发散模型空间中支持向量机的一致信息准则。

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2016-01-01
Xiang Zhang, Yichao Wu, Lan Wang, Runze Li
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引用次数: 0

摘要

信息准则在模型选择中得到了广泛的应用,并被证明具有良好的理论性质。在分类方面,Claeskens et al.(2008)提出了支持向量机信息标准用于特征选择,并提供了令人鼓舞的数值证据。然而,他们没有给出任何理论依据。本工作旨在填补这一空白,并为支持向量机信息准则在固定和发散模型空间中的应用提供一些理论依据。我们首先推导了支持向量机解的统一收敛速率,然后证明了即使特征数量以样本大小的指数速率发散,对支持向量机信息准则的修改也能实现模型选择的一致性。这一一致性结果可进一步应用于选择各种惩罚支持向量机方法的最优调优参数。利用蒙特卡罗研究和一个现实世界的基因选择问题,研究了所提出的信息准则的有限样本性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A Consistent Information Criterion for Support Vector Machines in Diverging Model Spaces.

A Consistent Information Criterion for Support Vector Machines in Diverging Model Spaces.

Information criteria have been popularly used in model selection and proved to possess nice theoretical properties. For classification, Claeskens et al. (2008) proposed support vector machine information criterion for feature selection and provided encouraging numerical evidence. Yet no theoretical justification was given there. This work aims to fill the gap and to provide some theoretical justifications for support vector machine information criterion in both fixed and diverging model spaces. We first derive a uniform convergence rate for the support vector machine solution and then show that a modification of the support vector machine information criterion achieves model selection consistency even when the number of features diverges at an exponential rate of the sample size. This consistency result can be further applied to selecting the optimal tuning parameter for various penalized support vector machine methods. Finite-sample performance of the proposed information criterion is investigated using Monte Carlo studies and one real-world gene selection problem.

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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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