Gaussian process library for machine learning
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Getting started

libgp is a C++ library for Gaussian process regression. A Gaussian process defines a distribution over functions and inference takes place directly in function space. It is fully specified by a mean function and a positive definite covariance function. This library uses two types of covariance functions, simple and composite. Composite functions can be composed of other composite functions, allowing flexible structures.

Building the code

Follow the standard CMake method of building:

mkdir build; cd $_
cmake ..

Testing the build

Once everything is built, you can check that all works fine with the following tests:

cd tests

And running an example:

cd examples

which should return a MSE.

Building the documentation

There are Doxygen comments in the header files. To compile (make sure you have doxygen installed):

mkdir doc; cd $_
doxygen ../doxygen/Doxyfile

Open doc/html/index.html with your favorite browser for the documentation. If you want a pdf, go into latex and run:

pdflatex refman.tex

Implemented covariance functions

Simple covariance functions

  • Linear covariance function.
  • Linear covariance function with automatic relevance detection.
  • Matern covariance function with nu=1.5 and isotropic distance measure.
  • Matern covariance function with nu=2.5 and isotropic distance measure.
  • Independent covariance function (white noise).
  • Radial basis covariance function with compact support.
  • Isotropic rational quadratic covariance function.
  • Squared exponential covariance function with automatic relevance detection.
  • Squared exponential covariance function with isotropic distance measure.

Composite covariance functions

  • Sums of covariance functions.

Mean function

  • The mean function is fixed to zero.

Training a model

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Initialize the model by specifying the input dimensionality and the covariance function.

GaussianProcess gp(2, "CovSum ( CovSEiso, CovNoise)");

Set log-hyperparameter of the covariance function (see the Doxygen documentation, parameters should be given in order as listed).


Add data to the training set. Input vectors x must be provided as double[] and targets y as double.

gp.add_pattern(x, y);

Predict value or variance of an input vector x.

f = gp.f(x);
v = gp.var(x);

Read and write

Use write function to save a Gaussian process model and the complete training set to a file.

void write(const char * filename);

A new instance of the Gaussian process can be instantiated from this file using the following constructor.

GaussianProcess (const char * filename);

Advanced topics

  • hyper-parameter optimization
  • custom covariance functions
  • the libgp file format

Hyper-parameter optimization

This library contains two methods for hyper-parameter optimization; the conjugate gradient method, and Rprop (resilient backpropagation). We recommend using Rprop.

For an example of how to call the optimizers, see

Reasons for using Rprop can be found in Blum & Riedmiller (2013), Optimization of Gaussian Process Hyperparameters using Rprop, European Symposium on Artificial Neural Networks, Computational Intelligence and Learning.


  • cmake: cross-platform, open-source build system
  • Eigen3: template library for linear algebra
  • googletest (optional)

Release Notes

  • 2012/10/11 version 0.1.4 \ log likelihood function and gradient computation \ hyper-parameter optimization using RProp \ online updates of the Cholesky decomposition \

  • 2011/09/28 version 0.1.3 \ improved organization of training data \ improved interfaces

  • 2011/06/03 version 0.1.2 \ added Matern5 covariance function \ added isotropic rational quadratic covariance function \ added function to draw random data according to covariance function

  • 2011/05/27 version 0.1.1 \ google-tests added \ added Matern3 covariance function \ various bugfixes

  • 2011/05/26 version 0.1.0 basic functionality for standard gp regression \ most important covariance functions implemented \ capability to read and write models to disk