  A generalized Gaussian process model (GGPM) is a unifying framework that
encompasses many existing Gaussian process (GP) models, such as GP regression,
classification, and counting. In the GGPM framework, the observation likelihood
of the GP model is itself parameterized using the exponential family
distribution (EFD). In this paper, we consider efficient algorithms for
approximate inference on GGPMs using the general form of the EFD. A particular
GP model and its associated inference algorithms can then be formed by changing
the parameters of the EFD, thus greatly simplifying its creation for
task-specific output domains. We demonstrate the efficacy of this framework by
creating several new GP models for regressing to non-negative reals and to real
intervals. We also consider a closed-form Taylor approximation for efficient
inference on GGPMs, and elaborate on its connections with other model-specific
heuristic closed-form approximations. Finally, we present a comprehensive set
of experiments to compare approximate inference algorithms on a wide variety of
GGPMs.
