Heteroscedastic Gaussian process regression using expectation propagation

Gaussian Processes (GPs) are Bayesian non-parametric models that achieve state-of-the-art performance in regression tasks. To allow for analytical tractability, noise power is usually considered constant in these models, which is unrealistic for many real world problems. In this work we consider a GP model with heteroscedastic (i.e., input dependent) noise power, and then, use Expectation Propagation (EP) to perform approximate inference on it. The proposed EP approach is much faster than Markov Chain Monte Carlo and more accurate than competing methods of similar computational cost. This superiority is illustrated in several experiments with synthetic and real-world data.