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Variable selection and estimation using a continuous approximation to the L₀ penalty

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2018年第1期70卷 191-214页

作者： Wang, Yanxin Fan, Qibin Zhu, Li Ningbo Univ Technol Sch Sci Ningbo 315211 Zhejiang Peoples R China Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China Xiamen Univ Technol Sch Appl Math Xiamen 361024 Peoples R China

Variable selection problems are typically addressed under the regularization framework. In this paper, an exponential type penalty which very closely resembles the L-0 penalty is proposed, we called it EXP penalty. The EXP penalized least squares procedure is shown to consistently select the correct model and is asymptotically normal, provided the number of variables grows slower than the number of observations. EXP is efficiently implemented using a coordinate descent algorithm. Furthermore, we propose a modified BIC tuning parameter selection method for EXP and show that it consistently identifies the correct model, while allowing the number of variables to diverge. Simulation results and data example show that the EXP procedure performs very well in a variety of settings.

关键词： Penalized least squares coordinate descent algorithm Variable selection MBIC Oracle property

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High-Performance GLR Detector for Moving Target Detection in OFDM Radar-Based Vehicular Networks

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WIRELESS PERSONAL COMMUNICATIONS 2019年第2期108卷 751-768页

作者： Kafshgari, Shaghayegh Mohseni, Reza Samadi, Sadegh Khosravi, Mohammad Reza Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

Nowadays, orthogonal frequency division multiplexing (OFDM) radars have been used in many applications such as target detection and recognition in vehicular networks and surveillance systems, according to their frequency diversity property. The model of the received signal in an OFDM radar based on target's parameters has a non-linear form with respect to unknown velocity and scattering coefficients, so there is no possibility of achieving a closed form solution for Maximum Likelihood Estimation of the unknown parameters and so the Neyman-Pearson detector. Therefore, in all published works, the generalized likelihood ratio (GLR) detector is obtained for the target with known velocity, or in case of simultaneous unknown velocity and scattering coefficients, only a wide two-dimensional grid search over all possible values of the unknown parameters is considered to maximize the Likelihood ratio. In this paper, a new method is proposed for simultaneous estimations of target velocity and scattering coefficients using a coordinate descent approach, which reduces the above nonlinear problem to two linear problems, and makes the implementation of GLR detector efficient. The simulation results confirm the efficiency of the proposed method.

关键词： OFDM radar Generalized likelihood ratio Maximum likelihood estimation coordinate descent algorithm

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Gene expression data classification with robust sparse logistic regression using fused regularisation

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INTERNATIONAL JOURNAL OF AD HOC AND UBIQUITOUS COMPUTING 2023年第4期42卷 281-291页

作者： Lavanya, Kampa Rambabu, Pemula Suresh, G. Vijay Bhandari, Rahul Acharya Nagarjuna Univ Univ Coll Sci Dept Comp Sci & Engn Guntur India RAGHU Engn Coll Dept Comp Sci & Engn Visakhapatnam Andhra Prades India Lakireddy Bali Reddy Coll Engn Dept Comp Sci & Engn Mylavaram 521230 AP India Chandigarh Univ Dept Comp Sci & Engn Mohali 140413 Punjab India

Microarray technology has become popular and is extensively used for gene classification. It is essential to identify a proper set of gene expressions that help to classify cancer data. However, microarray data comprises large number of genes with small set of samples. A penalised logistic regression (PLR) is good for variable selection in high dimensional microarray data. The techniques like Lasso, ridge and elastic net are suitable to reduce irrelevant features. However, they failed to produce properties like oracle property and sparsity resulted over fitting. To retain sparsity and oracle property, the weighted L1 and L2 penalties are used in logistic regression for gene expression data. In this paper, a new fused logistic regression (FLR) has been introduced using weighted L1 and L2 penalties for better gene selection. Regression algorithms were tested over the simulated as well as the real gene data sets.

