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We present a novel stochastic variational Gaussian process ($\mathcal{GP}$)inference method, based on a posterior over a learnable set of weighted pseudoinput-output points (coresets). Instead of a free-form variational family, theproposed coreset-based, variational tempered family for $\mathcal{GP}$s (CVTGP)is defined in terms of the $\mathcal{GP}$ prior and the data-likelihood; hence,accommodating the modeling inductive biases. We derive CVTGP's lower bound forthe log-marginal likelihood via marginalization of the proposed posterior overlatent $\mathcal{GP}$ coreset variables, and show it is amenable to stochasticoptimization. CVTGP reduces the learnable parameter size to $\mathcal{O}(M)$,enjoys numerical stability, and maintains $\mathcal{O}(M^3)$ time- and$\mathcal{O}(M^2)$ space-complexity, by leveraging a coreset-based temperedposterior that, in turn, provides sparse and explainable representations of thedata. Results on simulated and real-world regression problems with Gaussianobservation noise validate that CVTGP provides better evidence lower-boundestimates and predictive root mean squared error than alternative stochastic$\mathcal{GP}$ inference methods.

A Coreset-based, Tempered Variational Posterior for Accurate and Scalable Stochastic Gaussian Process Inference