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題名 Structured variable selection via prior-induced hierarchical penalty functions
作者 Yen, Tso-Jung;Yen, Yu-Min
顏佑銘
貢獻者 國貿系
關鍵詞 Group sparsity; Spike and slab priors; Log-sum approximation to the l0l0-norm; Majorization–minimization algorithms; Alternating direction method of multipliers
日期 2016-04
上傳時間 15-Jan-2016 15:44:10 (UTC+8)
摘要 The paper studies a grouped variable selection problem in a linear regression setting by proposing a hierarchical penalty function to model collective behavior of the regression coefficients. This hierarchical penalty function consists of two levels. At the top level, it models the group effect of covariates by introducing an index function on the event that the l 2 -norm of the corresponding regression coefficients is not equal to zero. At the bottom level, it models the individual effect of a covariate with an index function on the event that the corresponding regression coefficient is not equal to zero. Under this hierarchical penalty function, model estimation can be conducted by applying an iteration-based numerical procedure to solve a sequence of modified optimization problems. Simulation study shows that the proposed estimator performs relatively well when the number of covariates exceeds the sample size, and when both the true and false covariates are included in the same group. Theoretical analysis suggests that the l 2 estimation error of the proposed estimator can achieve a good upper bound if some regularity conditions are satisfied.
關聯 Computational Statistics & Data Analysis, 96, 87-103
資料類型 article
DOI http://dx.doi.org/10.1016/j.csda.2015.10.011
dc.contributor 國貿系
dc.creator (作者) Yen, Tso-Jung;Yen, Yu-Min
dc.creator (作者) 顏佑銘zh_TW
dc.date (日期) 2016-04
dc.date.accessioned 15-Jan-2016 15:44:10 (UTC+8)-
dc.date.available 15-Jan-2016 15:44:10 (UTC+8)-
dc.date.issued (上傳時間) 15-Jan-2016 15:44:10 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/80623-
dc.description.abstract (摘要) The paper studies a grouped variable selection problem in a linear regression setting by proposing a hierarchical penalty function to model collective behavior of the regression coefficients. This hierarchical penalty function consists of two levels. At the top level, it models the group effect of covariates by introducing an index function on the event that the l 2 -norm of the corresponding regression coefficients is not equal to zero. At the bottom level, it models the individual effect of a covariate with an index function on the event that the corresponding regression coefficient is not equal to zero. Under this hierarchical penalty function, model estimation can be conducted by applying an iteration-based numerical procedure to solve a sequence of modified optimization problems. Simulation study shows that the proposed estimator performs relatively well when the number of covariates exceeds the sample size, and when both the true and false covariates are included in the same group. Theoretical analysis suggests that the l 2 estimation error of the proposed estimator can achieve a good upper bound if some regularity conditions are satisfied.
dc.format.extent 959695 bytes-
dc.format.mimetype application/pdf-
dc.relation (關聯) Computational Statistics & Data Analysis, 96, 87-103
dc.subject (關鍵詞) Group sparsity; Spike and slab priors; Log-sum approximation to the l0l0-norm; Majorization–minimization algorithms; Alternating direction method of multipliers
dc.title (題名) Structured variable selection via prior-induced hierarchical penalty functions
dc.type (資料類型) article
dc.identifier.doi (DOI) 10.1016/j.csda.2015.10.011
dc.doi.uri (DOI) http://dx.doi.org/10.1016/j.csda.2015.10.011