Son Won, Lim Johan, Yu Donghyeon
Department of Information Statistics Dankook University Gyeonggi-do Korea.
Department of Statistics Seoul National University Seoul Korea.
Int Stat Rev. 2022 Oct 19. doi: 10.1111/insr.12521.
The fused lasso signal approximator (FLSA) is a smoothing procedure for noisy observations that uses fused lasso penalty on unobserved mean levels to find sparse signal blocks. Several path algorithms have been developed to obtain the whole solution path of the FLSA. However, it is known that the FLSA has model selection inconsistency when the underlying signals have a stair-case block, where three consecutive signal blocks are either strictly increasing or decreasing. Modified path algorithms for the FLSA have been proposed to guarantee model selection consistency regardless of the stair-case block. In this paper, we provide a comprehensive review of the path algorithms for the FLSA and prove the properties of the recently modified path algorithms' hitting times. Specifically, we reinterpret the modified path algorithm as the path algorithm for local FLSA problems and reveal the condition that the hitting time for the fusion of the modified path algorithm is not monotone in a tuning parameter. To recover the monotonicity of the solution path, we propose a pathwise adaptive FLSA having monotonicity with similar performance as the modified solution path algorithm. Finally, we apply the proposed method to the number of daily-confirmed cases of COVID-19 in Korea to identify the change points of its spread.
融合套索信号逼近器（FLSA）是一种针对噪声观测值的平滑方法，它对未观测到的均值水平使用融合套索惩罚来找到稀疏信号块。已经开发了几种路径算法来获得FLSA的完整解路径。然而，已知当潜在信号具有阶梯块时，FLSA存在模型选择不一致的问题，其中三个连续的信号块要么严格递增要么严格递减。已经提出了FLSA的改进路径算法，以确保无论阶梯块如何都具有模型选择一致性。在本文中，我们对FLSA的路径算法进行了全面综述，并证明了最近改进的路径算法命中时间的性质。具体而言，我们将改进的路径算法重新解释为局部FLSA问题的路径算法，并揭示了改进路径算法融合的命中时间在调谐参数中不单调的条件。为了恢复解路径的单调性，我们提出了一种具有单调性的逐路径自适应FLSA，其性能与改进的解路径算法相似。最后，我们将所提出的方法应用于韩国新冠肺炎每日确诊病例数，以识别其传播的变化点。
