GAN-based Priors for Quantifying Uncertainty
This work addresses uncertainty quantification problems in fields like image processing and physics-driven inverse problems, offering a novel method for handling complex priors, though it is incremental in combining GANs with Bayesian updates.
The authors tackled the challenge of performing Bayesian inference on high-dimensional fields with mathematically intractable priors by using GAN-learned distributions as priors, achieving superior out-of-distribution detection and accuracy in image classification, as well as built-in variance estimation in image inpainting.
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large dimension, and/or have prior distributions that are difficult to characterize mathematically. In this work we demonstrate how the approximate distribution learned by a deep generative adversarial network (GAN) may be used as a prior in a Bayesian update to address both these challenges. We demonstrate the efficacy of this approach on two distinct, and remarkably broad, classes of problems. The first class leads to supervised learning algorithms for image classification with superior out of distribution detection and accuracy, and for image inpainting with built-in variance estimation. The second class leads to unsupervised learning algorithms for image denoising and for solving physics-driven inverse problems.