# Interpolating Log-Determinant and Trace of the Powers of Matrix A + t B

arXiv: https://arxiv.org/abs/2009.07385 · HTML: https://mlsanity.com/paper/2009.07385/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression](https://mlsanity.com/paper/2207.08038/) (2022)

## Abstract (arXiv)

We develop heuristic interpolation methods for the functions t mapsto log det left( A + t B right) and t mapsto operatornametraceleft( (A + t B)p right) where the matrices A and B are Hermitian and positive (semi) definite and p and t are real variables. These functions are featured in many applications in statistics, machine learning, and computational physics. The presented interpolation functions are based on the modification of sharp bounds for these functions. We demonstrate the accuracy and performance of the proposed method with numerical examples, namely, the marginal maximum likelihood estimation for Gaussian process regression and the estimation of the regularization parameter of ridge regression with the generalized cross-validation method.