Bayesian Inference with Generative Adversarial Network Priors

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Dhruv let me know of the following

Hi Igor,

I hope you're doing well. Thanks for posting latest articles and relevant information on your blog. I'm a regular reader of it and really enjoy it.

Just wanted to share with you one of our recent work on Bayesian inference using Generative Adversarial Network priors (https://arxiv.org/abs/1907.09987). In the paper, we demonstrate the effectiveness of this approach (in learning better priors and efficient posterior sampling) for a physics-based inverse problem, but I think similar idea can be applied to compressive sensing and any other inverse problems and uncertainty quantification task. So, I thought it might be of interest to your community and thought of sharing with you just in case if you would like to share it.

Best,

Dhruv

Thanks Dhruv !

Bayesian Inference with Generative Adversarial Network Priors by Dhruv Patel, Assad A Oberai

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.

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