Maestrini, L., Aykroyd, R.G. orcid.org/0000-0003-3700-0816 and Wand, M.P. (2025) A variational inference framework for inverse problems. Computational Statistics and Data Analysis, 202. 108055. ISSN 0167-9473
Abstract
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model fitting times. The message passing and factor graph fragment approach to variational Bayes that is also described facilitates streamlined implementation of approximate inference algorithms and allows for supple inclusion of numerous response distributions and penalizations into the inverse problem model. Models for one- and two-dimensional response variables are examined and an infrastructure is laid down where efficient algorithm updates based on nullifying weak interactions between variables can also be derived for inverse problems in higher dimensions. An image processing application and a simulation exercise motivated by biomedical problems reveal the computational advantage offered by efficient implementation of variational Bayes over Markov chain Monte Carlo.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | block-banded matrices; fast approximate inference; image processing; penalized regression; positron emission tomography |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Sep 2024 11:33 |
Last Modified: | 01 Oct 2024 15:06 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.csda.2024.108055 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:216836 |