Multivariate Generalized Gaussian Process Models

We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a multivariate generalized Gaussian process model, and derive Taylor and Laplace algorithms for approximate inference on the generic model. By instantiating the EFD with specific parameter functions, we obtain two novel GP models (and corresponding inference algorithms) for correlated outputs: 1) a Von-Mises GP for angle regression; and 2) a Dirichlet GP for regressing on the multinomial simplex.