Bayesian Inference with Generative Adversarial Network Priors

2019/07/22 by Dhruv Patel, Patel, Dhruv, Assad A. Oberai +2 · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Image and Video Processing (eess.IV) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #cs.LG #eess.IV #electronic engineering #information engineering #physics.comp-ph #stat.ML

paper · pdf · doi:10.48550/arxiv.1907.09987

arxiv created 2019/07/22 · openalex publication_date 2019/07/22 · arxiv updated 2019/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bayesian inference is used extensively to infer and to quantify the uncertainty in a field of interest from a measurement of a related field when the two are linked by a physical 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 represent mathematically. In this manuscript we consider the use of Generative Adversarial Networks (GANs) in addressing these challenges. A GAN is a type of deep neural network equipped with the ability to learn the distribution implied by multiple samples of a given field. Once trained on these samples, the generator component of a GAN maps the iid components of a low-dimensional latent vector to an approximation of the distribution of the field of interest. In this work we demonstrate how this approximate distribution may be used as a prior in a Bayesian update, and how it addresses the challenges associated with characterizing complex prior distributions and the large dimension of the inferred field. We demonstrate the efficacy of this approach by applying it to the problem of inferring and quantifying uncertainty in the initial temperature field in a heat conduction problem from a noisy measurement of the temperature at later time.

Citations

• Bayesian Inference for Generalized Additive Mixed Models Based on Markov Random Field Priors
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Compressed Sensing using Generative Models
• MaskGAN: Better Text Generation via Filling in the______
• Large Scale GAN Training for High Fidelity Natural Image Synthesis
• Deep Compressed Sensing
• Deep Residual Learning for Image Recognition
• Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks

Cited by

• Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
• Application of Deep Learning-based Interpolation Methods to Nearshore Bathymetry

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