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Fast Cross-Validation for Kernel-Based Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence ( IF 23.6 ) Pub Date : 2019-01-14 , DOI: 10.1109/tpami.2019.2892371
Yong Liu , Shizhong Liao , Shali Jiang , Lizhong Ding , Hailun Lin , Weiping Wang

Cross-validation (CV) is a widely adopted approach for selecting the optimal model. However, the computation of empirical cross-validation error (CVE) has high complexity due to multiple times of learner training. In this paper, we develop a novel approximation theory of CVE and present an approximate approach to CV based on the Bouligand influence function (BIF) for kernel-based algorithms. We first represent the BIF and higher order BIFs in Taylor expansions, and approximate CV via the Taylor expansions. We then derive an upper bound of the discrepancy between the original and approximate CV. Furthermore, we provide a novel computing method to calculate the BIF for general distribution, and evaluate BIF criterion for sample distribution to approximate CV. The proposed approximate CV requires training on the full data set only once and is suitable for a wide variety of kernel-based algorithms. Experimental results demonstrate that the proposed approximate CV is sound and effective.

中文翻译:

基于核的算法的快速交叉验证

交叉验证(CV)是选择最佳模型的一种广泛采用的方法。然而,由于多次学习者训练,经验交叉验证误差(CVE)的计算具有很高的复杂性。在本文中,我们开发了一种新颖的CVE近似理论,并针对基于内核的算法提出了一种基于Bouligand影响函数(BIF)的CV近似方法。我们首先用泰勒展开表示BIF和高阶BIF,然后通过泰勒展开表示近似CV。然后,我们得出原始CV与近似CV之间差异的上限。此外,我们提供了一种新颖的计算方法来计算一般分布的BIF,并评估样本分布的BIF准则以近似CV。拟议的近似CV仅需要对整个数据集进行一次训练,并且适用于各种基于内核的算法。实验结果表明,提出的近似CV是合理有效的。
更新日期:2020-04-22
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