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English(EN) When Kernel Ridge Regression Meets the H\"older-Zygmund Class: Minimax Optimality and Failure of Properness

核岭回归分析揭示minimax最优性和正确性失效

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员在Hölder-Zygmund类中分析了用于非参数回归任务的核岭回归。他们的发现表明，错误设定的核岭回归可以达到n^{-2s/(2s+d)}的minimax L2速率。然而，该研究还揭示了在Hölder-Zygmund范数方面正确性失效的问题，即使在高斯噪声下回归函数为零，核岭回归噪声分量的期望平方范数也随着log n的增加而增加。 AI

影响 为特定数据类别的核岭回归的性能和局限性提供了理论见解。

排序理由 详细介绍机器学习算法理论分析的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv stat.ML 阅读 →

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核岭回归分析揭示minimax最优性和正确性失效

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报道来源 [1]

  1. arXiv stat.ML TIER_1 English(EN) · Yuxuan Hou ·

    当核岭回归遇上Hölder-Zygmund类：最小最大最优性和适当性失效

    arXiv:2607.26065v1 Announce Type: new Abstract: We study kernel ridge regression for nonparametric regression over the H\"older-Zygmund class. Using an RKHS equivalent to a Sobolev space of smoothness s+d/2, we prove that misspecified KRR attains the minimax L2 rate n^{-2s/(2s+d)…

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