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Efficient ?0 -norm feature selection based on augmented and penalized minimization.

ABSTRACT: 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 ?0 -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 ?0 -norm (eg, ?1 ) does not outperform their ?0 counterpart. The progress for ?0 -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 ?0 -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 ?0 -penalty variable selection, referred to as augmented penalized minimization-L0 (APM-L0 ). The APM-L0 targets ?0 -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 ?1 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.

SUBMITTER: Li X

PROVIDER: S-EPMC5768461 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Efficient ℓ<sub>0</sub> -norm feature selection based on augmented and penalized minimization.

Li Xiang X Xie Shanghong S Zeng Donglin D Wang Yuanjia Y

Statistics in medicine 20171030 3

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 ℓ<sub>0</sub> -penalty on the regression coefficients. Since this optimization is a nondeter ...[more]

PMID: 29082539

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Project description:In medical and industrial applications of computed tomography (CT) imaging, limited by the scanning environment and the risk of excessive X-ray radiation exposure imposed to the patients, reconstructing high quality CT images from limited projection data has become a hot topic. X-ray imaging in limited scanning angular range is an effective imaging modality to reduce the radiation dose to the patients. As the projection data available in this modality are incomplete, limited-angle CT image reconstruction is actually an ill-posed inverse problem. To solve the problem, image reconstructed by conventional filtered back projection (FBP) algorithm frequently results in conspicuous streak artifacts and gradual changed artifacts nearby edges. Image reconstruction based on total variation minimization (TVM) can significantly reduce streak artifacts in few-view CT, but it suffers from the gradual changed artifacts nearby edges in limited-angle CT. To suppress this kind of artifacts, we develop an image reconstruction algorithm based on ?0 gradient minimization for limited-angle CT in this paper. The ?0-norm of the image gradient is taken as the regularization function in the framework of developed reconstruction model. We transformed the optimization problem into a few optimization sub-problems and then, solved these sub-problems in the manner of alternating iteration. Numerical experiments are performed to validate the efficiency and the feasibility of the developed algorithm. From the statistical analysis results of the performance evaluations peak signal-to-noise ratio (PSNR) and normalized root mean square distance (NRMSD), it shows that there are significant statistical differences between different algorithms from different scanning angular ranges (p<0.0001). From the experimental results, it also indicates that the developed algorithm outperforms classical reconstruction algorithms in suppressing the streak artifacts and the gradual changed artifacts nearby edges simultaneously.

Dataset Information

Efficient ?0 -norm feature selection based on augmented and penalized minimization.

Publications

Efficient ℓ<sub>0</sub> -norm feature selection based on augmented and penalized minimization.

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