Bayesian Inference is almost always a very challenging mathematical and computational problem. In the context of Gaussian Process, only a Gaussian likelihood leads to an analytically tractable posterior.
We extend this tractability to a large class of non-conjugate likelihoods by augmenting our model with auxiliary variables.
The complete conditionals of the model can be computed in closed-form and we show two inference schemes given analytically : variational inference and Gibbs sampling.
We show the efficiency of our approach, and how it can be automatically applied without the need of mathematical derivations.
invited by Noa Malem Shinitski