In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property...In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.展开更多
Viticulturists traditionally have a keen interest in studying the relationship between the biochemistry of grapevines’ leaves/petioles and their associated spectral reflectance in order to understand the fruit ripeni...Viticulturists traditionally have a keen interest in studying the relationship between the biochemistry of grapevines’ leaves/petioles and their associated spectral reflectance in order to understand the fruit ripening rate, water status, nutrient levels, and disease risk. In this paper, we implement imaging spectroscopy (hyperspectral) reflectance data, for the reflective 330 - 2510 nm wavelength region (986 total spectral bands), to assess vineyard nutrient status;this constitutes a high dimensional dataset with a covariance matrix that is ill-conditioned. The identification of the variables (wavelength bands) that contribute useful information for nutrient assessment and prediction, plays a pivotal role in multivariate statistical modeling. In recent years, researchers have successfully developed many continuous, nearly unbiased, sparse and accurate variable selection methods to overcome this problem. This paper compares four regularized and one functional regression methods: Elastic Net, Multi-Step Adaptive Elastic Net, Minimax Concave Penalty, iterative Sure Independence Screening, and Functional Data Analysis for wavelength variable selection. Thereafter, the predictive performance of these regularized sparse models is enhanced using the stepwise regression. This comparative study of regression methods using a high-dimensional and highly correlated grapevine hyperspectral dataset revealed that the performance of Elastic Net for variable selection yields the best predictive ability.展开更多
The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficie...The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.展开更多
文摘In this paper, we have studied the nonparameter accelerated failure time (AFT) additive regression model, whose covariates have a nonparametric effect on high-dimensional censored data. We give the asymptotic property of the penalty estimator based on GMCP in the nonparameter AFT model.
文摘针对高光谱图像(hyperspectral images,HSI)去条带易引起影像结构细节丢失问题,提出一种基于加权块稀疏(weighted block sparsity,WBS)正则化联合最小最大非凸惩罚(minimax concave penalty,MCP)约束的HSI去条带方法。本算法采用加权ℓ_(2),1范数和MCP范数对条带稀疏结构和低秩约束,ℓ_(1)范数对干净图像结构保持正则化约束,构建加权块稀疏和MCP约束的条带去除模型,采用交替方向乘子(alternating direction method of multipliers,ADMM)算法迭代求解对应模型,重建获得干净的HSI图像。实验结果表明,提出方法在实际HSI的平均等效视数从28.45提高到83.47,边缘保持指数较其他算法至少增加0.056,特别是对于非周期条带噪声,采用自适应权值更新稀疏水平,增强了组稀疏性,在保持影像边缘和加强区域平滑性方面性能更佳,去噪声效果更好。
文摘Viticulturists traditionally have a keen interest in studying the relationship between the biochemistry of grapevines’ leaves/petioles and their associated spectral reflectance in order to understand the fruit ripening rate, water status, nutrient levels, and disease risk. In this paper, we implement imaging spectroscopy (hyperspectral) reflectance data, for the reflective 330 - 2510 nm wavelength region (986 total spectral bands), to assess vineyard nutrient status;this constitutes a high dimensional dataset with a covariance matrix that is ill-conditioned. The identification of the variables (wavelength bands) that contribute useful information for nutrient assessment and prediction, plays a pivotal role in multivariate statistical modeling. In recent years, researchers have successfully developed many continuous, nearly unbiased, sparse and accurate variable selection methods to overcome this problem. This paper compares four regularized and one functional regression methods: Elastic Net, Multi-Step Adaptive Elastic Net, Minimax Concave Penalty, iterative Sure Independence Screening, and Functional Data Analysis for wavelength variable selection. Thereafter, the predictive performance of these regularized sparse models is enhanced using the stepwise regression. This comparative study of regression methods using a high-dimensional and highly correlated grapevine hyperspectral dataset revealed that the performance of Elastic Net for variable selection yields the best predictive ability.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571263,11501579,11701571 and41572315)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant No.CUGW150809)
文摘The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.
