This repository contains MATLAB files for an empirical Bayes method to estimate hyperparameters using an approach based on the generalized Golub-Kahan (genGK) bidiagonalization. The codes accompany the paper:
"Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems"
- Hall-Hooper, Saibaba, Chung, and Miller, ACOM, 2024
We implement an empirical Bayes (EB) method to estimate hyperparameters
that maximize the marginal posterior, i.e., the probability density of
the hyperparameters conditioned on the data.
For problems where the computation of the square root and inverse of
prior covariance matrices are not feasible, we use an approach based on
the generalized Golub-Kahan bidiagonalization to approximate the
marginal posterior and seek hyperparameters that minimize the
approximate marginal posterior.
MATLAB 9.14 (R2023a)
These codes require the following packages:
Regularization Tools package: Hansen. Regularization tools: A
package for analysis and solution of discrete ill-posed
problems. Numerical Algorithms, 1994.
genHyBR: generalized hybrid iterative methods
by Julianne Chung and Arvind K. Saibaba
https://github.com/juliannechung/genHyBR
See Contents.m
Khalil A. Hall-Hooper
Department of Mathematics, North Carolina State University
Arvind K. Saibaba,
Department of Mathematics, North Carolina State University
Julianne Chung,
Department of Mathematics, Emory University
Scot M. Miller,
Department of Environmental Health and Engineering, Johns Hopkins University
If you use this codes, you must cite the original authors:
[1] Hall-Hooper et al. "Efficient iterative methods for
hyperparameter estimation in large-scale linear
inverse problems". ACOM, 2024.
This work was partially supported by the National Science Foundation under grants DMS-2208294, DMS-2341843, DMS-2026830, and DMS-2026835. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.