Title
Selective Inference Using Randomized Group Lasso Estimators for General Models.
Abstract
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of ex- ponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. At the core of our method is a randomized group-regularized optimization problem. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume.
Bio
