Heterogeneous Multi-output Gaussian Process Prediction

Authors: Pablo Moreno-Muñoz1 Antonio Artés-Rodríguez1 Mauricio A. Álvarez2

1 Dept. of Signal Theory and Communications, Universidad Carlos III de Madrid, Spain
2 Dept. of Computer Science, University of Sheffield, UK

Accepted for the thirty-second Conference on Neural Information Processing Systems (NIPS 2018)

We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in all likelihoods as latent functions. Our multi-output Gaussian process uses a covariance function with a linear model of coregionalisation form. Assuming conditional independence across the underlying latent functions together with an inducing variable framework, we are able to obtain tractable variational bounds amenable to stochastic variational inference. We illustrate the performance of the model on synthetic data and two real datasets: a human behavioral study and a demographic high-dimensional dataset.