B1981
Title: Selective inference using randomized group lasso estimators with general loss functions
Authors: Yiling Huang - University of Michigan (United States) [presenting]
Sarah Pirenne - ORStat, KU Leuven (Belgium)
Snigdha Panigrahi - University of Michigan (United States)
Gerda Claeskens - KU Leuven (Belgium)
Abstract: Group lasso is a popular method for producing group-sparse regression coefficients. In practice, inference on coefficients is performed only after observing a particular sparse model. Thus, adjustments for model selection are needed for valid inference on data-dependent parameters. Previous literature established the validity of inference conditioning on selecting the observed set of sparse covariates. We present selective inference methods for group lasso estimators, allowing for various general response variable distributions and loss functions. Our approach encompasses likelihood-based loss functions in generalized linear models and extends to quasi-likelihood modeling, e.g., for overdispersed count data. It accommodates categorical, grouped, and continuous covariates. We consider a randomized group-regularized optimization problem. Randomizing the optimization objective facilitates the construction of the selective likelihood by simplifying the characterization of the model selection event. This likelihood also yields a selection-aware point estimator, accounting for the group lasso selection. We construct confidence intervals for the selected regression parameters using the Wald-type method and show the intervals have bounded lengths. Simulation studies show that our selective inference method guarantees valid coverage and is more powerful compared to baseline methods. We illustrate the method with data from the National Health and Nutrition Examination Survey.
