Variational autoencoders in Bayesian linear inverse problems

Abstract

The Bayesian approach to inverse problems updates the prior distribution of an unknown quantity into a non-trivial posterior distribution conditioned on indirect observations. This thesis studies a methodology for constructing such a prior distribution through variational autoencoder learning. Variational autoencoder parameterizes the prior distribution using neural networks. The advantage of such an approach is that the Bayesian linear inverse problem can be formulated and solved in a latent space with a dimension lower than the initial space dimension using the VAE.