Research map / Probabilistic and scientific modeling / Causal discovery
Multi-Granularity Causal Structure Learning
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Proposes MGCSL, a method that uses a sparse autoencoder to learn macro-variables and MLPs with a simplified acyclicity constraint to discover multi-granularity causal DAGs.
Problem
Causal structure learning from observational data usually treats only individual micro-variables, missing collective macro-variable interactions and scaling poorly to high-dimensional data.
Approach
Combine a sparse autoencoder that abstracts micro-variables into macro-variables with MLP-based causal edge learning over both levels, using a cheaper Schur-decomposition-based acyclicity constraint in place of the matrix exponential.
Key results
- On ER graphs with 20 variables (additive GP), F1 is 78.60% vs 78.34% for NOTEARS-MLP, with runtime 9.57s vs 45.35s.
- On Sachs, precision is 100% and F1 46.15% with SHD 14, the best among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the proposed simplified acyclicity constraint to NOTEARS-MLP (ablation) | NOTEARS-MLP+ · Nonlinear models with additive Gaussian processes, d=50, 100, 200 | F1 score | Hurt |
| Add the proposed simplified acyclicity constraint to NOTEARS-MLP (ablation) | NOTEARS-MLP+ · Nonlinear models with additive Gaussian processes, d=50, 100, 200 | Precision | Helped |
| Add the proposed simplified acyclicity constraint to NOTEARS-MLP (ablation) | NOTEARS-MLP+ · Nonlinear models with additive Gaussian processes, d=50, 100, 200 | SHD | No clear effect |
| Add the proposed simplified acyclicity constraint to NOTEARS-MLP (ablation) | NOTEARS-MLP+ · Nonlinear models with additive Gaussian processes, d=50, 100, 200 | Runtime | Helped |
| Increase α₂ (ablation) | Multi-Granularity Causal Structure Learning · Parameter sensitivity study | Precision | Helped |
| Increase α₂ (ablation) | Multi-Granularity Causal Structure Learning · Parameter sensitivity study | Running time | Helped |
| Set α₂ too large (ablation) | Multi-Granularity Causal Structure Learning · Parameter sensitivity study | Graph sparsity | Hurt |
| Use Multi-Granularity Causal Structure Learning instead of NOTEARS-MLP | Causal structure learning on ER and Scale-Free graphs · Additive Gaussian processes, d=20 and d=50 | F1 score | Helped |
| Use Multi-Granularity Causal Structure Learning instead of NOTEARS-MLP | Causal structure learning on ER and Scale-Free graphs · Additive Gaussian processes, d=100 | F1 score | Mixed |
| Use Multi-Granularity Causal Structure Learning instead of NOTEARS-MLP | Causal structure learning on Sachs · Sachs protein signaling dataset | F1 score | Helped |
Surprising findings
- The proposed acyclicity constraint prunes correct edges, lowering F1 in the ablation even though SHD stays comparable to NOTEARS-MLP.
- On Sachs the method's recall is only 30%, so its gains come mainly from precision.
Limitations
- Modest F1 gains over NOTEARS-MLP on synthetic graphs with high variance
- Post-processing thresholding and weight elimination is heuristic
- fMRI case study is qualitative since anatomical ground truth contains cycles
Experimental setup
Datasets: synthetic ER/SF graphs with Gaussian process models Sachs protein signaling fMRI Hippocampus
Benchmarks: synthetic ER and SF graphs (d=20,50,100) Sachs fMRI Hippocampus case study
Metrics: Precision Recall F1 SHD Runtime
Baselines: PC GES DAG-GNN GAE GraN-DAG NOTEARS-MLP
Builds on: NOTEARS NOTEARS-MLP sparse autoencoder
Closest papers by meaning
- Emergence-Inspired Multi-Granularity Causal Learning (AAAI 2025 · similarity 0.90)
- Coarsening Linear Non-Gaussian Causal Models with Cycles (NeurIPS 2026 · similarity 0.88)
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.87)
- Local Identifying Causal Relations in the Presence of Latent Variables (ICML 2025 · similarity 0.87)
- Local Causal Structure Learning in the Presence of Latent Variables (ICML 2024 · similarity 0.86)
- CausalTab: Pretraining Across Causal Environments for Tabular Causal Discovery (NeurIPS 2026 · similarity 0.86)
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