Learning Gaussian Process Kernels via Hierarchical Bayes

We present a novel method for learning with Gaussian process regression in a hierarchical Bayesian framework. In a first step, kernel matrices on a fixed set of input points are learned from data using a simple and efficient EM algorithm. This step is nonparametric, in that it does not require a parametric form of covariance function. In a second step, kernel functions are fitted to approximate the learned covariance matrix using a generalized Nystroem method, which results in a complex, data driven kernel. We evaluate our approach as a recommendation engine for art images, where the proposed hierarchical Bayesian method leads to excellent prediction performance.