Research map / Probabilistic and scientific modeling / Causal discovery
Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises
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Proposes FANTOM, a Bayesian EM framework with conditional normalizing flows that jointly infers the number of regimes, their indices, and per-regime causal DAGs in multivariate time series with non-Gaussian or heteroscedastic noise, with identifiability proofs.
Problem
Causal structure learning from multivariate time series with multiple unknown regimes (non-stationarity), where noise is non-Gaussian or heteroscedastic, and the number of regimes, their boundaries, and their causal graphs are all unknown.
Approach
Combines a Bayesian Expectation Maximization procedure (maximizing an ELBO) with conditional spline normalizing flows for heteroscedastic/non-Gaussian noise, a time-varying softmax prior on regime membership, and Bayesian structure learning over per-regime DAGs; initialization with more windows than regimes that are merged during E-steps.
Key results
- On synthetic heteroscedastic data with d=10, K=3, FANTOM reaches 93.3% F1 on instantaneous links and 96.5% F1 on summary graphs, with 97.1% regime accuracy.
- On homoscedastic non-Gaussian data, FANTOM attains 99.4% regime accuracy and 99.5% instantaneous-link F1, while Rhino (given true regimes) remains better on lagged links (95.2% vs 89.1% F1).
- On Wind Tunnel data FANTOM achieves 38.5% F1 and 99.9% regime accuracy, and on EEG it reports 82.7% average regime detection accuracy across 10 patients.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FANTOM rather than Rhino | Synthetic MTS, homoscedastic non-Gaussian, instantaneous links · d=10, K=3 | F1: 96.8 -> 99.5 | Helped |
| Use FANTOM rather than Rhino | Synthetic MTS, homoscedastic non-Gaussian, lagged links · d=10, K=3 | F1: 95.2 -> 89.1 | Hurt |
| Use FANTOM rather than CASTOR | Synthetic MTS, homoscedastic non-Gaussian · d=10, K=3 | Regime accuracy: 51.6 -> 99.4 | Helped |
| Use FANTOM rather than PCMCI+ | Synthetic MTS, heteroscedastic, instantaneous links · d=10, K=3 | F1: 11.1 -> 93.3 | Helped |
| Use FANTOM rather than Rhino | Synthetic MTS, heteroscedastic, lagged links · d=10, K=3 | F1: 64.7 -> 90.9 | Helped |
| Use FANTOM rather than CD-NOD | Synthetic MTS, heteroscedastic summary graph · d=10, K=3 | F1: 6.15 -> 96.5 | Helped |
| Use FANTOM rather than CD-NOD | Synthetic MTS, homoscedastic non-Gaussian summary graph · d=10, K=3 | F1: 31.8 -> 95.6 | Helped |
| Use FANTOM rather than Rhino | Wind Tunnel · summary causal graph | F1: 32.0 -> 38.5 | Helped |
| Use FANTOM rather than CASTOR | Wind Tunnel · regime detection | Regime accuracy: 49.9 -> 99.9 | Helped |
| Use FANTOM for unsupervised regime detection | Temple University Hospital EEG Seizure Corpus · 10 patients | Regime accuracy | Helped |
Surprising findings
- Rhino, given ground-truth regime partitions, slightly outperforms FANTOM on time-lagged links under homoscedastic non-Gaussian noise.
- Two-step approaches (change point detection then causal discovery) fail to detect regime shifts driven by changes in causal mechanisms, according to the authors.
Limitations
- Performance deteriorates when a regime has very few samples or the sampling rate is very low.
- Requires suitable initial segmentation; over-pruning from too-large initial windows drops regimes below ground truth.
- Learned graphs risk spurious causality and should be used as decision support.
Experimental setup
Datasets: synthetic non-stationary MTS Wind Tunnel (Gamella et al.) TUH EEG Seizure Corpus (TUSZ)
Benchmarks: synthetic non-stationary MTS (d=5-40, K in {2,3}) Wind Tunnel TUSZ EEG epilepsy detection
Metrics: SHD F1 NHD Ratio NHD regime accuracy
Baselines: CASTOR CD-NOD RPCMCI Rhino PCMCI+ DYNOTEARS
Builds on: DYNOTEARS Rhino CASTOR CD-NOD RPCMCI
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