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Emergence-Inspired Multi-Granularity Causal Learning
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Proposes EMCausal, an emergence-inspired multi-granularity causal discovery method that aggregates micro variables into macro representations via a progressive mapping encoder and enforces a micro-macro consistency constraint.
Problem
Causal discovery algorithms focus on micro-level variables and miss or distort causal effects of macro systems composed of micro variables, since those effects are dispersed across micro-level interactions.
Approach
A Progressive Mapping Encoder with Gumbel-Softmax reweighting aggregates micro variables into macro representations, which jointly with micro variables reconstruct the data; a two-stage optimization adds an acyclicity constraint on the combined micro-macro adjacency so macro-level structure stays consistent with micro-level structure.
Key results
- On synthetic Erdos-Renyi graphs with 20 variables, EMCausal reaches 76.69% F1 and SHD 18.5 versus 42.96% F1 for MgCSL and 47.03% for DAG-GNN.
- On the Sachs dataset, EMCausal achieves the highest recall (41.18%) and F1 (43.75%) with SHD 11, tied with PC and GES on SHD.
- Causal consistency experiments show EMCausal keeps F1 near 80% at 10 variables versus 38.15% for MgCSL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EMCausal instead of MgCSL | Causal discovery · Nonlinear Erdős-Rényi, d=20 | F1 (%): 42.96±7.01 -> 76.69±8.82 | Helped |
| Use EMCausal instead of PC | Causal discovery · Nonlinear Scale-Free, d=20 | F1 (%): 48.70±8.57 -> 73.46±8.21 | Helped |
| Use EMCausal instead of GES | Causal discovery · Nonlinear Erdős-Rényi, d=40 | SHD: 160.00±12.68 -> 97.80±29.69 | Helped |
| Use EMCausal instead of GES | Causal discovery · Nonlinear Scale-Free, d=40 | SHD: 109.70±14.80 -> 111.67±37.28 | Hurt |
| Use EMCausal instead of PC | Causal discovery · Sachs dataset | F1 (%): 38.71 -> 43.75 | Helped |
| Use EMCausal instead of PC | Causal discovery · Sachs dataset | SHD: 11 -> 11 | No clear effect |
Surprising findings
- Score-based baselines such as GraN-DAG and DAG-GNN attain higher precision but much lower recall, so EMCausal trades a slight precision drop for substantially higher recall.
Limitations
- Gains in precision are slight or absent relative to some score-based baselines, which have higher precision.
- Macro-level results are evaluated mainly on synthetic data with a fixed number of macro variables (q=4) and fixed edge density.
Experimental setup
Datasets: synthetic multi-granularity data (Erdos-Renyi and scale-free graphs) Sachs
Benchmarks: synthetic multi-granularity data Sachs
Metrics: Precision Recall F1 SHD NNZ
Baselines: PC GES DAG-GNN GAE GraN-DAG MgCSL
Builds on: NOTEARS-MLP MgCSL Gumbel-Softmax NOTEARS acyclicity constraint
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