#5741. Consistent online Gaussian process regression without the sample complexity bottleneck

September 2026publication date
Proposal available till 10-07-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Statistics and Probability;
Statistics, Probability and Uncertainty;
Computational Theory and Mathematics;
Theoretical Computer Science;
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Abstract:
Gaussian processes provide a framework for nonlinear nonparametric Bayesian inference widely applicable across science and engineering. Unfortunately, their computational burden scales cubically with the training sample size, which in the case that samples arrive in perpetuity, approaches infinity. This issue necessitates approximations for use with streaming data, which to date mostly lack convergence guarantees. Thus, we develop the first online Gaussian process approximation that preserves convergence to the population posterior, i.e., asymptotic posterior consistency, while ameliorating its intractable complexity growth with the sample size. We propose an online compression scheme that, following each a posteriori update, fixes an error neighborhood with respect to the Hellinger metric centered at the current posterior, and greedily tosses out past kernel dictionary elements until its boundary is hit.
Keywords:
Bayesian inference; Gaussian process; Nonparametric statistics; Online learning

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