Moderately clipped LASSO

Kwon, Sunghoon; Lee, Sangin; Kim, Yongdai

doi:10.1016/j.csda.2015.07.001

Cited by 19 publications

(12 citation statements)

References 26 publications

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“…The MCL penalty is a smooth interpolation between the MCP and LASSO penalty that becomes the MCP when γ = 0 and the LASSO penalty when γ = λ (Figure 1). The MCL penalty has two regularization parameters λ and γ, where λ controls the sparsity of the MCL as the MCP and γ decides the amount of shrinkage for the nonzero regression coefficients as the LASSO (Kwon et al, 2015) penalty. Therefor, we expect that the MCL selects relevant predictive variables as the MCP (Zhang, 2010) and produces high prediction accuracy as the LASSO (Zhang and Huang, 2008) for finite samples.…”

Section: Definitionmentioning

confidence: 99%

“…There have been many penalties that combine two different penalties for preserving desirable properties of the combined penalties. Examples include the elastic net (Zou and Hastie, 2005), sparse ridge (Kwon et al, 2013) and moderately clipped LASSO (Kwon et al, 2015). The elastic net combines the LASSO and ridge for variable selection that also deals with highly correlated variables, which is the same idea for the sparse ridge that combines the MCP and ridge.…”

Section: Introductionmentioning

confidence: 99%

“…The elastic net combines the LASSO and ridge for variable selection that also deals with highly correlated variables, which is the same idea for the sparse ridge that combines the MCP and ridge. The moderately clipped LASSO (MCL) is designed to select variables as the MCP and achieve the same shrinkage effect as the LASSO, which is suitable for a high-dimensional linear regression model (Kwon et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

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Moderately clipped LASSO for the high-dimensional generalized linear model

Lee

Kown

2020

CSAM

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The least absolute shrinkage and selection operator (LASSO) is a popular method for a high-dimensional regression model. LASSO has high prediction accuracy; however, it also selects many irrelevant variables. In this paper, we consider the moderately clipped LASSO (MCL) for the high-dimensional generalized linear model which is a hybrid method of the LASSO and minimax concave penalty (MCP). The MCL preserves advantages of the LASSO and MCP since it shows high prediction accuracy and successfully selects relevant variables. We prove that the MCL achieves the oracle property under some regularity conditions, even when the number of parameters is larger than the sample size. An efficient algorithm is also provided. Various numerical studies confirm that the MCL can be a better alternative to other competitors.

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Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Moderately clipped LASSO for the high-dimensional generalized linear model

Lee

Kown

2020

CSAM

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“…The smoothly clipped absolute deviations penalty (SCAD, [3]) is another folded concave penalty that performs similarly to the MCP. Some other variants of the Lasso include the adaptive Lasso ( [4]), the relaxed Lasso ( [5]), Moderately Clipped Lasso ( [6]), etc. The regularization methods with the above penalties can perform well for variable selection in high-dimensional data settings when strong correlation does not appear among many covariates.…”

Section: Introductionmentioning

confidence: 99%

Stable Variable Selection for High-dimensional Genomic Data with Strong Correlations

Sarkar

Manage

Gao

2021

Preprint

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Background: High-dimensional genomic data studies are often found to exhibit strong correlations, which results in instability and inconsistency in the estimates obtained using commonly used regularization approaches including both the Lasso and MCP, and related methods. Result: In this paper, we perform a comparative study of regularization approaches for variable selection under different correlation structures, and propose a two-stage procedure named rPGBS to address the issue of stable variable selection in various strong correlation settings. This approach involves repeatedly running of a two-stage hierarchical approach consisting of a random pseudo-group clustering and bi-level variable selection. Conclusion: Both the simulation studies and high-dimensional genomic data analysis have demonstrated the advantage of the proposed rPGBS method over most commonly used regularization methods. In particular, the rPGBS results in more stable selection of variables across a variety of correlation settings, as compared to recent work addressing variable selection with strong correlations. Moreover, the rPGBS is computationally efficient across various settings.

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“…In this paper, we develop an R package ncpen for the non-convex penalized estimation based on the convex-concave procedure (CCCP) or difference-convex (DC) algorithm (Kim et al, 2008;Shen et al, 2012) and the modified local quadratic approximation algorithm (MLQA) (Lee et al, 2016). The main contribution of the package ncpen is that it encompasses most of existing non-convex penalties, including the truncated ℓ 1 (Shen et al, 2013), log (Zou and Li, 2008;Friedman, 2012), bridge (Huang et al, 2008), moderately clipped LASSO (Kwon et al, 2015), sparse ridge (Huang et al, 2013;Kwon et al, 2013) penalties as well as the SCAD and MCP and covers a broader range of regression models: multinomial and Cox models as well as the GLM. Further, ncpen provides two unique options: the investigation of initial dependent solution paths and non-standardization of input variables, which allow the users more flexibility.…”

Section: Introductionmentioning

confidence: 99%

A unified algorithm for the non-convex penalized estimation: The ncpen package

Kim¹,

Lee²,

Kwon³

2018

Preprint

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Various R packages have been developed for the non-convex penalized estimation but they can only be applied to the smoothly clipped absolute deviation (SCAD) or minimax concave penalty (MCP). We develop an R package, entitled ncpen, for the non-convex penalized estimation in order to make data analysts to experience other non-convex penalties. The package ncpen implements a unified algorithm based on the convex concave procedure and modified local quadratic approximation algorithm, which can be applied to a broader range of non-convex penalties, including the SCAD and MCP as special examples. Many user-friendly functionalities such as generalized information criteria, cross-validation and ℓ 2 -stabilization are provided also.

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Moderately clipped LASSO

Cited by 19 publications

References 26 publications

Moderately clipped LASSO for the high-dimensional generalized linear model

Moderately clipped LASSO for the high-dimensional generalized linear model

Stable Variable Selection for High-dimensional Genomic Data with Strong Correlations

A unified algorithm for the non-convex penalized estimation: The ncpen package

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