## Sparse group fused Lasso for model segmentation: a hybrid approach.(English)Zbl 07433033

Summary: 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.

### MSC:

 37M10 Time series analysis of dynamical systems 62J05 Linear regression; mixed models 62J07 Ridge regression; shrinkage estimators (Lasso) 65K10 Numerical optimization and variational techniques

### Software:

clusterpath; UNLocBoX; NESTA; R; wbs; Armadillo
Full Text:

### References:

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