The detection of anomalies in multivariate time series data is crucial for various practical applications, including smart power grids, traffic flow forecasting, and industrial process control. However, real-world time series data is usually not well-structured, posting significant challenges to existing approaches: (1) The existence of missing values in multivariate time series data along variable and time dimensions hinders the effective modeling of interwoven spatial and temporal dependencies, resulting in important patterns being overlooked during model training; (2) Anomaly scoring with irregularly-sampled observations is less explored, making it difficult to use existing detectors for multivariate series without fully-observed values. In this work, we introduce a novel framework called GST-Pro, which utilizes a graph spatiotemporal process and anomaly scorer to tackle the aforementioned challenges in detecting anomalies on irregularly-sampled multivariate time series. Our approach comprises two main components. First, we propose a graph spatiotemporal process based on neural controlled differential equations. This process enables effective modeling of multivariate time series from both spatial and temporal perspectives, even when the data contains missing values. Second, we present a novel distribution-based anomaly scoring mechanism that alleviates the reliance on complete uniform observations. By analyzing the predictions of the graph spatiotemporal process, our approach allows anomalies to be easily detected. Our experimental results show that the GST-Pro method can effectively detect anomalies in time series data and outperforms state-of-the-art methods, regardless of whether there are missing values present in the data. Our code is available: https://github.com/huankoh/GST-Pro.

翻译：多变量时间序列数据中的异常检测对于智能电网、交通流量预测和工业过程控制等实际应用至关重要。然而，现实世界中的时间序列数据通常结构不完整，给现有方法带来了巨大挑战：(1) 多变量时间序列数据在变量和时间维度上存在缺失值，阻碍了空间和时间依赖关系的有效建模，导致模型训练过程中重要模式被忽略；(2) 基于不规则采样观测值的异常评分方法研究较少，使得现有检测器难以用于缺少完整观测值的多变量序列。本文提出了一种名为GST-Pro的新型框架，利用图时空过程和异常评分器来解决在不规则采样多变量时间序列中检测异常所面临的上述挑战。该方法包含两个主要组成部分。首先，我们基于神经受控微分方程提出了一种图时空过程。该过程能够从空间和时间两个角度有效建模多变量时间序列，即使数据包含缺失值。其次，我们提出了一种新颖的基于分布的异常评分机制，减轻了对完整均匀观测值的依赖。通过分析图时空过程的预测结果，我们的方法能够轻松检测异常。实验结果表明，无论数据中是否存在缺失值，GST-Pro方法都能有效检测时间序列数据中的异常，并优于现有最优方法。我们的代码已公开：https://github.com/huankoh/GST-Pro。