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GCAD: Anomaly Detection in Multivariate Time Series from the Perspective of Granger Causality
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Proposes GCAD, which detects multivariate time series anomalies by computing dynamic Granger causality graphs from gradients of a Mixer-based predictor and scoring deviations from a normal causal pattern.
Problem
Existing graph-based multivariate time series anomaly detectors learn similarity between sequence embeddings via prediction or reconstruction and lack interpretable causal dependencies that change under anomalies.
Approach
Quantify nonlinear Granger causality as the time-lag integral of absolute gradients of channel-separated prediction errors with respect to inputs in a deep MLP-Mixer predictor, sparsify by subtracting the transpose to remove symmetric similarity, and score anomalies by deviation from a mean normal causal graph plus diagonal temporal deviation.
Key results
- GCAD reports AUROC 0.8690 and AUPRC 0.7758 on SWaT, versus best baseline GDN at 0.8493 AUROC.
- On SMD GCAD achieves AUROC 0.9533 and AUPRC 0.7502, versus best baseline USAD at 0.9274 AUROC and GDN at 0.5655 AUPRC.
- On MSL GCAD achieves AUPRC 0.3679 versus 0.0654 for the best baseline MEMTO; ablation removing Granger causality drops SWaT AUROC from 0.8690 to 0.8478.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add causality graph sparsification (ablation) | GCAD · SWaT | ROC AUC: 0.8559 -> 0.8690 | Helped |
| add causality graph sparsification (ablation) | GCAD · SWaT | PR AUC: 0.7676 -> 0.7758 | Helped |
| add causality graph sparsification (ablation) | GCAD · SMD | ROC AUC: 0.9531 -> 0.9533 | Helped |
| add causality graph sparsification (ablation) | GCAD · SMD | PR AUC: 0.6915 -> 0.7502 | Helped |
| use Granger causality for anomaly detection (ablation) | GCAD · SWaT | ROC AUC: 0.8478 -> 0.8690 | Helped |
| use Granger causality for anomaly detection (ablation) | GCAD · SWaT | PR AUC: 0.7513 -> 0.7758 | Helped |
| use Granger causality for anomaly detection (ablation) | GCAD · SMD | ROC AUC: 0.9405 -> 0.9533 | Helped |
| use Granger causality for anomaly detection (ablation) | GCAD · SMD | PR AUC: 0.6424 -> 0.7502 | Helped |
| include time pattern deviation in the anomaly score (ablation) | GCAD · SWaT | ROC AUC: 0.8400 -> 0.8690 | Helped |
| include time pattern deviation in the anomaly score (ablation) | GCAD · SWaT | PR AUC: 0.7558 -> 0.7758 | Helped |
| include time pattern deviation in the anomaly score (ablation) | GCAD · SMD | ROC AUC: 0.9498 -> 0.9533 | Helped |
| include time pattern deviation in the anomaly score (ablation) | GCAD · SMD | PR AUC: 0.6748 -> 0.7502 | Helped |
Surprising findings
- GANF achieves the best PRC on SMAP (0.5259), beating GCAD (0.4555), which the authors attribute to distribution shift handling.
- Anomaly Transformer performs near or below chance on several datasets (e.g., SMD AUROC 0.1765).
Limitations
- Captures only binary causal pairs between variables and cannot model multivariable interactions.
- Sparsification threshold and maximum time lag require tuning; performance depends on these hyperparameters.
- Reported PRC values on small, imbalanced datasets (MSL, SMAP) are low for most methods including GCAD.
Experimental setup
Datasets: SWaT SMD MSL SMAP PSM
Benchmarks: SWaT SMD MSL SMAP PSM
Metrics: AUROC AUPRC
Baselines: DAGMM USAD GDN Anomaly Transformer GANF MEMTO
Builds on: Granger causality MLP-Mixer GDN nonlinear Granger causality definition
Closest papers by meaning
- Structured Temporal Causality for Interpretable Multivariate Time Series Anomaly Detection (NeurIPS 2025 · similarity 0.90)
- Multi-Scale Dynamic Graph Learning for Time Series Anomaly Detection (Student Abstract) (AAAI 2024 · similarity 0.88)
- Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data (NeurIPS 2025 · similarity 0.88)
- Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection (ICML 2025 · similarity 0.88)
- CUTS+: High-Dimensional Causal Discovery from Irregular Time-Series (AAAI 2024 · similarity 0.87)
- Towards the Disappearing Truth: Fine-Grained Joint Causal Influences Learning with Hidden Variable-Driven Causal Hypergraphs in Time Series (AAAI 2024 · similarity 0.87)
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