Selective inference using randomized group lasso estimators for general models

TL;DR

This paper introduces a selective inference framework for group lasso estimators applicable to diverse models and distributions, enabling valid post-selection inference with confidence regions and estimators that account for the selection process.

Contribution

It develops a randomized group lasso approach that constructs valid post-selection likelihoods and confidence regions for a broad class of models and data types.

Findings

Confidence regions with bounded volume are achieved.

The method performs favorably compared to existing approaches.

Application to health survey data demonstrates practical utility.

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 exponential 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. A randomized group-regularized optimization problem is studied. 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. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.