Description:

Annie Qu, PhD
Professor of Statistics
Department of Statistics
University of Illinois at Urbana-Champaign

Individualized multi-directional variable selection

We propose an individualized variable selection approach to select different relevant variables for different individuals. In contrast to conventional model selection approaches, the key component of the new approach is to construct a separation penalty with multi-directional shrinkages including zero, which facilitates individualized modeling to distinguish strong signals from noisy ones. As a byproduct, the proposed model identifies subgroups among which individuals share similar effects, and thus improves estimation efficiency and personalized prediction accuracy. Another advantage of the proposed model is that it can incorporate within-subject correlation for longitudinal data. We provide a general theoretical foundation under a double-divergence modeling framework where the number of subjects and the number of repeated measurements both go to infinity, and therefore involves high-dimensional individual parameters. In addition, we present the oracle property for the proposed estimator to ensure its optimal large sample property. Simulation studies and an application to HIV longitudinal data are illustrated to compare the new approach to existing penalization methods.