Article
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Regularization, Bayesian Inference and Machine Learning methods for Inverse Problems†
Version 1
: Received: 1 November 2021 / Approved: 3 November 2021 / Online: 3 November 2021 (20:18:51 CET)
A peer-reviewed article of this Preprint also exists.
Mohammad-Djafari, A. Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems. Entropy 2021, 23, 1673. Mohammad-Djafari, A. Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems. Entropy 2021, 23, 1673.
Abstract
Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.
Keywords
Inverse problems; Regularization; Bayesian inference; Machine Learning; Artificial Intelligence; Gauss-Markov-Potts; Variational Bayesian Approach (VBA); Physics Informed ML
Subject
Computer Science and Mathematics, Artificial Intelligence and Machine Learning
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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