gptp_multi_output

MATLAB toolbox for Gaussian Process (GP), Student-t Process (TP), multivariate GP (MV-GP) and multivariate TP (MV-TP) regression built on top of GPML 3.6.

This code is proof-of-concept, not optimized for speed.

Requirements

• MATLAB R2016b or maybe newer
• GPML MATLAB Code v3.6 (run startup.m from GPML before using this repo)
• Add this repo to the MATLAB path via add_path.m

Quick start

1. Clone GPML 3.6 and run its startup.m.
2. Run add_path.m in this repo.
3. Call gptp_general with your data:

   % GP regression with defaults (SE kernel, sn = 0.1)
   GP = gptp_general(xtr, ytr, xte);
   
   % MV-TP regression with custom kernel and inits
   covfunc = @covSEard;
   para_init = @SE_init;
   sn = 0.05;
   mvTP = gptp_general(xtr, ytr, xte, sn, covfunc, para_init, "TPVS");

Key entry points

• gptp_general.m — high-level driver for GP, TP, MV-GP, MV-TP and their independent variants.
• solver/ — model-specific solvers that wrap GPML primitives:
  • gp_solve_gpml.m, tp_solve_gpml.m, mvgp_solve_gpml.m, mvtp_solve_gpml.m
• init/ — hyperparameter initialisation helpers. Adapt these to your data for best results:
  • SE_init.m (kernel hyperparameters)
  • Omega_init.m (output correlation) — provides a starting point only; production use should supply a task-specific initialiser.
  • nv_init.m (degrees of freedom for TP/MV-TP)
• util/ and cov/ — supporting math utilities and default SE covariance functions from GPML.
• sample/ and example/ — small scripts for sampling and simulation demos.

Notes on initialisation

Performance is sensitive to initial hyperparameters. The default SE_init.m, Omega_init.m, and nv_init.m are generic and meant as placeholders. For serious use, design problem-specific initialisation based on your training data and kernel choice (e.g., scale parameters, sensible output correlations, or informative priors on degrees of freedom).

Repository layout

• gptp_general.m — main API
• solver/ — optimisation and prediction routines
• init/ — hyperparameter initialisers
• util/, cov/ — utilities and covariance functions
• sample/, example/ — sampling and usage examples

References

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." Neural Computing and Applications 32.8 (2020): 3005–3028.
3. Chen, Zexun, Jun Fan, and Kuo Wang. "Remarks on multivariate Gaussian Process." Neural Computing and Applications (published version of arXiv:2010.09830), 2023.