Distributed Generalized Cross-Validation for Divide-and-Conquer Kernel Ridge Regression and Its Asymptotic Optimality
Distributed Generalized Cross-Validation for Divide-and-Conquer Kernel Ridge Regression and Its Asymptotic Optimality
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DOI：
10.1080/10618600.2019.1586714
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发表时间：
2016-12
影响因子：
2.4
通讯作者：
Ganggang Xu;Zuofeng Shang;Guang Cheng
中科院分区：
文献类型：
--
作者：
Ganggang Xu;Zuofeng Shang;Guang Cheng
摘要 调整参数选择对于核岭回归至关重要。迄今为止，文献中缺乏数据驱动的分治核岭回归（d-KRR）调整方法，这限制了 d-KRR 对于大型数据集的适用性。在本文中，通过修改广义交叉验证（GCV）分数，我们提出了一种分布式广义交叉验证（dGCV）作为数据驱动工具，用于选择 d-KRR 中的调整参数。所提出的 dGCV 不仅对于海量数据集具有计算可扩展性，而且在温和条件下也显示出渐近最优性，即最小化 dGCV 分数相当于最小化平均函数估计器的真实全局条件经验损失，将 GCV 的现有最优性结果扩展到分治框架。本文的补充材料可在线获取。
Abstract Tuning parameter selection is of critical importance for kernel ridge regression. To date, a data-driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the applicability of d-KRR for large datasets. In this article, by modifying the generalized cross-validation (GCV) score, we propose a distributed generalized cross-validation (dGCV) as a data-driven tool for selecting the tuning parameters in d-KRR. Not only the proposed dGCV is computationally scalable for massive datasets, it is also shown, under mild conditions, to be asymptotically optimal in the sense that minimizing the dGCV score is equivalent to minimizing the true global conditional empirical loss of the averaged function estimator, extending the existing optimality results of GCV to the divide-and-conquer framework. Supplemental materials for this article are available online.