关键词： microarray data regularisation feature selection sparse logistic regression robust Lasso penalised logistic regression PLR fused logistic regression FLR coordinate descent algorithm CDA

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Lasso regression under stochastic restrictions in linear regression: An application to genomic data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2024年第8期53卷 2816-2839页

作者： Genc, Murat Ozkale, M. Revan Tarsus Univ Fac Econ & Adm Sci Dept Management Informat Syst Mersin Turkiye Cukurova Univ Fac Sci & Letters Dept Stat Adana Turkiye

Variable selection approaches are often employed in high-dimensionality and multicollinearity problems. Since lasso selects variables by shrinking the coefficients, it has extensive use in many fields. On the other, we may sometime have extra information on the model. In this case, the extra information should be considered in the estimation procedure. In this paper, we propose a stochastic restricted lasso estimator in linear regression model which uses the extra information as stochastic linear restrictions. The estimator is a generalization of mixed estimator with L-1 type penalization. We give the coordinate descent algorithm to estimate the coefficient vector of the proposed method and strong rules for the coordinate descent algorithm to discard variables from the model. Also, we propose a method to estimate the tuning parameter. We conduct two real data analyses and simulation studies to compare the new estimator with several estimators including the ridge, lasso and stochastic restricted ridge. The real data analyses and simulation studies show that the new estimator enjoys the automatic variable selection property of the lasso while outperforms standard methods, achieving lower test mean squared error.

关键词： Bayesian information criterion coordinate descent algorithm genomic data lasso variable selection

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Additive regression splines with total variation and non negative garrote penalties

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2022年第22期51卷 7713-7736页

作者： Jhong, Jae-Hwan Bak, Kwan-Young Shin, Jae-Kyung Koo, Ja-Yong Korea Univ Dept Stat Seoul South Korea Chungbuk Natl Univ Dept Informat Stat Cheongju South Korea

This study examines a penalized additive regression spline estimator with total variation and non negative garrote-type penalties. The proposed estimator is obtained based on a two-stage procedure. In the first stage, an initial estimator is obtained via total variation penalization. The total variation penalty enables data-adaptive knot selection and regularizes the overall smoothness of the estimator. The second stage imposes the non negative garrote penalty on the estimated functional components to attain variable selectivity. Regarding the theoretical aspect, a non asymptotic oracle inequality for the total variation penalized estimator is established under some regularity conditions. Based on the oracle inequality, we prove that the estimator attains the optimal rate of convergence up to a logarithmic factor, which in turn leads to the selection and estimation consistency of the second-stage garrote estimator. Numerical studies are presented to illustrate the usefulness of a combination of these two penalties. The results show that the proposed method outperforms existing methods.

关键词： coordinate descent algorithm model selection non parametric smoothing oracle inequality penalized least squares

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Automatic structure discovery for varying-coefficient partially linear models

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第15期46卷 7703-7716页

作者： Yang, Guangren Sun, Yanqing Cui, Xia Jinan Univ Sch Econ Dept Stat Guangzhou Guangdong Peoples R China Univ N Carolina Dept Math & Stat Charlotte NC USA Guangzhou Univ Sch Econ & Stat Guangzhou 510006 Guangdong Peoples R China

Varying-coefficient partially linear models provide a useful tools for modeling of covariate effects on the response variable in regression. One key question in varying-coefficient partially linear models is the choice of model structure, that is, how to decide which covariates have linear effect and which have non linear effect. In this article, we propose a profile method for identifying the covariates with linear effect or non linear effect. Our proposed method is a penalized regression approach based on group minimax concave penalty. Under suitable conditions, we show that the proposed method can correctly determine which covariates have a linear effect and which do not with high probability. The convergence rate of the linear estimator is established as well as the asymptotical normality. The performance of the proposed method is evaluated through a simulation study which supports our theoretical results.

关键词： B-spline coordinate descent algorithm group MCP varying-coefficient partially linear models

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Penalized B-spline estimator for regression functions using total variation penalty

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2017年 184卷 77-93页

作者： Jhong, Jae-Hwan Koo, Ja-Yong Lee, Seong-Whan Korea Univ Dept Stat Seoul 136701 South Korea Korea Univ Dept Brain & Cognit Engn Seoul 136701 South Korea

We carry out a study on a penalized regression spline estimator with total variation penalty. In order to provide a spatially adaptive method, we consider total variation penalty for the estimating regression function. This paper adopts B-splines for both numerical implementation and asymptotic analysis because they have small supports, so the information matrices are sparse and banded. Once we express the estimator with a linear combination of B-splines, the coefficients are estimated by minimizing a penalized residual sum of squares. A new coordinate descent algorithm is introduced to handle total variation penalty determined by the B-spline coefficients. For large-sample inference, a nonasymptotic oracle inequality for penalized B-spline estimators is obtained. The oracle inequality is then used to show that the estimator is an optimal adaptive for the estimation of the regression function up to a logarithm factor. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Adaptive estimation coordinate descent algorithm LASSO Oracle inequalities Penalized least squares

