# Bayesian neural network priors for edge-preserving inversion

arXiv: https://arxiv.org/abs/2112.10663 · HTML: https://mlsanity.com/paper/2112.10663/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Builds on (most cited first, 8 of 8)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Optimal Approximation with Sparsely Connected Deep Neural Networks](https://mlsanity.com/paper/1705.01714/) (2017)
- [A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion](https://mlsanity.com/paper/1308.1313/) (2013)
- [Dimension-Robust MCMC in Bayesian Inverse Problems](https://mlsanity.com/paper/1803.03344/) (2018)
- [Cauchy Markov Random Field Priors for Bayesian Inversion](https://mlsanity.com/paper/2105.12488/) (2021)

## Built on by (most cited first, 2 of 2)

- [Bayesian Deep Learning with Multilevel Trace-class Neural Networks](https://mlsanity.com/paper/2203.12961/) (2022)
- [Leveraging joint sparsity in hierarchical Bayesian learning](https://mlsanity.com/paper/2303.16954/) (2023)

## Abstract (arXiv)

We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is introduced, motivated by existing results concerning the infinite-width limit of such networks. We show theoretically that samples from such priors have desirable discontinuous-like properties even when the network width is finite, making them appropriate for edge-preserving inversion. Numerically we consider deconvolution problems defined on one- and two-dimensional spatial domains to illustrate the effectiveness of these priors; MAP estimation, dimension-robust MCMC sampling and ensemble-based approximations are utilized to probe the posterior distribution. The accuracy of point estimates is shown to exceed those obtained from non-heavy tailed priors, and uncertainty estimates are shown to provide more useful qualitative information.