Transcription of The group lasso for logistic regression
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The group lasso for logistic regression
J. R. Statist. Soc. B (2008). 70, Part 1, pp. 53 71. The group lasso for logistic regression Lukas Meier, Sara van de Geer and Peter B hlmann Eidgen ssische Technische Hochschule, Z rich, Switzerland [Received March 2006. Final revision July 2007]. Summary. The group lasso is an extension of the lasso to do variable selection on (predefined). groups of variables in linear regression models. The estimates have the attractive property of being invariant under groupwise orthogonal reparameterizations. We extend the group lasso to logistic regression models and present an efficient algorithm, that is especially suitable for high dimensional problems, which can also be applied to generalized linear models to solve the corresponding convex optimization problem. The group lasso estimator for logistic regression is shown to be statistically consistent even if the number of predictors is much larger than sam- ple size but with sparse true underlying structure.
order of the number of parameters dfg. The same rescaling was used in Yuan and Lin (2006). Lemma 1. Assume that 0<Σn i=1yi <n.Forλ>0 and s.d/>0 for all d∈N, the minimum in optimization problem (2.2) is attained. The first condition in lemma 1 is a minimal requirement for the observed data. If the design
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