The paper argues against using the Gaussian (squared exponential/RBF) kernel as a default in Gaussian process regression, citing its brittleness. It shows that the kernel leads to unrealistically small conditional variances, causing overconfidence in predictive uncertainty, and that this small variance induces numerical ill‑conditioning, necessitating tricks like nugget terms that alter the model. The authors attribute these issues to the kernel’s analytic, highly smooth nature and suggest that analytic stationary kernels in general should be avoided.
arXiv:2403.12187v2 Announce Type: replace-cross
Abstract: Motivated by the abundance of functional data, such as time series and images, we study the approximation and statistical learning of nonline...
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The paper argues against using the Gaussian (squared exponential/RBF) kernel as a default in Gaussian process regression, citing its brittleness. Two key issues are highlighted: the kernel produces unrealistically small conditional variances leading to overconfident predictions, and it causes numerical ill‑conditioning that necessitates ad‑hoc fixes like nugget terms. The authors attribute these problems to the kernel’s analytic, infinitely smooth nature, suggesting that analytic stationary kernels in general should be avoided.
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arXiv:2608.28446v1 Announce Type: cross
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We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.
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arXiv:2608.20610v1 Announce Type: cross
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arXiv:2607.28844v2 Announce Type: replace-cross
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arXiv:2608.29265v1 Announce Type: cross
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