The composite absolute penalties family for grouped and hierarchical variable selection
نویسندگان
چکیده
منابع مشابه
The Composite Absolute Penalties Family for Grouped and Hierarchical Variable Selection
Extracting useful information from high-dimensional data is an important focus of today’s statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has been popular in regression models and b...
متن کاملGrouped and Hierarchical Model Selection through Composite Absolute Penalties
Recently much attention has been devoted to model selection through regularization methods in regression and classification where features are selected by use of a penalty function (e.g. Lasso in Tibshirani, 1996). While the resulting sparsity leads to more interpretable models, one may want to further incorporate natural groupings or hierarchical structures present within the features. Natural...
متن کاملThe Composite Absolute Penalties Family for Grouped and Hierarchical Variable Selection1 By
Extracting useful information from high-dimensional data is an important focus of today’s statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and empirically. With the virtues of both regularization and sparsity, the L1-penalized squared error minimization method Lasso has been popular in regression models and b...
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Traditionally, variable selection in the context of linear regression has been approached using optimization based approaches like the classical Lasso. Such methods provide a sparse point estimate with respect to regression coefficients but are unable to provide more information regarding the distribution of regression coefficients like expectation, variance estimates etc. In the recent years, ...
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We consider the problem of variable group selection for least squares regression, namely, that of selecting groups of variables for best regression performance, leveraging and adhering to a natural grouping structure within the explanatory variables. We show that this problem can be efficiently addressed by using a certain greedy style algorithm. More precisely, we propose the Group Orthogonal ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2009
ISSN: 0090-5364
DOI: 10.1214/07-aos584