Extracting the underlying trend signal is a crucial step to facilitate time
series analysis like forecasting and anomaly detection. Besides noise signal,
time series can contain not only outliers but also abrupt trend changes in
real-world scenarios. To deal with these challenges, we propose a robust trend
filtering algorithm based on robust statistics and sparse learning.
Specifically, we adopt the Huber loss to suppress outliers, and utilize a
combination of the first order and second order difference on the trend
component as regularization to capture both slow and abrupt trend changes.
Furthermore, an efficient method is designed to solve the proposed robust trend
filtering based on majorization minimization (MM) and alternative direction
method of multipliers (ADMM). We compared our proposed robust trend filter with
other nine state-of-the-art trend filtering algorithms on both synthetic and
real-world datasets. The experiments demonstrate that our algorithm outperforms
existing methods.

本文提出一种基于鲁棒统计和稀疏学习的趋势过滤算法，采用 Huber 损失压制离群值并利用一阶和二阶差分组合作为正则化以捕捉缓慢和突变的趋势变化，通过主元最小化与多项式替代方向法设计出有效的方法来解决鲁棒趋势过滤，实验证明该算法优于其他九种最先进的趋势过滤算法。