Response to Promises and Pitfalls of Deep Kernel Learning Article Swipe

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Andrew Gordon Wilson , Zhiting Hu , Ruslan Salakhutdinov , Eric P. Xing ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2509.21228

This note responds to "Promises and Pitfalls of Deep Kernel Learning" (Ober et al., 2021). The marginal likelihood of a Gaussian process can be compartmentalized into a data fit term and a complexity penalty. Ober et al. (2021) shows that if a kernel can be multiplied by a signal variance coefficient, then reparametrizing and substituting in the maximized value of this parameter sets a reparametrized data fit term to a fixed value. They use this finding to argue that the complexity penalty, a log determinant of the kernel matrix, then dominates in determining the other values of kernel hyperparameters, which can lead to data overcorrelation. By contrast, we show that the reparametrization in fact introduces another data-fit term which influences all other kernel hyperparameters. Thus, a balance between data fit and complexity still plays a significant role in determining kernel hyperparameters.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2509.21228
PDF: https://arxiv.org/pdf/2509.21228
OA Status: green
OpenAlex ID: https://openalex.org/W4414790786

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OpenAlex ID: https://openalex.org/W4414790786

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DOI: https://doi.org/10.48550/arxiv.2509.21228

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Title: Response to Promises and Pitfalls of Deep Kernel Learning

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-09-25

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Authors: Andrew Gordon Wilson, Zhiting Hu, Ruslan Salakhutdinov, Eric P. Xing

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Landing page: https://arxiv.org/abs/2509.21228

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PDF URL: https://arxiv.org/pdf/2509.21228

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Open access: Yes

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OA status: green

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OA URL: https://arxiv.org/pdf/2509.21228

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Cited by: 0

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