title: The group exponential lasso for bi-level variable selection.
abstract: In many applications, covariates possess a grouping structure that can be incorporated into the analysis to select important groups as well as important members of those groups. One important example arises in genetic association studies, where genes may have several variants capable of contributing to disease. An ideal penalized regression approach would select variables by balancing both the direct evidence of a feature's importance as well as the indirect evidence offered by the grouping structure. This work proposes a new approach we call the group exponential lasso (GEL) which features a decay parameter controlling the degree to which feature selection is coupled together within groups. We demonstrate that the GEL has a number of statistical and computational advantages over previously proposed group penalties such as the group lasso, group bridge, and composite MCP. Finally, we apply these methods to the problem of detecting rare variants in a genetic association study.
authors.affiliation: Department of Biostatistics, University of Iowa, 145 N. Riverside Dr., N336 CPHB Iowa City, Iowa 52242, U.S.A.
authors.forename: Patrick
authors.initials: P
authors.lastname: Breheny
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015340:Epidemiologic Research Design; D056726:Genetic Association Studies / Q000379:methods*; D020022:Genetic Predisposition to Disease / Q000453:epidemiology* / Q000235:genetics*; D014644:Genetic Variation / Q000235:genetics; D006801:Humans; D015233:Models, Statistical; D020641:Polymorphism, Single Nucleotide / Q000235:genetics*; D012044:Regression Analysis; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Group variable selection; Penalized regression; Rare variants