Due to their capacity to condense the spatiotemporal structure of a data set in a format amenable for human interpretation, forecasting, and anomaly detection, causality graphs are routinely estimated in social sciences, natural sciences, and engineering. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models, which constitutes an alternative to the well-known but usually intractable Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Despite using data in a sequential fashion, both algorithms are shown to asymptotically attain the same average performance as a batch estimator with all data available at once. Moreover, their constant complexity per update renders these algorithms appealing for big-data scenarios. Theoretical and experimental performance analysis support the merits of the proposed algorithms. Remarkably, no probabilistic models or stationarity assumptions need to be introduced, which endows the developed algorithms with considerable generality

中文翻译：

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向量自回归时间序列的在线拓扑识别

由于它们能够以适合人类解释、预测和异常检测的格式压缩数据集的时空结构，因果关系图在社会科学、自然科学和工程中经常被估计。在数学上形式化因果关系的一种流行方法是基于向量自回归 (VAR) 模型，它构成了众所周知但通常难以处理的格兰杰因果关系的替代方法。依靠这种 VAR 因果关系概念，本文开发了两种具有互补优势的算法，以在线方式跟踪时变因果关系图。尽管以顺序方式使用数据，但两种算法都显示出与所有数据同时可用的批量估计器渐近地获得相同的平均性能。而且，它们每次更新的恒定复杂性使这些算法对大数据场景具有吸引力。理论和实验性能分析支持所提出算法的优点。值得注意的是，不需要引入概率模型或平稳性假设，这使得开发的算法具有相当大的通用性