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Reinforced Angle-Based Multicategory Support Vector Machines

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2016年第3期25卷 806-825页

作者： Zhang, Chong Liu, Yufeng Wang, Junhui Zhu, Hongtu Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON N2L 3G1 Canada Univ North Carolina Chapel Hill Dept Stat & Operat Res Dept Genet Chapel Hill NC 28223 USA Univ North Carolina Chapel Hill Dept Biostat Chapel Hill NC 28223 USA City Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China Univ North Carolina Chapel Hill Dept Biostat Chapel Hill NC 28223 USA

The support vector machine (SVM) is a very popular classification tool with many successful applications. It was originally designed for binary problems with desirable theoretical properties. Although there exist various multicategory SVM (MSVM) extensions in the literature, some challenges remain. In particular, most existing MSVMs make use of k classification functions for a k-class problem, and the corresponding optimization problems are typically handled by existing quadratic programming solvers. In this article, we propose a new group of MSVMs, namely, the reinforced angle-based MSVMs (RAMSVMs), using an angle-based prediction rule with k - 1 functions directly. We prove that RAMSVMs can enjoy Fisher consistency. Moreover, we show that the RAMSVM can be implemented using the very efficient coordinate descent algorithm on its dual problem. Numerical experiments demonstrate that our method is. highly competitive in terms of computational speed, as well as classification prediction performance. Supplemental materials for the article are available online.

关键词： coordinate descent algorithm Fisher consistency Multicategory classification Quadratic programming Reproducing kernel Hilbert space

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Joint variable selection of both fixed and random effects for Gaussian process-based spatially varying coefficient models

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INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2022年第12期36卷 2525-2548页

作者： Dambon, Jakob A. Sigrist, Fabio Furrer, Reinhard Univ Zurich Dept Math Zurich Switzerland Lucerne Univ Appl Sci & Arts Inst Financial Serv Zug Rotkreuz Switzerland Swiss Re Management Ltd Zurich Switzerland Univ Zurich Inst Computat Sci Zurich Switzerland

Spatially varying coefficient (SVC) models are a type of regression models for spatial data where covariate effects vary over space. If there are several covariates, a natural question is which covariates have a spatially varying effect and which not. We present a new variable selection approach for Gaussian process-based SVC models. It relies on a penalized maximum likelihood estimation and allows joint variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach in a simulation study as well as a real world data set. In the simulation study, the penalized maximum likelihood estimation correctly identifies zero fixed and random effects, while the penalty-induced bias of non-zero estimates is negligible. In the real data application, our proposed penalized maximum likelihood estimation yields sparser SVC models and achieves a smaller information criterion than classical maximum likelihood estimation. In a cross-validation study applied on the real data, we show that our proposed penalized maximum likelihood estimation consistently yields the sparsest SVC models while achieving similar predictive performance compared to other SVC modeling methodologies.

关键词： Adaptive LASSO Bayesian optimization coordinate descent algorithm model-based optimization penalized maximum likelihood estimation spatial statistics

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Usage of the GO estimator in high dimensional linear models

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COMPUTATIONAL STATISTICS 2021年第1期36卷 217-239页

作者： Genc, Murat Ozkale, M. Revan Cukurova Univ Fac Sci & Letters Dept Stat TR-01330 Adana Turkey

This paper discusses simultaneous parameter estimation and variable selection and presents a new penalized regression method. The method is based on the idea that the coefficient estimates are shrunken towards a predetermined coefficient vector which represents the prior information. This method can result in smaller length estimates of the coefficients depending on the prior information compared to elastic net. In addition to the establishment of the grouping property, we also show that the new method has the grouping effect when the predictors are highly correlated. Simulation studies and real data example show that the prediction performance of the new method is improved over the well-known ridge, lasso and elastic net regression methods yielding a lower mean squared error and competes about the variable selection under sparse and non-sparse situations.

关键词： coordinate descent algorithm Elastic net Grouping property Lasso Shrinkage Variable selection

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