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.
Group Lasso for Logistic Regression 55 Linear logistic regression models the conditional probability pβ.xi/=Pβ.Y =1|xi/ by log pβ.xi/ 1−pβ.xi/ =ηβ.xi/, .2:1/ with ηβ.xi/=β0 + G g=1 xT i,gβg, where β0 is the intercept and βg ∈Rdfg is the parameter vector corresponding to the gth predic- tor. We denote by β∈Rp+1 the whole parameter vector, i.e. β=.β0,βT
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