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Multiple Change Point Detection in Low Rank and Sparse High Dimensional Vector Autoregressive Models
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.2993145
Peiliang Bai , Abolfazl Safikhani , George Michailidis

Identifying change/break points in multivariate time series represents a canonical problem in signal processing, due to numerous applications related to anomaly detection problems. The underlying detection methodology heavily depends on the nature of the mechanism determining the temporal dynamics of the data. Vector auto-regressive models (VAR) constitute a widely used model in diverse areas, including surveillance applications, economics/finance and neuroscience. In this work, we consider piece-wise stationary VAR models exhibiting break points between the corresponding stationary segments, wherein the transition matrices that govern the model's temporal evolution are decomposed into a common low-rank component and time evolving sparse ones. Further, we assume that the number of available time points are smaller than the number of model parameters and hence we are operating in a high-dimensional regime. We develop a three-step strategy that accurately detects the number of change points together with their location and subsequently estimates the model parameters in each stationary segment. The effectiveness of the proposed procedure is illustrated on both synthetic and real data sets.

中文翻译:

低秩稀疏高维向量自回归模型中的多变化点检测

由于与异常检测问题相关的众多应用,识别多元时间序列中的变化/断点代表了信号处理中的一个典型问题。潜在的检测方法在很大程度上取决于确定数据时间动态的机制的性质。矢量自回归模型 (VAR) 构成了在不同领域中广泛使用的模型,包括监控应用、经济/金融和神经科学。在这项工作中,我们考虑分段平稳 VAR 模型在相应的平稳段之间表现出断点,其中控制模型时间演化的转移矩阵被分解为常见的低秩分量和时间演化稀疏矩阵。更多,我们假设可用时间点的数量小于模型参数的数量,因此我们在高维状态下运行。我们开发了一个三步策略,可以准确地检测变化点的数量及其位置,然后估计每个静止段中的模型参数。在合成数据集和真实数据集上都说明了所提出程序的有效性。
更新日期:2020-01-01
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