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English(EN) Learning between the peaks: sharp asymptotics for kernel ridge regression under power-law anisotropy

核岭回归分析揭示各向异性对学习的影响

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员分析了各向异性高斯数据下的核岭回归，特别研究了输入协方差的幂律衰减如何影响学习曲线。研究表明，弱各向异性保留了各向同性情况的一些特征，同时引入了新的动力学，例如阻尼方差峰值和与插值峰值解耦的偏差转换。对于强各向异性，问题的有效维度变为常数，偏差表现出依赖于目标衰减率的尖锐转换，结果针对单索引目标进行了专门化。 AI

影响 为核方法提供了关于输入数据几何形状如何影响泛化特性的理论见解。

排序理由 详细阐述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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核岭回归分析揭示各向异性对学习的影响

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详细阐述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]
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报道来源 [1]

  1. arXiv stat.ML TIER_1 English(EN) · Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro ·

    峰值间的学习：核岭回归在幂律各向异性下的尖锐渐近线

    arXiv:2608.28564v1 Announce Type: new Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the…

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