Decoupled Sparse Gaussian Processes Components]{Decoupled Sparse Gaussian Processes Components : Separating Decision Making from Data Manifold Fitting

Sebastian Popescu, David J. Sharp, James H. Cole, Ben Glocker

Keywords: Gaussian Processes, Approximate Inference, Uncertainty Quantification

Abstract: We propose a decoupling in Reproducing Kernel Hilbert Space of the parametric and non-parametric components of Sparse Gaussian Processes. We demonstrate that this decoupling results in a set of inducing points concentrated around the decision boundaries, respectively one that fits the data manifold in terms of variance. Moreover, we make connections between Bayesian Kernel Ridge Regression and Sparse Gaussian Processes in posterior function space. Inspired from this equivalence, we introduce a inducing points' locations linked parametrization of the variational variance term of inducing point values, hence resulting in models that only have variational mean parameters to optimize. We compare our model to counterparts and show improvements at testing time on large scale regression and classification datasets, alongside faster convergence rates to the full Gaussian Process.