Multi-output Gaussian Process Software

This page describes examples of how to use the Multi-output Gaussian Process Software (MULTIGP).

The MULTIGP software can be downloaded here.

Release Information

Current release is 0.11.

As well as downloading the MULTIGP software you need to obtain the toolboxes specified below. These can be downloaded using the same password you get from registering for the MULTIGP software.

Toolbox	Version
NETLAB	3.3
OPTIMI	0.132
MLTOOLS	0.1311
KERN	0.222
NDLUTIL	0.161
GP	0.132
MOCAP	0.135
DATASETS	0.136
VOICEBOX	1.12

Release Notes

Current Release

Updates to allow variational outputs for working with latent functions that are white noise processes.

Version 0.1

This is the very first version of the multi-ouput Gaussian Process toolbox. It shows toy examples for a full covariance model and two approximations proposed in the paper Sparse Convolved Gaussian Processes for Multi-ouput regression

Examples

Multi-output Gaussian process using a Gaussian kernel and a Gaussian covariance function

This example shows how it is possible to make multiple regression over four outputs using a Gaussian process constructed with the convolution process approach. Note that there are some ranges of missing data for outputs one and four.

>> demGpToy1

Left First output in the four outputs of the demo. Right Fourth output for the same example.

Multi-output Gaussian process using the PITC approximation and the FITC approximation

In the paper, two approximations that exploit conditional independencies in the model were proposed. Due to their similarities with the PITC and FITC approximations for the one output case, these multi-output approximations are named in a similar way. For PITC run

>> demSpmgpGgToy1

For FITC run

>> demSpmgpGgToy2



Up The same two outputs using PITC Down The same two outputs using FITC.

Multi-ouput Gaussian processes for the Swiss Jura Dataset

The experiment for the Swiss Jura Dataset using the full covariance matrix can be recreated using ( you will need to obtain the files prediction.dat and validation.dat from here. Go to the Publications link and then to the Book link)

>> demGgJura

The result with the approximation can be recreated using

>> demSpmgpGgJura

Mean absolute error and standard deviation for ten repetitions of the experiment for the Jura dataset In the bottom of each figure, IGP stands for independent GP, P(M) stands for PITC with M inducing values, FGP stands for full GP and CK stands for ordinary co-kriging. On the left, regression over Cadmium (Cd) and on the rigth, regression over Copper (Cu)