Generative Bayesian Inference with GANs

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

Yuexi Wang and Veronika Rockova introduce a novel Bayesian Generative Adversarial Network (B-GAN) sampler designed for Bayesian inference in scenarios lacking explicit or tractable likelihoods. Published in 2026, this work integrates Approximate Bayesian Computation (ABC) with deep neural implicit samplers, specifically GANs and adversarial variational Bayes. The B-GAN directly targets the posterior distribution by solving an adversarial optimization problem, learning a deterministic mapping from an ABC reference using conditional GANs. Once trained, the model generates independent and identically distributed (iid) posterior samples efficiently. The authors also propose two local refinement post-processing techniques: data-driven proposals with importance reweighting and variational Bayes. Empirical results on simulated data demonstrate competitive performance against other likelihood-free posterior simulators, with theoretical findings indicating convergence of the total variation distance between true and approximate posteriors to zero under specific neural network configurations.

Key takeaway

For research scientists developing Bayesian inference methods where explicit likelihoods are intractable, the B-GAN sampler offers a robust alternative. You should consider integrating this GAN-based approach to directly target posteriors, potentially reducing computational overhead for sampling. Explore its post-processing refinements to enhance the accuracy of your approximate posteriors.

Key insights

B-GAN bridges ABC and GANs to enable direct posterior sampling without explicit likelihoods.

Principles

• Adversarial optimization can target posteriors directly.
• Deterministic mappings can generate iid posterior samples.

Method

B-GAN learns a deterministic mapping via conditional GANs on an ABC reference, then filters noise for iid posterior samples, optionally refined by importance reweighting or variational Bayes.

In practice

• Apply B-GAN for inference with intractable likelihoods.
• Use post-processing for local posterior refinements.

Topics

• Generative Bayesian Inference
• Generative Adversarial Networks
• Approximate Bayesian Computation
• Posterior Sampling
• Adversarial Optimization

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.