Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maxim...

Full description

Saved in:
Bibliographic Details
Main Authors Sanz-Alonso, Daniel, Waniorek, Nathan
Format Journal Article
LanguageEnglish
Published 05.01.2024
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Mathematics - Statistics Theory
Statistics - Theory
Online AccessGet full text

Cover

More Information
Summary:This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.
DOI:10.48550/arxiv.2401.03074