论文标题
使用趋势过滤检测分段多项式信号中的变更点
Detection of Change Points in Piecewise Polynomial Signals Using Trend Filtering
论文作者
论文摘要
尽管已经提出了许多方法来发现分段恒定信号的突然变化，但很少有方法可以捕获分段多项式信号中的这些变化。在本文中，我们根据趋势过滤提出了一种更改点检测方法PRUTF。通过为趋势过滤提供全面的双重解决方案路径，PRUTF允许我们发现正则化参数的给定值或算法的特定步骤的给定值的基础信号的变更点。我们证明双重解路径构成了高斯桥工艺，该过程使我们能够得出一个精确有效的停止规则，以终止搜索算法。我们还证明，该算法产生的估计值在模式恢复中渐近一致。即使在信号中的楼梯（相同符号的连续更改点）的情况下，该结果也保持不变。最后，我们研究了我们提出的各种信号方法的性能，然后在变化点检测的背景下将其性能与某些最新方法进行比较。我们将我们的方法应用于三个现实世界数据集，包括英国房价指数（HPI），GISS表面温度分析（GISTEMP）和冠状病毒病（Covid-19）大流行。
While many approaches have been proposed for discovering abrupt changes in piecewise constant signals, few methods are available to capture these changes in piecewise polynomial signals. In this paper, we propose a change point detection method, PRUTF, based on trend filtering. By providing a comprehensive dual solution path for trend filtering, PRUTF allows us to discover change points of the underlying signal for either a given value of the regularization parameter or a specific number of steps of the algorithm. We demonstrate that the dual solution path constitutes a Gaussian bridge process that enables us to derive an exact and efficient stopping rule for terminating the search algorithm. We also prove that the estimates produced by this algorithm are asymptotically consistent in pattern recovery. This result holds even in the case of staircases (consecutive change points of the same sign) in the signal. Finally, we investigate the performance of our proposed method for various signals and then compare its performance against some state-of-the-art methods in the context of change point detection. We apply our method to three real-world datasets including the UK House Price Index (HPI), the GISS surface Temperature Analysis (GISTEMP) and the Coronavirus disease (COVID-19) pandemic.
