基于对偶交替方向乘子法求解罚分位数回归问题

A DUAL ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR PENALIZED QUANTILE REGRESSION

分位数回归是对数据进行分析与预测的有效方法.由于分位数回归的损失函数具有非光滑性,有关分位数回归的计算问题仍面临着一些挑战.本文通过从罚分位数回归的对偶问题出发基于交替方向乘子法(Alternating Direction Method of Multipliers,简称ADMM)求解罚分位数回归问题.并在一些温和的条件下,给出对偶交替方向乘子法(dual ADMM,简称dADMM)的全局收敛性及局部线性收敛速度.数值试验验证了该算法的有效性.

Quantile regression is an effective method for data analysis and prediction. Due to the non-smoothness of the loss function of quantile regression, the computation of quantile regression problems still faces some challenges. This paper adopts a dual alternating direction method of multipliers to solve the penalized quantile regression. This paper also presents the global convergence and the local linear convergence rate for the algorithm under some mild conditions. Numerical experiments demonstrate the effectiveness of the algorithm.