Group Regularized Estimation under Strong Hierarchy

Abstract

[evdate 2013-12-19] IAS Distinguished Lecture. HKUST International Forum on Probability and Statistics. Talk no. 5.

Title from slide title.

The Second HKUST International Forum on Probability and Statistics (2013), held 19 December, 2013, at the Hong Kong University of Science and Technology. Co-sponsored by the HKUST Jockey Club Institute for Advanced Study and the Center for Statistical Science.

Abstract: In high-dimensional models involving between-term interactions, statisticians usually favor variable selection obeying certain logical hierarchical constraints. The talk focuses on strong hierarchy which means that the existence of an interaction term implies that both associated main effects must be present. Although lately the hierarchical lasso has been proposed, the existing computational algorithms converge very slow and cannot meet the challenge of big data. There is a lack of finite-sample studies in the literature partially due to the difficulty that multiple sparsity-promoting penalties are enforced on the same subject. The talk propose a new estimator based on group multi-regularization to capture various types of structural parsimony. The speaker presents some nonasymptotic results and develop a general-purpose algorithm with a theoretical guarantee of strict iterate convergence. A predictive information criterion is proposed for data-dependent tuning and can help achieve the optimal error rate in a minimax sense.

Duration: 30 min.