A conditional one-output likelihood formulation for multitask Gaussian processes

Multitask Gaussian processes (MTGP) are the process (GP) framework’s solution for multioutput regression problems in which T elements of regressors cannot be considered conditionally independent given observations. Standard MTGP models assume that there exist both a multitask covariance matrix as function an intertask matrix, and noise matrix. These matrices need to approximated by low rank simplification order P reduce number parameters learnt from T2 TP. Here we introduce novel approach simplifies learning reducing it set conditioned univariate GPs without any approximations, therefore completely eliminating select adequate value hyperparameter P. At same time, extending this with hierarchical approximate model, proposed extensions capable recovering after only 2T parameters, avoiding validation model overall complexity well risk overfitting. Experimental results over synthetic real confirm advantages inference its ability accurately recover original signal matrices, achieved performance improvement comparison other state art approaches. We have also integrated standard GP toolboxes, showing is computationally competitive options.