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Blockwise sparse regression. (English) Zbl 1096.62076
Summary: M. Yuan and Y. Lin [Model selection and estimation in regression with grouped variables. Tech. Rep. 1095, Dpt. Stat., Univ. Wisconsin, Madison (2004)] proposed the grouped LASSO, which achieves shrinkage and selection simultaneously, as LASSO does, but works on blocks of covariates. That is, the grouped LASSO provides a model where some blocks of regression coefficients are exactly zero. The grouped LASSO is useful when there are meaningful blocks of covariates such as polynomial regression and dummy variables from categorical variables.
We propose an extension of the grouped LASSO, called ‘Blockwise Sparse Regression’ (BSR). The BSR achieves shrinkage and selection simultaneously on blocks of covariates similarly to the grouped LASSO, but it works for general loss functions including generalized linear models. An efficient computational algorithm is developed and a blockwise standardization method is proposed. Simulation results show that the BSR compromises the ridge and LASSO for logistic regression. The proposed method is illustrated with two datasets.

62J12 Generalized linear models (logistic models)
62J99 Linear inference, regression
65C60 Computational problems in statistics (MSC2010)