高维惩罚分位数回归及优化算法

High-dimensional penalized quantile regression and optimization algorithm

针对具有异常值或离群点的高维数据线性回归模型,提出了一种基于误差函数正则化的惩罚分位数回归的新方法,与经典的L1惩罚方法相比,新方法具有更好的稳健性以及更小的估计偏差和预测误差;为解决分位数损失函数非光滑性与误差函数非凸性所带来的计算挑战,结合迭代再加权L1算法以及ADMM算法,提出了一种有效的IRW-ADMM算法,并对回归系数进行了求解.模拟结果表明,与已有的惩罚分位数回归方法相比,新方法在参数估计和变量选择等方面均具有更好的表现.将新方法应用于核黄素基因数据分析,以证实其有效性和可行性.

For linear regression models of high-dimensional data with outliers,a new penalized quantile estimation was proposed based on error function regularization.Compared with classical penalized method,the proposed method had stronger robustness and smaller estimation bias and prediction errors.To solve computational challenges caused by non-smoothness of quantile loss function and non-convexity of error function,an efficient IRW-ADMM algorithm was proposed to obtain numerical solutions of regression coefficients by combining iterative reweighted algorithm and ADMM algorithm.Simulations showed that the proposed method has better performance in terms of parameter estimation and variable selection compared with existing penalized quantile estimators.This method was further applied to riboflavin gene data analysis to confirm its validity and feasibility.