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Systems with Switching Causal Relations: A Meta-Causal Perspective

ICLR 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Interventional causal discovery · 0 citations (OpenAlex)

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Introduces meta-causal models (finite-state machines over typed causal graphs) to capture switching causal mechanisms, with a theoretical framework, an EM+LO-RANSAC method for counting mechanisms in the bivariate case, and a stress-fatigue dynamical example.

Problem

Causal relations in real systems can change qualitatively (new edges emerge, existing ones switch type or vanish) due to agent actions or tipping points, but classical SCM assume a constant causal graph and cannot describe these switching dynamics.

Approach

Generalize binary causal edges to typed edges via type encoders over a mediation process, group SCMs into meta-causal states (matrices of types), and model transitions between states as a finite-state machine (meta-causal model); infer the number of linear mechanisms in the bivariate case with EM embedded in LO-RANSAC and an Anderson-Darling test on Laplacian residuals.

Key results

• On synthetic bivariate data, the mechanism-count method is conservative (often makes no decision) but when it decides, the diagonal dominates: over 60% accuracy for k=4 with d in {0.0, 0.1} and above 80% for k != 4 at d=0.0.
• Empirical EM convergence needed far fewer restarts than the theoretical bound, e.g. 177 vs 14,859 resamples for k=4, d=0.2.
• In the stress-fatigue dynamical system, the same structural equations yield three meta-causal states, showing meta-causal states can emerge from inherent dynamics without external conditioning.

Measured effects reported in the paper

Surprising findings

• Empirical EM convergence is much more favorable than the theoretical resample bound, reducing required restarts by up to 83x.
• Intervening on the meta-causal state in the stress example is ill-defined because positive and negative reinforcement share the same structural equation.

Limitations

• Mechanism-count identification is conservative and only demonstrated in the bivariate linear case with Laplacian noise.
• No general algorithm yet for unsupervised full meta-causal state discovery on full causal graphs.
• Meta-causal models are abstract; mapping types back to structural equations is not general, and the controlling vs observational role remains open.

Experimental setup

Datasets: synthetic bivariate linear mechanisms with Laplacian noise

Benchmarks: synthetic bivariate mechanism-count recovery

Metrics: confusion matrix accuracy for number of mechanisms EM convergence rate mean absolute error of slope and intercept

Baselines: classical counterfactual analysis actual causality

Builds on: Structural Causal Models Markov Decision Processes invariant causal prediction LO-RANSAC

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