A Selective Review of Group Selection in High-Dimensional Models.

By Jian Huang, Patrick Breheny, Shuangge Ma. Statistical Science, 2012

407 citations recorded by the source corpus.

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a selective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular attention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several applications of these methods in nonparametric additive models, semiparametric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3daa1216f7e6f7118ecc52c5f453d05891214bab

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Citations in the corpus

Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors (2012, methodology): “Although originally proposed for univariate penalized regression, these penalties may be extended to the grouped-variable selection problem by substituting (2.10) and (2.11) into (2.2), as has been proposed in Wang et al. (2007) and discussed in Huang et al. (2012).”
Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression (2015, methodology): “By contrast, if nonconvex regularizers such as the MCP or SCAD are used, then this type of condition is not necessary (Loh and Wainwright, 2015; Huang et al., 2012; Zhang, 2010).”
Causal Interaction in Factorial Experiments: Application to Conjoint Analysis (2018, neutral): “…exist other regularization methods for categorical variables (e.g., Yuan and Lin 2006; Meier, Van De Geer, and Bühlmann 2008; Zhao, Rocha, and Yu 2009; Huang et al. 2009; Huang, Breheny, and Ma 2012; Lim and Hastie 2015), these methods regularize coe ffi cients rather than their di ff erences.”
A simple new approach to variable selection in regression, with application to genetic fine mapping (2018, methodology): “…in R that can be used for detecting change points include changepoint (Killick and Eckley, 2014), DNAcopy (Seshan and Olshen, 2018; Olshen et al., 2004), bcp (Erdman and Emerson, 2007) and genlasso (Tibshirani, 2014; Arnold and Tibshirani, 2016); see Killick and Eckley (2014) for a longer list.”