  We propose a new scalable multi-class Gaussian process classification
approach building on a novel modified softmax likelihood function. The new
likelihood has two benefits: it leads to well-calibrated uncertainty estimates
and allows for an efficient latent variable augmentation. The augmented model
has the advantage that it is conditionally conjugate leading to a fast
variational inference method via block coordinate ascent updates. Previous
approaches suffered from a trade-off between uncertainty calibration and speed.
Our experiments show that our method leads to well-calibrated uncertainty
estimates and competitive predictive performance while being up to two orders
faster than the state of the art.
