论文标题
在存在局部波动和自相关噪声的情况下检测突然的变化
Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise
论文作者
论文摘要
尽管有很多用于检测单变量时间序列中平均值变化的算法，但在存在自相关噪声或平均值在一个希望检测到的突然变化之间局部波动的实际应用中，几乎所有的都在挣扎。在这些情况下，默认实现通常基于对变化和独立噪声之间恒定平均值的假设，可能会导致更改数量的大量过度估计。我们提出了一种原则性的方法来检测这种突然的变化，以通过AR（1）过程将局部波动建模为随机行走过程和自相关噪声。然后，我们通过根据此模型最大程度地减少惩罚成本来估算更改点的数量和位置。我们开发了一种新颖有效的动态编程算法，即DeCafs，可以解决这个最小化问题。尽管各个细分市场的依赖性面临额外的挑战，但由于自相关的噪声，这使现有算法无法应用。理论和经验结果表明，与现有方法相比，我们的方法在检测突然变化方面具有更大的能力。我们将我们的方法应用于细菌中基因表达水平。
Whilst 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 minimising a penalised cost based on this model. We develop a novel and efficient dynamic programming algorithm, DeCAFS, that can solve this minimisation 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.
