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Coarsening Linear Non-Gaussian Causal Models with Cycles

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Constraint-based structure learning with latents · 0 citations (OpenAlex)

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Shows that in linear non-Gaussian cyclic SCMs the condensation (SCC-cluster DAG) is identifiable from observational data via ICA-LiNG-D plus Tarjan's algorithm, with cubic-time recovery and sample-complexity bounds.

Problem

Causal abstraction via DAG coarsening assumes acyclicity at both the high- and low-dimensional levels, excluding cyclic models; observational identification of cyclic linear non-Gaussian SCMs yields only a distributional equivalence class with exponential enumeration cost.

Approach

Extends DAG coarsenings to cyclic graphs, showing the SCC partition is the finest valid DAG-coarsening (the structural floor), and that its condensation is invariant across the LiNG equivalence class (differing only by cycle reversals), so it can be recovered by one ICA admissible permutation plus Tarjan's algorithm.

Key results

• Cluster-DAG F1 converges to 1 with sample size in both stable and unstable regimes on d=10 synthetic cyclic SCMs, while variable-level F1 saturates below 1 in the unstable regime.
• On the scalability sweep (d up to 100), the proposed method saturates cluster-DAG F1 at n>=10^4 while the disjointCycles baseline plateaus below 0.3 for d in {50,100}; fit time ~10 s vs 10^4 s for baseline.
• Threshold sensitivity shows a safe band roughly tau in [0.1, 0.5] at n>=5000 where ARI=1 and F1=1.

Surprising findings

• The disjoint-cycles baseline performs poorly even on a strictly disjoint-cycle micro experiment (median ARI about 0.13 at n=10^5), attributed to low power of its third-moment tests.
• Empirical log-log slopes of error decay (-4.0 for Hamming distance, -2.9 for exact recovery) are steeper than the -2 predicted by the sample-complexity bound.

Limitations

• Requires linear non-Gaussian noise, no latent confounders, and at most one Gaussian noise component.
• Hard single-variable interventions inside SCCs are excluded; the interventional extension is not explored empirically.
• Sample complexity bound depends on knowledge of beta_min; the threshold choice tau=beta_min/2 requires a priori information.

Experimental setup

Datasets: synthetic linear non-Gaussian cyclic SCMs

Benchmarks: synthetic linear non-Gaussian cyclic SCMs (d=10 main grid; d in {20,50,100} scalability sweep)

Metrics: adjusted Rand index cluster-DAG F1 variable-level F1 fit time

Baselines: disjointCycles first-stable filter (ICA-LiNG-D)

Builds on: LiNGAM for cyclic models (ICA-LiNG-D) coarsening of DAGs (C-DAG) FastICA Tarjan's algorithm disjoint-cycles identification

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