This article introduces the sparse group fused lasso (SGFL) as a statistical framework for segmenting sparse regression models with multivariate time series. To compute solutions of the SGFL, a nonsmooth and nonseparable convex program, we develop a hybrid optimization method that is fast, requires no tuning parameter selection, and is guaranteed to converge to a global minimizer. In numerical experiments, the hybrid method compares favorably to state-of-the-art techniques with respect to computation time and numerical accuracy; benefits are particularly substantial in high dimension. The method’s statistical performance is satisfactory in recovering nonzero regression coefficients and excellent in change point detection. An application to air quality data is presented. The hybrid method is implemented in the R package sparseGFL available on the author’s Github page.

本文介绍了稀疏群融合套索（SGFL）作为用于统计具有多元时间序列的稀疏回归模型的统计框架。为了计算SGFL（一个非光滑且不可分离的凸程序）的解决方案，我们开发了一种混合优化方法，该方法快速，不需要调整参数选择，并且可以保证收敛到全局最小化器。在数值实验中，在计算时间和数值精度方面，混合方法优于最新技术。高尺寸的好处尤其明显。该方法的统计性能在恢复非零回归系数方面令人满意，并且在变化点检测方面非常出色。介绍了空气质量数据的应用。混合方法在R包中实现sparseGFL在作者的Github页面上可用。