Fast and Flexible ADMM Algorithms for Trend Filtering
This work addresses a practical bottleneck for researchers and practitioners in statistics and data science by providing a more efficient and flexible algorithm for trend filtering, though it is incremental as it builds on existing ADMM techniques.
The paper tackles the lack of scalable and numerically stable algorithms for trend filtering, a nonparametric regression tool, by presenting a fast and robust ADMM algorithm that is competitive with existing methods and extends to related problems like sparse and isotonic trend filtering.
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. Our algorithm is competitive with the specialized interior point methods that are currently in use, and yet is far more numerically robust. Furthermore, the proposed ADMM implementation is very simple, and importantly, it is flexible enough to extend to many interesting related problems, such as sparse trend filtering and isotonic trend filtering. Software for our method is freely available, in both the C and R languages.