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

• URL: http://arxiv.org/abs/2311.01409v1
• Date: Thu, 2 Nov 2023 17:22:22 GMT
• Title: A Coreset-based, Tempered Variational Posterior for Accurate and Scalable Stochastic Gaussian Process Inference
• Authors: Mert Ketenci and Adler Perotte and No\'emie Elhadad and I\~nigo Urteaga
• Abstract summary: We present a novel variational Gaussian process ($mathcalGP$) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets) We deriveGP's lower bound for the log-marginal likelihood via marginalization of latent $mathcalGP$ coreset variables.
• Score: 2.7855886538423187
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a novel stochastic variational Gaussian process ($\mathcal{GP}$) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed 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 for the log-marginal likelihood via marginalization of the proposed posterior over latent $\mathcal{GP}$ coreset variables, and show it is amenable to stochastic optimization. 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 tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic $\mathcal{GP}$ inference methods.

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