Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure.
We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study.
Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, 48109, U.S.A.
Yanming
Y
Li
Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, 48109, U.S.A.
Bin
B
Nan
Department of Statistics, University of Michigan, Ann Arbor, Michigan, 48109, U.S.A.
Ji
J
Zhu
D000465:Algorithms; D001699:Biometry; D003198:Computer Simulation; D005800:Genes, Fungal; D056726:Genetic Association Studies / Q000706:statistics & numerical data; D006801:Humans; D016014:Linear Models; D015999:Multivariate Analysis; D040641:Quantitative Trait Loci; D012441:Saccharomyces cerevisiae / Q000235:genetics
Coordinate descent algorithm; EQTL; Genetic association; High-dimensional data; Oracle inequalities; Sparsity