A Duality Analysis of Kernel Ridge Regression in the Noiseless Regime

• URL: http://arxiv.org/abs/2402.15718v1
• Date: Sat, 24 Feb 2024 04:57:59 GMT
• Title: A Duality Analysis of Kernel Ridge Regression in the Noiseless Regime
• Authors: Jihao Long, Xiaojun Peng and Lei Wu
• Abstract summary: We prove that KRR can attain the minimax optimal rate, which depends on both the eigenvalue decay of the associated kernel and the relative smoothness of target functions. Our proof leverages a novel extension of the duality framework introduced by Chen et al. (2023), which could be useful in analyzing kernel-based methods beyond the scope of this work.
• Score: 5.153104177051464
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we conduct a comprehensive analysis of generalization properties of Kernel Ridge Regression (KRR) in the noiseless regime, a scenario crucial to scientific computing, where data are often generated via computer simulations. We prove that KRR can attain the minimax optimal rate, which depends on both the eigenvalue decay of the associated kernel and the relative smoothness of target functions. Particularly, when the eigenvalue decays exponentially fast, KRR achieves the spectral accuracy, i.e., a convergence rate faster than any polynomial. Moreover, the numerical experiments well corroborate our theoretical findings. Our proof leverages a novel extension of the duality framework introduced by Chen et al. (2023), which could be useful in analyzing kernel-based methods beyond the scope of this work.

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