Scalable multiple changepoint detection for functional data sequences
Scalable multiple changepoint detection for functional data sequences
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DOI：
10.1002/env.2710
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发表时间：
2020-08
期刊：
影响因子：
1.7
通讯作者：
Trevor Harris;Bo Li;J. D. Tucker
中科院分区：
文献类型：
--
作者：
Trevor Harris;Bo Li;J. D. Tucker
我们提出了多变点隔离（MCI）的方法来检测多个变化的均值和协方差的功能过程。我们首先引入一对投影来表示函数观测值之间和内部的变化。然后，我们提出了一个增强的融合套索程序分割成多个区域的投影鲁棒。这些区域的作用是将每个变点与其他变点隔离开来，以便可以按区域应用强大的单变量统计量来识别变点。仿真结果表明，我们的方法准确地检测在许多不同的情况下的变点的数量和位置。这些包括轻尾和重尾数据，对称和偏态分布的数据，稀疏和密集采样的变点，以及均值和协方差变化。我们表明，我们的方法优于最近的多功能变点检测器和几个单变量变点检测器应用到我们提出的预测。我们还表明，MCI是更强大的比现有的方法和规模与样本量呈线性关系。最后，我们证明了我们的方法上的一个大的时间序列的水汽混合比剖面从大气发射辐射干涉仪测量。
We propose the multiple changepoint isolation (MCI) method for detecting multiple changes in the mean and covariance of a functional process. We first introduce a pair of projections to represent the variability “between” and “within” the functional observations. We then present an augmented fused lasso procedure to split the projections into multiple regions robustly. These regions act to isolate each changepoint away from the others so that the powerful univariate CUSUM statistic can be applied region‐wise to identify the changepoints. Simulations show that our method accurately detects the number and locations of changepoints under many different scenarios. These include light and heavy tailed data, data with symmetric and skewed distributions, sparsely and densely sampled changepoints, and mean and covariance changes. We show that our method outperforms a recent multiple functional changepoint detector and several univariate changepoint detectors applied to our proposed projections. We also show that MCI is more robust than existing approaches and scales linearly with sample size. Finally, we demonstrate our method on a large time series of water vapor mixing ratio profiles from atmospheric emitted radiance interferometer measurements.