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When constructing a Bayesian Machine Learning model, we might be faced withmultiple different prior distributions and thus are required to properlyconsider them in a sensible manner in our model. While this situation isreasonably well explored for classical Bayesian Statistics, it appears usefulto develop a corresponding method for complex Machine Learning problems. Giventheir underlying Bayesian framework and their widespread popularity, GaussianProcesses are a good candidate to tackle this task. We therefore extend theidea of Mixture models for Gaussian Process regression in order to work withmultiple prior beliefs at once - both a analytical regression formula and aSparse Variational approach are considered. In addition, we consider the usageof our approach to additionally account for the problem of priormisspecification in functional regression problems.

Mixtures of Gaussian Processes for regression under multiple prior distributions