This toolkit is used to implement multivariate Gaussian process regression (MV-GPR) and multivariate Student-t process regression (MV-TPR).
The main function is gptp_general.m. It can return GPR, TPR, MV-GPR, MV-TPR and their comparisons. There are four useful sub-functions:
- gp_solve_gpml.m
- tp_solve_gpml.m，
- mvgp_solve_gpml.m
- mvtp_solve_gpml.m
These four functions are used to solve GPR, TPR, MV-GPR and MV-TPR, respectively.
- BE CAREFUL TO these initialisation funciton: nv_init.m, Omega_init.m, SE_init.m, and nu (in TPR and MV-TPR). These functions are used to initialise parameters. These functions play an important role in the final results, if you would like to obtain considerable results, PLEASE USE YOUR OWN FUNCTIONS according to YOUR OWN EXPERT OPINIONS using training data.
- MultiGamma.m and vec2mat_diag.m are two small functions, which are used in the mvgp_solve_gpml.m and mvtp_solve_gpml.m.
- Omega(in MV-GPR and MV-TPR), and hyperparameters in the specific kernel.
Becasue the initial hyperparameters play an important role in the performance of regression. If possible, you should write your own initialisation function.
Do not forget to replace SE_init.m by the corresponding kernel initialation function if you write a new for yourself.
This tookkit is based on GPML Matlab Code http://www.gaussianprocess.org/gpml/code/matlab/doc/, version 3.6.
covSEiso.m, covSEard.m and sq_dist.m are collected from GPML Matlab Code.
covSEiso and covSEard are used as default covariance function. More covariance functions can be selected in the GPML Code toolbox.
File added: SimulatedExample.m
Add a simple example for multi-output prediction (MV-GP and MV-TP) compared with independent prediction using GP and TP
Update optimset setting for Matlab 2017 and later in gptp_general.m
Add gptp_sample.m file This file is to generate a sample from GP or TP with specificed row and column covariance and zero mean function.
Add mv_gptp_sample.m file This file is to generate a sample from MV-GP or MV-TP with specificed row and column covariance and zero mean function.
This code is proof-of-concept, not optimized for speed.
[1] Chen, Zexun, and Bo Wang. "How priors of initial hyperparameters affect Gaussian process regression models." Neurocomputing 275 (2018): 1702-1710.
[2] Chen, Zexun, Bo Wang, and Alexander N. Gorban. "Multivariate Gaussian and Student $-t $ Process Regression for Multi-output Prediction." arXiv preprint arXiv:1703.04455 (2017).