title: Group variable selection via convex log-exp-sum penalty with application to a breast cancer survivor study.
abstract: In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. Among existing successful group variable selection methods, some methods fail to conduct the within group selection. Some methods are able to conduct both group and within group selection, but the corresponding objective functions are non-convex. Such a non-convexity may require extra numerical effort. In this article, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting where the number of covariates can be much larger than the sample size. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and may help design intervention programs to improve the qualify of life for breast cancer survivors.
authors.affiliation: Department of Statistics, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.
authors.forename: Zhigeng
authors.initials: Z
authors.lastname: Geng
authors.affiliation: Department of Statistics, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.|Department of Biostatistics & Medical Informatics, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.
authors.forename: Sijian
authors.initials: S
authors.lastname: Wang
authors.affiliation: Department of Biostatistics & Medical Informatics, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.
authors.forename: Menggang
authors.initials: M
authors.lastname: Yu
authors.affiliation: School of Medicine, Indiana University, Indianapolis, Indiana, 46202, U.S.A.
authors.forename: Patrick O
authors.initials: PO
authors.lastname: Monahan
authors.affiliation: School of Nursing, Indiana University, Indianapolis, Indiana, 46202, U.S.A.
authors.forename: Victoria
authors.initials: V
authors.lastname: Champion
authors.affiliation: Department of Statistics, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.|Department of Biostatistics & Medical Informatics, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.|Department of Computer Sciences, University of Wisconsin, Madison, Wisconsin, 53706, U.S.A.
authors.forename: Grace
authors.initials: G
authors.lastname: Wahba
mesh_terms: D000293:Adolescent; D000328:Adult; D001943:Breast Neoplasms / Q000453:epidemiology* / Q000523:psychology / Q000628:therapy*; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008875:Middle Aged; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000379:methods*; D015995:Prevalence; D011788:Quality of Life / Q000523:psychology*; D015996:Survival Rate; D017741:Survivors / Q000523:psychology* / Q000706:statistics & numerical data*; D016896:Treatment Outcome; D014481:United States / Q000453:epidemiology; D055815:Young Adult
keywords: Breast cancer survivor; Finite sample bound; Group variable selection; High-dimensional data; Penalized estimation; Sparsity recovery