Statistics and Its Interface

Volume 2 (2009)

Number 3

Penalized methods for bi-level variable selection

Pages: 369 – 380



Patrick Breheny (Department of Biostatistics, University of Kentucky, Lexington, Ky, U.S.A.)

Jian Huang (Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Ia., U.S.A.)


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. This work focuses on the incorporation of grouping structure into penalized regression. We investigate the previously proposed group lasso and group bridge penalties as well as a novel method, group MCP, introducing a framework and conducting simulation studies that shed light on the behavior of these methods. To fit these models, we use the idea of a locally approximated coordinate descent to develop algorithms which are fast and stable even when the number of features is much larger than the sample size. Finally, these methods are applied to a genetic association study of age-related macular degeneration.


high-dimensional data, grouping structure, minimax concave penalty, local coordinate descent algorithms, genetic association studies

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