# The covariance matrix of Green's functions and its application to machine learning

arXiv: https://arxiv.org/abs/2004.06481 · HTML: https://mlsanity.com/paper/2004.06481/

## Key facts

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

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

- [Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification](https://mlsanity.com/paper/2402.09281/) (2024)

## Abstract (arXiv)

In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a reproducing kernel of a suitable Hilbert space. We next consider a covariance matrix composed of the normalized Green's function, which is regarded as aprobability density function. By supporting Bayesian approach, the covariance matrix gives predictive distribution, which has the predictive mean μ and the confidence interval [μ-2s, μ+2s], where s stands for a standard deviation.