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Causal Discovery from Conditionally Stationary Time Series
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Proposes SDCI, a VAE-style causal discovery method for conditionally stationary time series with latent discrete states, proving partial identifiability of state-dependent conditional summary graphs.
Problem
Causal discovery from nonstationary time series where dynamics change with discrete latent states that may depend on observations or past events (states determined/recurrent), without knowing the number of states.
Approach
Introduces conditional summary graphs (one graph per state value) and a GNN-based generative model with discrete edge-type labels conditioned on latent states, with identifiability established under unique-indexing and function-type assumptions, and inference via variational Gumbel-softmax.
Key results
- On DynGen GRN structure, SDCI-Determined reaches AUROC 0.936 and F1 0.347, versus Rhino AUROC 0.933 / F1 0.081 and ACD F1 0.187.
- On NBA trajectories, ACD and SDCI achieve better long-term forecasts than VRNN and NRI-NPM, with SDCI giving a slight advantage over ACD.
- Fixed-graph spring experiments: SDCI achieves perfect structure estimation in both determined and recurrent state settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SDCI in the determined-state setting | SDCI · Gene Regulatory Networks | AUROC: 0.933 -> 0.936 | Helped |
| Use SDCI in the determined-state setting | SDCI · Gene Regulatory Networks | F1 score: 0.187 -> 0.347 | Helped |
| Use SDCI in the recurrent-state setting | SDCI · Gene Regulatory Networks | F1 score: 0.187 -> 0.276 | Helped |
| Use SDCI with observed states | SDCI · Gene Regulatory Networks | F1 score: 0.187 -> 0.182 | No clear effect |
Surprising findings
- Recurrent-state SDCI underperforms determined-state SDCI on GRN data, attributed to exponential cost of exact inference.
- N-GC achieves strong results on variable-graph springs data, surpassing ACD despite its simplicity, while scoring only AUROC 0.556 on GRN data.
Limitations
- Consistency of SDCI and variational objective under variable structures is an open challenge, as noted by the authors.
- Exact inference in the recurrent state case is exponentially costly, limiting scalability with many variables.
- State distribution identifiability is not established; partial identifiability only.
Experimental setup
Datasets: Springs and magnets simulated particle data (adapted from NRI spring data) DynGen gene expression simulations NBA player movement tracking data
Benchmarks: Springs and magnets particle data DynGen gene regulatory networks NBA player trajectories
Metrics: F1 score AUROC forecast MSE reconstruction MSE
Baselines: ACD Rhino Neural Granger Causality R-PCMCI VRNN NRI-NPM
Builds on: Amortized Causal Discovery TiMINo Markov switching models Neural relational inference
Closest papers by meaning
- Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems (NeurIPS 2024 · similarity 0.88)
- On the Identification of Temporal Causal Representation with Instantaneous Dependence (ICLR 2025 · similarity 0.88)
- CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery (ICLR 2024 · similarity 0.88)
- UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems (NeurIPS 2025 · similarity 0.88)
- Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes (ICLR 2025 · similarity 0.87)
- Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises (NeurIPS 2025 · similarity 0.87)
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