# GAN-based Priors for Quantifying Uncertainty

arXiv: https://arxiv.org/abs/2003.12597 · HTML: https://mlsanity.com/paper/2003.12597/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [Learning Functional Priors and Posteriors from Data and Physics](https://mlsanity.com/paper/2106.05863/) (2021)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)

## Abstract (arXiv)

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.