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Gaussian Processes (GPs) are a versatile and popular method in BayesianMachine Learning. A common modification are Sparse Variational GaussianProcesses (SVGPs) which are well suited to deal with large datasets. While GPsallow to elegantly deal with Gaussian-distributed target variables in closedform, their applicability can be extended to non-Gaussian data as well. Theseextensions are usually impossible to treat in closed form and hence requireapproximate solutions. This paper proposes to approximate the inverse-linkfunction, which is necessary when working with non-Gaussian likelihoods, by apiece-wise constant function. It will be shown that this yields a closed formsolution for the corresponding SVGP lower bound. In addition, it isdemonstrated how the piece-wise constant function itself can be optimized,resulting in an inverse-link function that can be learnt from the data at hand.

A piece-wise constant approximation for non-conjugate Gaussian Process models