文章基本信息

标题：A general framework for tensor screening through smoothing
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作者：Keqian Min ; Qing Mai
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2022
卷号：16
期号：1
页码：451-497
DOI：10.1214/21-EJS1954
语种：English
出版社：Institute of Mathematical Statistics
摘要：Screening is an important technique for analyzing high-dimensional data. Most screening tools have been developed for vectors and are marginal in the sense that each variable is evaluated individually at a time. Many multi-dimensional arrays (tensors) are generated nowadays. In addition to being high-dimensional, these data further have the tensor structure that should be exploited for more efficient analysis. Variables adjacent to each other in a tensor tend to be important or unimportant at the same time. Such information is ignored by marginal screening methods. In this article, we propose a general framework for tensor screening called smoothed tensor screening (STS). STS combines the strength of current marginal screening methods with tensor structural information by aggregating the information of its adjacent variables when evaluating one variable. STS is widely applicable since the statistical utility used in screening can be chosen based on the underlying model or data type of the responses and predictors. Moreover, we establish the SURE screening property for STS under mild conditions. Numerical studies demonstrate that STS has better performance than marginal screening methods.
关键词：62F07;62P10;Screening;smooth structure;sure screening property;tensor