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Discovering Mixtures of Structural Causal Models from Time Series Data
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Proposes MCD, a variational inference (ELBO) framework that jointly infers multiple time-series SCMs and per-sample mixture memberships, with linear and nonlinear variants, and proves identifiability results.
Problem
Causal discovery from time series generated by a heterogeneous mixture of structural causal models, where the component SCM and the membership of each sample are both unknown.
Approach
Learn K SCMs (temporal adjacency matrices with Gumbel-Softmax-sampled Bernoulli edges plus structural equations) and per-sample categorical membership by maximizing an ELBO on the data likelihood; the nonlinear variant builds each component on Rhino with embeddings, and the paper gives mixture identifiability conditions.
Key results
- On Netsim-mixture, MCD-Nonlinear reaches AUROC 0.94 and F1 0.69, above the best baseline Rhino (0.84 / 0.62) and DYNOTEARS-s (0.85 AUROC).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MCD-Nonlinear instead of DYNOTEARS-s | causal discovery on Netsim-mixture · Netsim-mixture | AUROC: 0.85 -> 0.94 \pm 0.03 | Helped |
| Use MCD-Nonlinear instead of PCMCI+-s | causal discovery on Netsim-mixture · Netsim-mixture | F1: 0.67 -> 0.69 \pm 0.08 | Helped |
| Use MCD-Nonlinear instead of Rhino | causal discovery on DREAM3 · DREAM3 | AUROC: 0.57 \pm 0.01 -> 0.58 \pm 0.01 | Helped |
| Use MCD-Nonlinear instead of Rhino | causal discovery on DREAM3 · DREAM3 | F1: 0.08 \pm 0.01 -> 0.10 \pm 0.01 | Helped |
| Use a linear rather than nonlinear MCD variant | MCD on Netsim-mixture · Netsim-mixture | AUROC: 0.94 \pm 0.03 -> 0.73 \pm 0.02 | Hurt |
| Use a linear rather than nonlinear MCD variant | MCD on DREAM3 · DREAM3 | F1: 0.10 \pm 0.01 -> 0.00 \pm 0.00 | Hurt |
| Underspecify the number of mixture components (ablation) | MCD-Nonlinear · Nonlinear synthetic, D=10, K*=10 | clustering accuracy | Hurt |
| Overspecify the number of mixture components (K>K*) rather than set K=K* (ablation) | MCD-Nonlinear · Nonlinear synthetic, D=10, K*=10 | clustering accuracy | Helped |
Surprising findings
- MCD-Nonlinear performs better when the number of mixture components K is overspecified relative to the true K*, with extra components acting as buffers.
Limitations
- All methods, including MCD-Nonlinear, perform poorly on DREAM3 (AUROC about 0.58, F1 0.10), a high-dimensional dataset with few samples.
- Assumes causal sufficiency (no latent confounders) and stationarity; both are listed as future work.
- The identifiability condition for general SCMs is a sufficient condition that is hard to verify directly, and K must be specified in advance.
Experimental setup
Datasets: synthetic linear and nonlinear time series (Erdos-Renyi graphs) Netsim DREAM3 S&P 100 daily log-returns via yahoofinancials
Benchmarks: Netsim-mixture DREAM3 synthetic linear datasets synthetic nonlinear datasets S&P 100 (qualitative)
Metrics: orientation F1 AUROC clustering accuracy
Baselines: PCMCI+ DYNOTEARS VARLiNGAM Rhino
Builds on: Rhino DYNOTEARS VARLiNGAM PCMCI+
Closest papers by meaning
- Learning Mixtures of Unknown Causal Interventions (NeurIPS 2024 · similarity 0.91)
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- Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises (NeurIPS 2025 · similarity 0.90)
- Learning Causal Relations from Subsampled Time Series with Two Time-Slices (ICML 2024 · similarity 0.90)
- CausalDynamics: A large‐scale benchmark for structural discovery of dynamical causal models (NeurIPS 2025 · similarity 0.89)
- CausalRivers - Scaling up benchmarking of causal discovery for real-world time-series (ICLR 2025 · similarity 0.89)
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