Gaussian Process Modelling

R functions for Gaussian process (GP) modelling. The core functions are coded in C++ and based on the EIGEN library (through RcppEigen)

Feature Implementation Checklist

Core Capabilities & Completed Features

• Posterior Gaussian Process with Gaussian Likelihood
  • Gaussian process conditioned on both noise-free and noisy observations (gpCond).
• Space-Time Gaussian Process Support
  • Supported via gpCond and coordinate mapping utilities such as setPosTime.
• Gaussian Process with Monomial Mean Functions
  • Supports vague Gaussian priors on coefficient parameters (gpLogLikMean_rcpp).
• Gaussian Process Conditioned on Derivative Observations
  • Supports derivative data conditioning for specialized spatial-temporal models.
• Anisotropic Covariance Functions
  • Generalized scale parameters and custom rotation matrices $M$.
• Log Marginal Likelihood Evaluation
  • Fast likelihood evaluation via gpLogLik, gpLogLik_rcpp, and gpLogLikMean_rcpp.
• Cross-Matrix Distance Calculations
  • Efficient distance computations: crossDist(x, y, M), crossDist_rcpp, and crossDist_sparse.
• Flexible Kernel Selection
  • Matérn 3/2 & 5/2
  • Gaussian / Squared Exponential (sqex)
  • Exponential
  • Linear
• Maximum Likelihood Hyper-Parameter Estimation (gpFit)
  • Optimization via gpNegLogLik and numerical gradients (.centralDiffGrad).
• Gaussian Process Simulation & Trajectory Generation (gpSim)
  • Simulates Gaussian process sample paths across evaluation grids.
• Robust Numerical Stabilization
  • Automatic jitter addition (cholfac) and positive-definiteness adjustments (correctCovMat).
• High-Performance C++ Backend (Rcpp Integration)
  • C++ acceleration for prediction, likelihood evaluations, distance matrices, and Cholesky decompositions (src/).
• Efficient Multivariate Normal Sampling (mvrnorm2)
  • Fast sampling routine for high-dimensional normal distributions.
• Evaluation Grid Utilities
  • Domain grid generation tools (matGrid, vecGrid).

Planned & Future Enhancements

• MCMC Hyper-Parameter Sampling: Bayesian inference via Markov Chain Monte Carlo for full posterior uncertainty over hyper-parameters.
• Spatially Varying (Non-Stationary) Covariance Functions: Support for spatially dynamic length-scales and non-stationary kernels.
• Large-Scale Gaussian Process Approximations: Scalable GP methods for large datasets (e.g., Sparse GPs, Inducing Point Methods, FITC, VFE).
• Moving / Rolling Covariance Functions for Time Series: Online/sequential covariance updates with exponential forgetting mechanisms for dynamic time-series models.

Core Technical Implementation Details

This is an ongoing project. If you have any questions, requirements, suggestions, don’t hesitate to contact me (in english, french or german):
emanuel.huber@alumni.ethz.ch</p>

Thank you!

How to install/load

1. Install R

Download R from the R Cran website and install it.

1. Optionally install a R-editor:
   • Notepad++ combined with NppToR
   • Rstudio
   • RKward
2. If necessary, learn some R basics:
   • An interactive introduction to R
   • Short R introduction
   • R course

2. Install a R-editor [optionally]

Possible R-editor choices:

• Rstudio (recommanded if you start)
• Notepad++ combined with NppToR
• RKward

3. Install & load GauProMod

if(!require("devtools")) install.packages("devtools")
devtools::install_github("emanuelhuber/GauProMod")
library(GauProMod)