New analysis explores optimal random features for kernel methods

This paper presents a comprehensive analysis of kernel ridge regression with random features (KRR-RF), focusing on its performance under general conditions including misspecified models and heavy-tailed noise. The research improves upon existing worst-case uniform bounds, achieving minimax optimal learning rates in light-tailed noise settings. Furthermore, it extends these optimal results to heavy-tailed noise by employing a Hilbert-valued Fuk-Nagaev inequality, demonstrating that the additional cost for robustness is a mildly stronger sample-size requirement. The findings suggest that KRR-RF can be minimax optimal under weak moment conditions in misspecified settings, a novel contribution to the field, and are validated by numerical experiments and real-world data analysis. AI

IMPACT Provides theoretical groundwork for more robust and efficient kernel methods in machine learning applications.

RANK_REASON This is a research paper published on arXiv detailing theoretical advancements in machine learning algorithms. [lever_c_demoted from research: ic=1 ai=1.0]

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• heavy-tailed noise
• Hilbert-valued Fuk-Nagaev inequality
• Kernel Ridge Regression
• KRR-RF
• misspecified models

• paper
• other

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