state-of-the-art likelihood-free methods, with favorable scaling and flexibility.
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.