A conditional one-output likelihood formulation for multitask Gaussian processes Articles uri icon

publication date

  • October 2022

start page

  • 257

end page

  • 270

volume

  • 509

International Standard Serial Number (ISSN)

  • 0925-2312

Electronic International Standard Serial Number (EISSN)

  • 1872-8286

abstract

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

subjects

  • Telecommunications

keywords

  • gaussian processes; multi task learning