Graph-Augmented LSTM for Forecasting Sparse Anomalies in Graph-Structured Time Series

Anomaly detection in time series data is a well-studied problem due to its importance in detecting faults, intrusions, and unusual events in critical systems [1, 3]. Extensive surveys have reviewed methods for general anomaly detection [1], outlier analysis [3], and specifically for temporal data [4]. Despite this progress, accurately identifying anomalies in time series remains challenging [14]. A key difficulty is that anomalies are often sparse--comprising only a tiny fraction of observations [2]. This extreme class imbalance makes it hard for models to recognize anomalies without producing many false alarms [6]. One strategy to detect anomalies is to forecast future behavior and flag deviations between predictions and actual values [15, 16]. Classical forecasting models, such as ARIMA [12] and exponential smoothing, as well as decomposition-based methods like Prophet [13], have been applied to model normal time series patterns and identify outliers when residuals exceed a threshold. Numerous other approaches leverage deep generative models (e.g., variational autoencoders [17], GANs [18]) or attention mechanisms [19] to improve multivariate time series anomaly detection. However, most prior methods treat multivariate time series as an unstructured collection of variables, not accounting for known relationships among them.