High-dimensional data have frequently been collected in many scientific areas including genomewide association study, biomedical imaging, tomography, tumor classifications, and finance. Analysis of highdimensional dat...High-dimensional data have frequently been collected in many scientific areas including genomewide association study, biomedical imaging, tomography, tumor classifications, and finance. Analysis of highdimensional data poses many challenges for statisticians. Feature selection and variable selection are fundamental for high-dimensional data analysis. The sparsity principle, which assumes that only a small number of predictors contribute to the response, is frequently adopted and deemed useful in the analysis of high-dimensional data.Following this general principle, a large number of variable selection approaches via penalized least squares or likelihood have been developed in the recent literature to estimate a sparse model and select significant variables simultaneously. While the penalized variable selection methods have been successfully applied in many highdimensional analyses, modern applications in areas such as genomics and proteomics push the dimensionality of data to an even larger scale, where the dimension of data may grow exponentially with the sample size. This has been called ultrahigh-dimensional data in the literature. This work aims to present a selective overview of feature screening procedures for ultrahigh-dimensional data. We focus on insights into how to construct marginal utilities for feature screening on specific models and motivation for the need of model-free feature screening procedures.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11401497 and 11301435)the Fundamental Research Funds for the Central Universities(Grant No.T2013221043)+3 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry,the Fundamental Research Funds for the Central Universities(Grant No.20720140034)National Institute on Drug Abuse,National Institutes of Health(Grant Nos.P50 DA036107 and P50 DA039838)National Science Foundation(Grant No.DMS1512422)The content is solely the responsibility of the authors and does not necessarily represent the official views of National Institute on Drug Abuse, National Institutes of Health, National Science Foundation or National Natural Science Foundation of China
文摘High-dimensional data have frequently been collected in many scientific areas including genomewide association study, biomedical imaging, tomography, tumor classifications, and finance. Analysis of highdimensional data poses many challenges for statisticians. Feature selection and variable selection are fundamental for high-dimensional data analysis. The sparsity principle, which assumes that only a small number of predictors contribute to the response, is frequently adopted and deemed useful in the analysis of high-dimensional data.Following this general principle, a large number of variable selection approaches via penalized least squares or likelihood have been developed in the recent literature to estimate a sparse model and select significant variables simultaneously. While the penalized variable selection methods have been successfully applied in many highdimensional analyses, modern applications in areas such as genomics and proteomics push the dimensionality of data to an even larger scale, where the dimension of data may grow exponentially with the sample size. This has been called ultrahigh-dimensional data in the literature. This work aims to present a selective overview of feature screening procedures for ultrahigh-dimensional data. We focus on insights into how to construct marginal utilities for feature screening on specific models and motivation for the need of model-free feature screening procedures.
