Why not to use the Gaussian kernel

arXiv:2608.26974 · stat.ML, cs.LG, cs.NA, math.NA, math.ST, stat.TH · Submitted 2026-08-27 · Read on arXiv

stat.ML, cs.LG, cs.NA, math.NA, math.ST, stat.TH

Submitted: 2026-08-27

Updated: 2026-08-27

Code: https://github.com/heffieldML/GPy

Terminology

• Hilbert Space — 12× in this paper · explained in 2 episodes
• Uncertainty Quantification — 10× in this paper · explained in 8 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Activation Function — 1× in this paper · explained in 1 episode
• Analytic Activation Functions — 1× in this paper · explained in 1 episode
• Bayesian Optimization — 1× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Downstream Tasks — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences
• Bumps and polynomials in RKHSs of translation-invariant kernels
• Scale estimation and rate-unbiasedness for Gaussian processes under smoothness misspecification
• Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization

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