The Rényi Gaussian Process
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In this article we introduce an alternative closed form lower bound on the Gaussian process (GP) likelihood based on the Rényi α-divergence. This new lower bound can be viewed as a convex combination of the Nyström approximation and the exact GP. The key advantage of this bound, is its capability to control and tune the enforced regularization on the model and thus is a generalization of the traditional sparse variational GP regression. From the theoretical perspective, we show that with probability at least 1-δ, the Rényi α-divergence between the variational distribution and the true posterior becomes arbitrarily small as the number of data points increase.
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