The group lasso for logistic regression

The group lasso for logistic regression

Received March 2006. Final revision July 2007 | Lukas Meier, Sara van de Geer and Peter Bühlmann
The paper introduces the group lasso for logistic regression, extending the lasso method to select groups of variables in linear regression models. The group lasso is shown to be statistically consistent even when the number of predictors is much larger than the sample size. Efficient algorithms are presented, including a block coordinate descent algorithm and a block coordinate gradient descent algorithm, which are particularly suitable for high-dimensional problems. The group lasso estimator is compared with other methods, demonstrating its effectiveness in terms of prediction performance and variable selection. A two-stage procedure is proposed to construct more sparse and hierarchical models, which often yield better results. The methods are applied to simulated and real data sets, specifically to splice site detection in DNA sequences, where the group lasso and its variants perform competitively with maximum entropy models.The paper introduces the group lasso for logistic regression, extending the lasso method to select groups of variables in linear regression models. The group lasso is shown to be statistically consistent even when the number of predictors is much larger than the sample size. Efficient algorithms are presented, including a block coordinate descent algorithm and a block coordinate gradient descent algorithm, which are particularly suitable for high-dimensional problems. The group lasso estimator is compared with other methods, demonstrating its effectiveness in terms of prediction performance and variable selection. A two-stage procedure is proposed to construct more sparse and hierarchical models, which often yield better results. The methods are applied to simulated and real data sets, specifically to splice site detection in DNA sequences, where the group lasso and its variants perform competitively with maximum entropy models.
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