Online Gaussian Process regression with non-Gaussian likelihood

We present a new algorithm for GP regression over data with non-Gaussian likelihood that does not require costly MCMC sampling, or variational Bayes optimization. In our method, which we term Meta-GP, we model the likelihood by another Gaussian Process point-wise in time. This approach allows for the calculation of the posterior predictive mean and variance in an analytical way pointwise in time, leading to an online inference algorithm. As a result, our method can work with streaming data, is analytically tractable, computationally efficient while being as accurate or better than Expectation Propagation, Laplace Approximation, and MCMC inference methods for non-Gaussian likelihood data.