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.
This project was supported in part by the grant CCF-1908969 from the U.S. National Science Foundation.
The authors thank the associate editor and referees, whose comments led to significant improvements of this paper. The authors are also grateful to Dr. Wen Li (Psychology, Florida State University) for helpful discussion.
Keqian Min. Qing Mai. "A general framework for tensor screening through smoothing." Electron. J. Statist. 16 (1) 451 - 497, 2022. https://doi.org/10.1214/21-EJS1954