FastGP: An R Package for Gaussian Processes

TL;DR

FastGP is an R package that significantly improves the computational efficiency of Gaussian process operations, especially for Toeplitz matrices and sampling, making GPs more practical for real-world applications.

Contribution

The paper introduces an R package that leverages Rcpp and RcppEigen for faster Gaussian process computations, including Toeplitz matrix inversion and elliptical slice sampling.

Findings

Efficient inversion of Toeplitz matrices in O(n^2) time.

Implementation of elliptical slice sampling for Gaussian processes.

Enhanced practical usability of Gaussian processes in R.

Abstract

Despite their promise and ubiquity, Gaussian processes (GPs) can be difficult to use in practice due to the computational impediments of fitting and sampling from them. Here we discuss a short R package for efficient multivariate normal functions which uses the Rcpp and RcppEigen packages at its core. GPs have properties that allow standard functions to be sped up; as an example we include functionality for Toeplitz matrices whose inverse can be computed in O(n^2) time with methods due to Trench and Durbin (Golub & Van Loan 1996), which is particularly apt when time points (or spatial locations) of a Gaussian process are evenly spaced, since the associated covariance matrix is Toeplitz in this case. Additionally, we include functionality to sample from a latent variable Gaussian process model with elliptical slice sampling (Murray, Adams, & MacKay 2010).