Unscented Bayes Methods for Hierarchical Gaussian Processes

In this paper, we propose an unscented Bayes method for hierarchical Gaussian processes. The hierarchical Gaussian process consists of multiple layers of Gaussian process, which leads to intractable marginal likelihood and posterior distributions. Instead of resorting to the traditional sampling approach, we use the unscented transform to compute the intractable quantities in a hierarchical model, which allows us to optimize the hyperparameters using a gradient based approach and to obtain the predictive distributions. We develop the proposed approach to different application scenarios. The performance of the proposed method is validated in two experiments with comparison to the state-of-art methods.