提出自适应参数选择方法，提升核梯度下降的泛化性能。
Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descents
- 基于偏差-方差分析与分裂法设计自适应参数策略
- 理论证明可达到最优泛化误差界，适配不同核函数和目标函数
- 适用于需高效调参的核学习场景，如高维非线性建模
本文提出一种新型核梯度下降（KGD）算法的参数选择策略，结合偏差-方差分析与分裂法。引入经验有效维度来量化KGD中的迭代增量，推导出可实施的自适应参数选择方法。在学习理论框架下提供理论验证。利用最近发展的积分算子方法，严格证明：采用该自适应策略的KGD能实现最优泛化误差界，并有效适应不同核函数、目标函数及误差度量。因此，该策略相较现有KGD参数选择方法具有显著优势。
原文摘要 · Abstract (English)
This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify iteration increments in KGD, deriving an adaptive parameter selection strategy that is implementable. Theoretical verifications are provided within the framework of learning theory. Utilizing the recently developed integral operator approach, we rigorously demonstrate that KGD, equipped with the proposed adaptive parameter selection strategy, achieves the optimal generalization error bound and adapts effectively to different kernels, target functions, and error metrics. Consequently, this strategy showcases significant advantages over existing parameter selection methods for KGD.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。