论文标题
功能数据序列的可扩展多重更改点检测
Scalable Multiple Changepoint Detection for Functional Data Sequences
论文作者
论文摘要
我们提出了多个变更点隔离方法（MCI）方法，用于检测功能过程的均值和协方差的多个变化。我们首先引入一对投影，以表示功能观察中“和”之间的变异性。然后，我们提出了一个增强的融合套索程序，将预测牢固地分为多个区域。这些区域起作用，将每个变更点隔离到其他变化点，以便可以在区域上应用强大的单变量cusum统计量来识别更改点。模拟表明，我们的方法准确地检测到许多不同情况下的变更点的数量和位置。其中包括轻巧和重型的尾部数据，具有对称和偏斜分布的数据，稀疏和密集采样的更改点以及平均值和协方差变化。我们表明，我们的方法的表现优于最近的多个功能更改点检测器，以及应用于我们提出的预测的几个单变量更改点检测器。我们还表明，MCI比现有方法更强大，并且与样本大小线性缩放。最后，我们在大气发射辐射干涉仪测量的大量水蒸气混合比曲线上演示了我们的方法。
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.
