Selbosh / basis_functions_approach_to_GP

Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming

Approximate eigendecomposition of the covariance function of a Gaussian process (GP). The method is based on interpreting the covariance function as the kernel of a pseudo-differential operator and approximating it using Hilbert space methods. This results in a reduced-rank approximation for the covariance function (Solin and Särkkä, 2020).

We denote this reduced rank GP model as the Hilbert space approximate Gaussian process (HSGP).

Contents

This repo contains three folders:

1. Paper

This contains the main manuscript of the work, the supplemental material associated to the main manuscript and a poster presentated at StanCon 2020 conference. Additionally, this folder contains the Stan codes for every case study developed in the paper.

2. uni_dimensional

This contains a first R-notebook presenting the method for some examples and comparison to exact GPs and splines. Furthermore, this folder contains some initial material of the investigation with R-code and Stan code for some univariate data sets. There are the Stan codes for implementing the approximate GP (HSGP) model, the exact GP model and a spline model on the data sets.

2. multi_dimensional

This contains some initial material of the investigation with R-code and Stan code for some multivariate data sets. There are the Stan codes for implementing the approximate GP (HSGP) model, the exact GP model and a spline model on the data sets.