Sparse Group Fused Lasso for Model Segmentation

TL;DR

This paper proposes the sparse group fused lasso (SGFL) for segmenting multivariate time series regression models, introducing a fast, tuning-free optimization method with strong theoretical guarantees and practical effectiveness.

Contribution

It develops a novel hybrid optimization algorithm for SGFL that is fast, tuning-free, and guarantees convergence to a global minimum, with demonstrated superior performance.

Findings

Outperforms existing methods in computation time and accuracy

Effectively recovers nonzero coefficients in high-dimensional data

Excels in change point detection in practical applications

Abstract

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.