Fast and Flexible ADMM Algorithms for Trend Filtering

Understand

This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool.

• It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves the minimax optimal error rate, while other popular methods like smoothing splines and kernels do not.
• Standing in the way of a more widespread practical adoption, however, is a lack of scalable and numerically stable algorithms for fitting trend filtering estimates.
• This paper presents a highly efficient, specialized ADMM routine for trend filtering.