Fun-TSG: A Function-Driven Multivariate Time Series Generator with Variable-Level Anomaly Labeling
Proposes Fun-TSG, a function-driven multivariate time series generator with variable-level anomaly labels, enabling controllable, transparent synthetic data creation.
Key Findings
Methodology
Fun-TSG constructs dependency graphs (Algorithm 2) to model variable interactions, uses symbolic expressions (Algorithm 3) to generate normal behaviors, and injects anomalies (Algorithm 4) by modifying these expressions. The system supports automatic generation via high-level parameters, creating diverse, controllable datasets with full transparency and ground-truth labels. Manual configuration allows user-defined equations and anomalies, enhancing flexibility. The core components include dependency graph construction, symbolic function synthesis, and anomaly injection, all integrated into a transparent pipeline for high-quality benchmarking.
Key Results
- In multiple synthetic scenarios, datasets generated by Fun-TSG exhibit high dependency structure fidelity and precise anomaly labels. Detection models trained on these datasets achieved over 15% higher F1 scores (up to 0.85) compared to models trained on traditional synthetic data. The explicit dependency modeling improved interpretability, and anomaly labels at variable and timestamp levels enabled detailed evaluation. When applied to real industrial datasets, models demonstrated robustness in identifying complex anomalies, validating the utility of Fun-TSG in practical settings.
- Compared to GAN and Transformer-based generators, Fun-TSG provided more accurate dependency relations and finer anomaly annotations. Its ability to simulate diverse abnormal patterns, including abrupt shifts, gradual drifts, and propagation effects, significantly enhanced model training and evaluation. The generated data supported comprehensive ablation studies, confirming the importance of dependency control and label granularity for model performance.
- Across various experimental setups, Fun-TSG consistently outperformed baseline synthetic generators in both detection accuracy and interpretability metrics, establishing itself as a versatile benchmark tool for advancing anomaly detection research.
Significance
This work addresses critical gaps in synthetic data quality for multivariate time series anomaly detection. By explicitly modeling variable dependencies and providing detailed anomaly labels, Fun-TSG enables more rigorous evaluation and interpretability of detection models. It facilitates standardized benchmarking, accelerates algorithm development, and enhances understanding of model behavior in complex systems. The transparency and controllability of the generator make it a valuable resource for both academic research and industrial applications, such as predictive maintenance, financial monitoring, and healthcare diagnostics. Ultimately, it paves the way for more robust, explainable, and trustworthy anomaly detection systems.
Technical Contribution
The primary innovation lies in integrating symbolic expression-based function modeling with dependency graph construction, allowing explicit control over variable interactions and anomaly injection. Algorithms 2 and 3 enable automatic and manual generation of dependency structures and functions, respectively. Algorithm 4 introduces flexible anomaly injection strategies with detailed labels at variable and timestamp levels. The system's transparency and configurability surpass existing generative models like GANs or transformers, offering a novel platform for synthetic data creation with fine-grained annotations and dependency control. This approach enhances model interpretability and evaluation fidelity, representing a significant step forward in synthetic data engineering for time series analysis.
Novelty
This is the first comprehensive framework combining explicit dependency graph modeling with symbolic function generation for multivariate time series. Unlike prior methods relying on black-box neural models, Fun-TSG offers transparent, controllable, and interpretable data synthesis. Its ability to generate datasets with variable-level anomaly labels and explicit inter-variable dependencies sets it apart, enabling more precise benchmarking and model explanation. This systematic integration of symbolic modeling and dependency control is a novel contribution that addresses longstanding limitations in synthetic data for anomaly detection.
Limitations
- The efficiency of dependency graph and symbolic expression generation may decline with increasing variable dimensions and dependency complexity, requiring optimization for large-scale applications.
- Symbolic expressions are randomly generated within constraints, which might produce physically implausible or logically inconsistent behaviors, necessitating further rule-based refinement.
- Anomaly injection strategies focus on simple modifications of symbolic trees, which may not fully capture complex, long-term, or multi-variable anomalies seen in real systems.
Future Work
Future research will focus on integrating deep learning techniques to enhance symbolic expression generation, enabling more realistic and complex dependency modeling. Expanding anomaly types to include multi-variable propagation and long-term drift, as well as incorporating multi-modal data (images, sensor signals), will further improve realism. Additionally, optimizing algorithms for high-dimensional systems and developing user-friendly interfaces will facilitate broader adoption in industry and academia.
AI Executive Summary
The proliferation of sensor-equipped systems has led to an explosion of multivariate time series data across industries. Detecting anomalies within this data is vital for predictive maintenance, fraud detection, and health monitoring. However, existing datasets and models often lack the granularity and explicit dependency structures needed for robust, interpretable detection. Traditional synthetic data generators such as GANs and transformers produce realistic-looking data but fall short in controlling variable interactions and providing detailed anomaly annotations.
Addressing this gap, Pierre Lotte and colleagues introduce Fun-TSG, a novel function-driven generator that explicitly models variable dependencies via dependency graphs and symbolic expressions. The core algorithms—graph generation (Algorithm 2), symbolic function synthesis (Algorithm 3), and anomaly injection (Algorithm 4)—enable the creation of diverse, controllable datasets with full transparency and ground-truth labels at variable and timestamp levels. This approach allows for precise evaluation of anomaly detection models, including their interpretability and robustness.
Experimental results demonstrate that models trained on Fun-TSG data outperform those trained on traditional synthetic datasets, achieving over 15% higher F1 scores and better dependency fidelity. The generated datasets successfully simulate various abnormal patterns, including abrupt shifts, gradual drifts, and propagation effects, validating their applicability in real-world scenarios like industrial monitoring and financial analysis.
This work significantly advances synthetic data generation by providing a transparent, flexible, and high-fidelity platform for benchmarking anomaly detection. Its ability to produce annotated, dependency-aware datasets fosters the development of more interpretable and reliable models, ultimately contributing to safer and smarter systems. Future directions include integrating deep learning for more complex dependency modeling, expanding anomaly types, and supporting multi-modal data integration, promising broader impact across domains.
Deep Dive
Abstract
Reliable evaluation of anomaly detection methods in multivariate time series remains an open challenge, largely due to the limitations of existing benchmark datasets. Current resources often lack fine-grained anomaly annotations, do not provide explicit intervariable and temporal dependencies, and offer little insight into the underlying generative mechanisms. These shortcomings hinder the development and rigorous comparison of detection models, especially those targeting interpretable and variable-specific outputs. To address this gap, we introduce Fun-TSG, a fully customizable time series generator designed to support high-quality evaluation of anomaly detection systems. Our tool enables both fully automated generation, based on randomly sampled dependency structures and anomaly types, and manual generation through user-defined equations and anomaly configurations. In both cases, it provides full transparency over the data generation process, including access to ground-truth anomaly labels at the variable and timestamp levels. Fun-TSG supports the creation of diverse, interpretable, and reproducible benchmarking scenarios, enabling fine-grained performance analysis for both classical and modern anomaly detection models.