We develop and study methods for selective inference for group lasso estimators. The approach can be used with a wide class of distributions and loss functions, including applications with generalized linear models and quasi-likelihood models for overdispersed count data. The use of group lasso allows for categorical or grouped covariates in the models, as well as for continuous covariates. Extra randomization is added to the optimization problem. This allows us to construct a post-selection likelihood which we show to be useful for obtaining selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood provides too a selective point estimator, accounting for the selection by the group lasso. The confidence regions for the regression parameters in the selected model constructed via this method take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey.

This is joint work with Sarah Pirenne (KU Leuven) and with Snigdha Panigrahi and Yiling Huang (University of Michigan).

Personal website of Gerda Claeskens