Model Selection for High-Dimensional Quadratic Regression via Regularization
AffiliationUniv Arizona, Dept Math
KeywordsGeneralized quadratic regression
MetadataShow full item record
PublisherAMER STATISTICAL ASSOC
CitationNing Hao, Yang Feng & Hao Helen Zhang (2018) Model Selection for High-Dimensional Quadratic Regression via Regularization, Journal of the American Statistical Association, 113:522, 615-625, DOI: 10.1080/01621459.2016.1264956
Rights© 2018 American Statistical Association
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractQuadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects and interaction effects. Existing regularization methods generally achieve this goal by solving complex optimization problems, which usually demands high computational cost and hence are not feasible for high-dimensional data. This article focuses on scalable regularization methods for model selection in high-dimensional QR. We first consider two-stage regularization methods and establish theoretical properties of the two-stage LASSO. Then, a new regularization method, called regularization algorithm under marginality principle (RAMP), is proposed to compute a hierarchy-preserving regularization solution path efficiently. Both methods are further extended to solve generalized QR models. Numerical results are also shown to demonstrate performance of the methods.
Note12 month embargo; published online: 08 February 2018
VersionFinal accepted manuscript
SponsorsNSF [DMS-1309507, DMS-1308566, DMS-1554804, DMS-1418172]; NSFC