Efficient Bi-Level Variable Selection in High-Dimensional Models

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This project proposes a class of novel bi-level variable selection methodin high-dimensional regression models when there is group structure in covariates. The existing variable selection methods are designed for either individual variable selection or group selection, but not for both. Furthermore, standard methods for evaluating a statistical procedure assume that the number of variables in a model is fixed and much smaller than the sample size which, in general, are not applicable for high-dimensional settings. Analysis of high-dimensional data presents novel and challenging theoretical and computational questions in statistics. The proposed methods are capable of simultaneous group and individual variable selection within selected groups. For the proposed bi-level selection methods, computational algorithms will be developed and the theoretical properties in a class of important regression models will be investigated. The proposed methods are expected to be able to correctly select the important groups and variables simultaneously with high probability in sparse models even when the number of covariates is much larger than the sample size.High-dimensional data arise in many scientific fields, including biology, economics, finance, information technology, and health sciences. In all these fields, the identification of important features from data is a crucial step in the process of scientific discovery. The intended applications of the proposed study are to the analysis of high-dimensional genomic data. In particular, the proposed research will obtain novel methods for genome wide association studies and genetic pathway regression analysis. These are two of the most important approaches for understanding how genes and genetic pathways cause common and complex diseases such as various types of cancers. The proposed research aims to translate novel statistical approaches into new methodologies for analyzing high-dimensional genomic data.