A differential-geometric approach to generalized linear models with grouped predictors

• 成果类型: Article
• 署名作者: Augugliaro, Luigi; Mineo, Angelo M.; Wit, Ernst C.
• 署名单位: University of Palermo; University of Groningen
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw023
• 发表日期: 2016
• 页码: 563577
• 关键词: group lasso; Group selection; path algorithm; Consistency; regression

摘要

We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important properties that distinguish it from the group lasso. First, its solution curve is based on the invariance properties of a generalized linear model. Second, it adds groups of variables based on a group equiangularity condition, which is shown to be related to score statistics. An adaptive version, which includes weights based on the Kullback-Leibler divergence, improves its variable selection features and is shown to have oracle properties when the number of predictors is fixed.