Efficient ℓ0 -norm feature selection based on augmented and penalized minimization.
Advances in high-throughput technologies in genomics and imaging yield unprecedentedly large numbers of prognostic biomarkers. To accommodate the scale of biomarkers and study their association with disease outcomes, penalized regression is often used to identify important biomarkers. The ideal vari...
| Publicado en: | Statistics in Medicine Vol. 36; no. 24 |
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| Autores principales: | , , , |
| Formato: | Journal Article |
| Publicado: |
Wiley-Blackwell
10/30/2017
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ccm&AN=125980332&site=ehost-live header: @attributes: shortDbName: ccm uiTerm: 125980332 longDbName: CINAHL Complete uiTag: AN controlInfo: bkinfo: dissinfo: jinfo: jid: 02776715 2DZ jtl: Statistics in Medicine issn: 02776715 maglogo: Y pubinfo: dt: 10/30/2017 vid: 36 iid: 24 pid: 480 pub: Wiley-Blackwell place: Malden, Massachusetts artinfo: ui: 125980332 125980332 NLM29082539 10.1002/sim.7526 NLM29082539 125980332 ppct: 1 formats: tig: atl: Efficient ℓ0 -norm feature selection based on augmented and penalized minimization. aug: au: Li, Xiang Xie, Shanghong Zeng, Donglin Wang, Yuanjia affil: Statistics and Decision Sciences, Janssen Research & Development, LLC, Raritan, NJ, USA sug: subj: Algorithms Models, Statistical Prognosis Regression Probability Computer Simulation Genomics Scales ab: Advances in high-throughput technologies in genomics and imaging yield unprecedentedly large numbers of prognostic biomarkers. To accommodate the scale of biomarkers and study their association with disease outcomes, penalized regression is often used to identify important biomarkers. The ideal variable selection procedure would search for the best subset of predictors, which is equivalent to imposing an ℓ0 -penalty on the regression coefficients. Since this optimization is a nondeterministic polynomial-time hard (NP-hard) problem that does not scale with number of biomarkers, alternative methods mostly place smooth penalties on the regression parameters, which lead to computationally feasible optimization problems. However, empirical studies and theoretical analyses show that convex approximation of ℓ0 -norm (eg, ℓ1 ) does not outperform their ℓ0 counterpart. The progress for ℓ0 -norm feature selection is relatively slower, where the main methods are greedy algorithms such as stepwise regression or orthogonal matching pursuit. Penalized regression based on regularizing ℓ0 -norm remains much less explored in the literature. In this work, inspired by the recently popular augmenting and data splitting algorithms including alternating direction method of multipliers, we propose a 2-stage procedure for ℓ0 -penalty variable selection, referred to as augmented penalized minimization-L0 (APM-L0 ). The APM-L0 targets ℓ0 -norm as closely as possible while keeping computation tractable, efficient, and simple, which is achieved by iterating between a convex regularized regression and a simple hard-thresholding estimation. The procedure can be viewed as arising from regularized optimization with truncated ℓ1 norm. Thus, we propose to treat regularization parameter and thresholding parameter as tuning parameters and select based on cross-validation. A 1-step coordinate descent algorithm is used in the first stage to significantly improve computational efficiency. Through extensive simulation studies and real data application, we demonstrate superior performance of the proposed method in terms of selection accuracy and computational speed as compared to existing methods. The proposed APM-L0 procedure is implemented in the R-package APML0. pubtype: Academic Journal doctype: Journal Article ougenre: Article language: English refInfo: holdings: @attributes: islocal: N |
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