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Hierarchy-preserving regularization solution paths for identifying interactions in high dimensional data

Presented by: 
Helen Zhang University of Arizona
Thursday 6th July 2017 - 09:00 to 09:45
INI Seminar Room 1
Co-authors: Ning Hao (University of Arizona), Yang Feng (Columbia University)

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 regular ization 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. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons