Multivariate Generalized Gaussian Process Models
This work addresses the need for flexible Gaussian process models for correlated outputs in specific domains like angle and multinomial data, representing an incremental advancement by extending existing frameworks.
The authors tackled the problem of modeling correlated outputs with Gaussian processes by proposing a family of multivariate generalized Gaussian process models based on the multivariate exponential family distribution, resulting in two novel models for angle regression and regressing on the multinomial simplex with derived inference algorithms.
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.