Research map / Probabilistic and scientific modeling / Causal discovery
CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery
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Introduces CausalTime, a pipeline that fits a causally disentangled LSTM with normalizing-flow noise to real time-series, extracts a hypothesized causal graph (DeepSHAP or prior geography), and generates realistic time-series with ground-truth causal graphs, then benchmarks nine TSCD algorithms on AQI, Traffic and Medical subsets.
Problem
Existing time-series causal discovery benchmarks are either unrealistic synthetic data (VAR, Lorenz-96) or real data without ground-truth causal graphs, so algorithm performance on real data cannot be properly evaluated.
Approach
Fit a causally disentangled neural network with normalizing-flow noise to real observations, extract a hypothesized causal graph via DeepSHAP or prior knowledge, then split the model into causal, residual and noise terms so that autoregressive generation from the fitted model yields realistic series whose ground-truth graph is known.
Key results
- Full model achieves discriminative scores of 0.054 (AQI), 0.039 (Traffic), and 0.017 (Medical), near chance, and lowest MMD on AQI and Traffic.
- CUTS+ and LCCM perform best on CausalTime, but most TSCD algorithms fail to reach AUROC above 0.9; CUTS+ reaches AUROC 0.8928 on AQI and 0.8202 on Medical.
- Several algorithms yield AUROC below 0.5 on some subsets, indicating inverted classifications.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace normalizing-flow noise with additive Gaussian noise (ablation) | CausalTime · AQI | discriminative score: 0.054 { $\pm$ 0.025} -> 0.488 { $\pm$ 0.001} | Hurt |
| replace normalizing-flow noise with additive Gaussian noise (ablation) | CausalTime · Traffic | discriminative score: 0.039 { $\pm$ 0.020} -> 0.499 { $\pm$ 0.000} | Hurt |
| replace normalizing-flow noise with additive Gaussian noise (ablation) | CausalTime · Medical | discriminative score: 0.017 { $\pm$ 0.027} -> 0.445 { $\pm$ 0.003} | Hurt |
| remove the noise term (ablation) | CausalTime · AQI | discriminative score: 0.054 { $\pm$ 0.025} -> 0.361 { $\pm$ 0.008} | Hurt |
| remove the noise term (ablation) | CausalTime · Traffic | discriminative score: 0.039 { $\pm$ 0.020} -> 0.391 { $\pm$ 0.006} | Hurt |
| remove the noise term (ablation) | CausalTime · Medical | MMD: 0.461 { $\pm$ 0.033} -> 0.453 { $\pm$ 0.029} | No clear effect |
| remove the residual term during NAR fitting (ablation) | CausalTime · Traffic | MMD: 0.215 { $\pm$ 0.013} -> 0.858 { $\pm$ 0.020} | Hurt |
| remove the residual term during data generation (ablation) | CausalTime · Traffic | MMD: 0.215 { $\pm$ 0.013} -> 0.657 { $\pm$ 0.016} | Hurt |
| use scheduled sampling (ablation) | CausalTime prediction model · AQI, Traffic, and Medical, autoregressive steps n=2, 5, 10, 20 | prediction MSE | Mixed |
| use LSTM with a shared decoder instead of other CDNN implementations (ablation) | CausalTime fitting · AQI | MSE: 0.0017± 0.0002 -> 0.0014 $\pm$ 0.0002 | Helped |
Surprising findings
- Some TSCD algorithms obtain AUROC below 0.5 on CausalTime, meaning inverted classifications.
- Scores on CausalTime are significantly lower than on synthetic VAR and Lorenz-96 benchmarks, where some methods approach 1.
Limitations
- The extracted hypothesized causal graph is not guaranteed to be the true causal graph; the pipeline is not a causal discovery method.
- Assumes no instantaneous effects, causal sufficiency, stationarity and a bounded maximum time lag, which may not hold in real data.
- Generated series are short (length 40) and rely on multiple-sample settings, requiring altered algorithm inputs.
Experimental setup
Datasets: AQI (Chinese air quality, Microsoft urban computing) Traffic (PeMS San Francisco Bay Area) MIMIC-IV medical subset
Benchmarks: CausalTime (AQI, Traffic, Medical)
Metrics: AUROC AUPRC discriminative score MMD cross-correlation score
Baselines: NGC eSRU SCGL TCDF CUTS CUTS+ PCMCI LCCM NGM
Builds on: Neural Granger Causality cMLP/cLSTM DeepSHAP normalizing flows scheduled sampling
Closest papers by meaning
- Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems (NeurIPS 2024 · similarity 0.90)
- CausalRivers - Scaling up benchmarking of causal discovery for real-world time-series (ICLR 2025 · similarity 0.89)
- CausalDynamics: A large‐scale benchmark for structural discovery of dynamical causal models (NeurIPS 2025 · similarity 0.89)
- CUTS+: High-Dimensional Causal Discovery from Irregular Time-Series (AAAI 2024 · similarity 0.89)
- Arrow: Accelerator for Time Series Causal Discovery with Time Weaving (ICML 2025 · similarity 0.89)
- Causal Discovery from Conditionally Stationary Time Series (ICML 2025 · similarity 0.88)
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