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...
By Tian-Yi Zhou, Namjoon Suh, Guang Cheng, Xiaoming Huo
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.
By Toni Karvonen, Chris J. Oates
arXiv:2603. 16481v3 Announce Type: replace Abstract: Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control.
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arXiv:2608.28446v1 Announce Type: cross
Abstract: For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes...
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arXiv:2602. 23006v2 Announce Type: replace-cross Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations.
By Arsalan Jawaid, Abdullah Karatas, J\"org Seewig