Bayesian neural network priors for edgepreserving inversion
Abstract
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 heavytailed weights is introduced, motivated by existing results concerning the infinitewidth limit of such networks. We show theoretically that samples from such priors have desirable discontinuouslike properties even when the network width is finite, making them appropriate for edgepreserving inversion. Numerically we consider deconvolution problems defined on one and twodimensional spatial domains to illustrate the effectiveness of these priors; MAP estimation, dimensionrobust MCMC sampling and ensemblebased approximations are utilized to probe the posterior distribution. The accuracy of point estimates is shown to exceed those obtained from nonheavy tailed priors, and uncertainty estimates are shown to provide more useful qualitative information.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.10663
 Bibcode:
 2021arXiv211210663L
 Keywords:

 Computer Science  Machine Learning;
 Mathematics  Optimization and Control