Heterogeneous Multi-output Gaussian Process Prediction

Multi-output Gaussian processes (MOGP) generalise the powerful Gaussian process (GP) predictive model to the vector-valued random field setup (Alvarez et al., 2012). It has been experimentally shown that by simultaneously exploiting correlations between multiple outputs and across the input space, it is possible to provide better predictions, particularly in scenarios with missing or noisy data (Bonilla et al., 2008; Dai et al., 2017). The main focus in the literature for MOGP has been on the definition of a suitable cross-covariance function between the multiple outputs that allows for the treatment of outputs as a single GP with a properly defined covariance function (Alvarez et al., 2012). The two classical alternatives to define such cross-covariance functions are the linear model of coregionalisation (LMC) (Journel and Huijbregts, 1978) and process convolutions (Higdon, 2002). In the former case, each output corresponds to a weighted sum of shared latent random functions.