SEVIS方法的局部线性估计及其在超高维数据下的应用

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SEVIS方法的局部线性估计及其在超高维数据下的应用连亦旻¹, 陈钊², 舒明良³1. 中国科学技术大学统计与金融系, 合肥 230026;
2. Department of Statistics, Pennsylvania State University, State College, USA, PA 16802;
3. 中国科学院数学与系统科学研究院, 北京 100190 Local Estimation of Sure Explained Variability Independence Screening and Its Application for Ultrahigh-dimensional Data LIAN Yimin¹, CHEN Zhao², SHU Mingliang³1. Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China;
2. Department of Statistics, Pennsylvania State University, State College, PA 16802, U.S.A.;
3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China

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摘要在大数据时代的背景下，如何从超高维数据中筛选出真正重要的特征成为许多相关行业的研究者们广泛关注的一个问题.特征筛选的核心思想就在于排除那些明显与因变量不相关的特征以达到这一目的.基于核估计的SEVIS （Sure Explained Variability and Independence Screening）特征筛选方法在处理非对称，非线性数据下要在一定程度上优于之前的特征筛选模型，但其采用核估计的方式对非参数部分进行估计的方法仍存在进一步改进的空间.本文就从这个角度出发，将其核估计的算法修改为局部线性估计，并考虑部分特殊情况下的变量选择过程.结果显示，基于局部线性估计的SEVIS方法在准确性，运行效率上都要优于基于核估计的SEVIS的方法.

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收稿日期: 2016-11-18

PACS:

O212.7

基金资助:国家自然科学基金（11671102，11361011）和广西自然科学基金（2016GXNSFAA3800163）资助项目.

引用本文:

连亦旻, 陈钊, 舒明良. SEVIS方法的局部线性估计及其在超高维数据下的应用[J]. 应用数学学报, 2018, 41(1): 1-13. LIAN Yimin, CHEN Zhao, SHU Mingliang. Local Estimation of Sure Explained Variability Independence Screening and Its Application for Ultrahigh-dimensional Data. Acta Mathematicae Applicatae Sinica, 2018, 41(1): 1-13.

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