- Buchanan 1930
Title: Hierarchy-preserving regularization solution paths for identifying interactions in high dimensional data
Interaction screening for high-dimensional settings has recently drawn much attention in the literature. A variety of interaction screening approaches have been proposed for regression and classification problems. However, most of existing regularization methods for interaction selections are limited to low or moderate dimensional data analysis, due to their complex programing with inequality constraints and demanded prohibitive storage and computational cost when handling high dimensional data. This talk will present our recent work on scalable regularization methods to interaction selection under hierarchical constraints for high dimensional regression and classification. We first consider two-stage LASSO methods and establish their theoretical properties. Then a new regularization method, called Regularization Algorithm under Marginality Principle (RAMP), is developed to compute hierarchy-preserving regularization solution paths efficiently. In contrast to existing regularization methods, the proposed methods avoid storing the entire design matrix and sidestep complex constraints and penalties, making them feasible to ultra-high dimensional data analysis. The new methods are further extended to handling binary responses. Extensive numerical results will be presented as well.
Helen Zhang is a professor at the University of Arizona, in the Department of Mathematics, Statistics Interdisciplinary Program, and Applied Mathematics Interdisciplinary Program there. With Bertrand Clarke and Ernest Fokoué, she is the author of the book Principles and Theory for Data Mining and Machine Learning. Zhang earned a bachelor's degree in mathematics in 1996 from Peking University. She completed her Ph.D. in statistics in 2002 from the University of Wisconsin–Madison. Her dissertation, supervised by Grace Wahba, was Nonparametric Variable Selection and Model Building Via Likelihood Basis Pursuit. Zhang was elected to the International Statistical Institute and as a fellow of the American Statistical Association in 2015. She became a fellow in the Institute of Mathematical Statistics in 2016, and has been selected as the 2019 Medallion Lecturer of the Institute of Mathematical Statistics.