利用层次贝叶斯学习中的联合稀疏性

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-05-24 DOI:10.1137/23m156255x

Jan Glaubitz, Anne Gelb

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引用次数: 0

摘要

SIAM/ASA 不确定性量化期刊》，第 12 卷，第 2 期，第 442-472 页，2024 年 6 月。摘要：我们提出了一种分层贝叶斯学习方法，用于从多个测量向量中联合推断稀疏参数向量。我们的模型对每个参数向量使用单独的条件高斯前验，并使用共同的伽玛分布超参数来执行联合稀疏性。由此产生的联合稀疏性促进先验与现有的贝叶斯推理方法相结合，产生了一系列新算法。我们的数值实验（包括多线圈磁共振成像应用）表明，我们的新方法始终优于常用的分层贝叶斯方法。

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Leveraging Joint Sparsity in Hierarchical Bayesian Learning

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 442-472, June 2024.
Abstract.We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyperparameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multicoil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.