6533b7dafe1ef96bd126f644
RESEARCH PRODUCT
A differential-geometric approach to generalized linear models with grouped predictors
Ernst WitAngelo MineoLuigi Augugliarosubject
Statistics and ProbabilityGeneralized linear modelStatistics::TheoryMathematical optimizationProper linear modelGeneral MathematicsORACLE PROPERTIESGeneralized linear modelSPARSITYGeneralized linear array model01 natural sciencesGeneralized linear mixed modelCONSISTENCY010104 statistics & probabilityScore statistic.LEAST ANGLE REGRESSIONLinear regressionESTIMATORApplied mathematicsDifferential geometry0101 mathematicsDivergence (statistics)MathematicsVariance functionDifferential-geometric least angle regressionPATH ALGORITHMApplied MathematicsLeast-angle regressionScore statistic010102 general mathematicsAgricultural and Biological Sciences (miscellaneous)Group lassoGROUP SELECTIONStatistics Probability and UncertaintyGeneral Agricultural and Biological SciencesSettore SECS-S/01 - Statisticadescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-09-01 |