Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with OSCAR. Variable selection can be challenging, particularly in situations with a large number of predictors with possibly high correlations, such as gene expression data. In this article, a new method, called OSCAR (octagonal shrinkage and clustering algorithm for regression), is proposed to simultaneously select variables while grouping them into predictive clusters. In addition to improving prediction accuracy and interpretation, these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior. The technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero. Additionally, this penalty yields exact equality of some coefficients, encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient. The proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity, while yielding the additional grouping information.

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  1. Cui, Qiurong; Xu, Yuqing; Zhang, Zhengjun; Chan, Vincent: Max-linear regression models with regularization (2021)
  2. Calderon, Hernan; Santibañez, Felipe; Silva, Jorge F.; Ortiz, Julián M.; Egaña, Alvaro: Geological facies recovery based on weighted (\ell_1)-regularization (2020)
  3. Do, Hyungrok; Cheon, Myun-Seok; Kim, Seoung Bum: Graph structured sparse subset selection (2020)
  4. Ren, Sheng; Kang, Emily L.; Lu, Jason L.: MCEN: a method of simultaneous variable selection and clustering for high-dimensional multinomial regression (2020)
  5. Sherwood, Ben; Molstad, Aaron J.; Singha, Sumanta: Asymptotic properties of concave (L_1)-norm group penalties (2020)
  6. Chakraborty, Sounak; Lozano, Aurelie C.: A graph Laplacian prior for Bayesian variable selection and grouping (2019)
  7. Lederer, Johannes; Yu, Lu; Gaynanova, Irina: Oracle inequalities for high-dimensional prediction (2019)
  8. Liu, Jianyu; Yu, Guan; Liu, Yufeng: Graph-based sparse linear discriminant analysis for high-dimensional classification (2019)
  9. Zhang, Yingying; Wang, Huixia Judy; Zhu, Zhongyi: Quantile-regression-based clustering for panel data (2019)
  10. Hui, Francis K. C.; Müller, Samuel; Welsh, A. H.: Sparse pairwise likelihood estimation for multivariate longitudinal mixed models (2018)
  11. Song, Anchao; Ma, Tiefeng; Lv, Shaogao; Lin, Changsheng: A model-free variable selection method for reducing the number of redundant variables (2018)
  12. Zhang, Yan; Bondell, Howard D.: Variable selection via penalized credible regions with Dirichlet-Laplace global-local shrinkage priors (2018)
  13. Zhao, Shangwei; Ullah, Aman; Zhang, Xinyu: A class of model averaging estimators (2018)
  14. Alkenani, Ali; Dikheel, Tahir R.: Robust group identification and variable selection in regression (2017)
  15. Hamedani, Hamideh D.; Moosavi, Sara Sadat: Dealing with big data: comparing dimension reduction and shrinkage regression methods (2017)
  16. Jeon, Jong-June; Kwon, Sunghoon; Choi, Hosik: Homogeneity detection for the high-dimensional generalized linear model (2017)
  17. Ke, Yuan; Li, Jialiang; Zhang, Wenyang: Structure identification in panel data analysis (2016)
  18. Nguyen, Tu Dinh; Tran, Truyen; Phung, Dinh; Venkatesh, Svetha: Graph-induced restricted Boltzmann machines for document modeling (2016)
  19. Su, Weijie; Candès, Emmanuel: SLOPE is adaptive to unknown sparsity and asymptotically minimax (2016)
  20. Bogdan, Małgorzata; van den Berg, Ewout; Sabatti, Chiara; Su, Weijie; Candès, Emmanuel J.: SLOPE-adaptive variable selection via convex optimization (2015)

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