# A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression

@article{Ameli2022ASW, title={A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression}, author={Siavash Ameli and Shawn C. Shadden}, journal={ArXiv}, year={2022}, volume={abs/2207.08038} }

We study a matrix that arises in a singular formulation of the Woodbury matrix identity when the Woodbury identity no longer holds. We present generalized inverse and pseudo-determinant identities for such matrix that have direct applications to the Gaussian process regression, in particular, its likelihood representation and its precision matrix. We also provide an eﬃcient algorithm and numerical analysis for the presented determinant identities and demonstrate their advantages in certain…

## 2 Citations

### Interpolating log-determinant and trace of the powers of matrix bfA + tbfB

- Computer ScienceStat. Comput.
- 2022

The presented interpolation functions are based on the modification of sharp bounds for these functions, and the accuracy and performance of the proposed method is demonstrated with numerical examples.

### Interpolating log-determinant and trace of the powers of matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textb

- Materials ScienceStatistics and Computing
- 2022

We develop heuristic interpolation methods for the functions t↦logdetA+tB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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