A variational inference framework for inverse problems

Luca Maestrini, Robert G. Aykroyd and Matt P. Wand

Computational Statistics & Data Analysis, 2025, vol. 202, issue C

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.

Keywords: Block-banded matrices; Fast approximate inference; Image processing; Penalized regression; Positron emission tomography (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:202:y:2025:i:c:s0167947324001397

DOI: 10.1016/j.csda.2024.108055

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