Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise
Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise
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DOI：
10.1080/01621459.2021.1909598
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发表时间：
2021-05-15
影响因子：
3.7
通讯作者：
Fearnhead, Paul
中科院分区：
文献类型：
--
作者：
Romano, Gaetano;Rigaill, Guillem;Fearnhead, Paul
虽然有大量的算法用于检测单变量时间序列中的均值变化，但几乎所有算法都在真实的应用中挣扎，其中存在自相关噪声或均值在人们希望检测的突然变化之间局部波动。在这些情况下，通常基于变化和独立噪声之间的恒定平均值的假设的默认实现可能导致对变化数量的大量高估。我们提出了一个原则性的方法来检测这种突然的变化，模型局部波动作为一个随机游走过程和自相关噪声通过AR（1）过程。然后，我们估计的数量和位置的变化点通过最小化基于这个模型的惩罚成本。我们开发了一种新的和有效的动态规划算法，DeCAFS，可以解决这个最小化问题，尽管额外的挑战，跨段的依赖，由于自相关噪声，这使得现有的算法不适用。理论和实证结果表明，我们的方法有更大的权力在检测突变比现有的方法。我们将我们的方法应用于测量细菌中的基因表达水平。本文的补充材料可在网上查阅。
While there are a plethora of algorithms for detecting changes in mean in univariate time-series, almost all struggle in real applications where there is autocorrelated noise or where the mean fluctuates locally between the abrupt changes that one wishes to detect. In these cases, default implementations, which are often based on assumptions of a constant mean between changes and independent noise, can lead to substantial over-estimation of the number of changes. We propose a principled approach to detect such abrupt changes that models local fluctuations as a random walk process and autocorrelated noise via an AR(1) process. We then estimate the number and location of changepoints by minimizing a penalized cost based on this model. We develop a novel and efficient dynamic programming algorithm, DeCAFS, that can solve this minimization problem; despite the additional challenge of dependence across segments, due to the autocorrelated noise, which makes existing algorithms inapplicable. Theory and empirical results show that our approach has greater power at detecting abrupt changes than existing approaches. We apply our method to measuring gene expression levels in bacteria. Supplementary materials for this article are available online.