广义线性模型组LASSO路径算法

An algorithm for the estimation of regularization paths of generalized linear models with group LASSO penalty

广义线性模型组LASSO(least absolute shrinkage and selection operator)路径β(λ)的计算有两项核心内容:选择路径参数λ的取值;计算组LASSO估计,即给定λ值的β(λ).目前,在广义线性模型组LASSO路径的计算中,使用格点法选择λ值,基于广义线性模型似然函数一阶Taylor近似的坐标下降算法则常用于计算组LASSO估计.本文给出的广义线性模型组LASSO路径算法由两个子算法组成:第一个子算法的目的是选出使得活跃集恰好改变的λ值;第二个子算法是计算组LASSO估计的二阶近似坐标下降算法.模拟和实际数据分析均表明,第一个子算法能高效地发现使得活跃集恰好改变的λ值,相比基于广义线性模型似然函数一阶Taylor近似的坐标下降算法,本文的二阶近似算法有较明显的速度优势.

Computing the regularization paths of generalized linear models（GLM） with group LASSO penalty can be decomposed into two problems： Selecting the path parameter λ and computing group LASSO solution？β（λ） given λ. In practice,grid method is usually used to solve the first one and coordinate descent algorithm based on the first order Taylor expansion of loss function of GLM is then used to solve the second. This paper aims at proposing algorithms that solve these two problems more efficiently. Firstly,we give a path following algorithm that attempts to find the λ＇s that correspond to the change of active set. Secondly,we take advantage of the properties of GLM,and use second-order,instead of first-order,Taylor approximation of the loss function of GLM in coordinate descent method to achieve better precision in less time. Simulated and real data sets show that our algorithm is capable of efficiently pinpointing the critical λ＇s that pair with changes of active set and that our proposed coordinate descent algorithm based on second-order approximation is competitive in speed compared with that based on second-order approximation.