Research map / Probabilistic and scientific modeling / Causal discovery
Local Causal Structure Learning in the Presence of Latent Variables
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Proposes MMB-by-MMB, a sequential local causal discovery method that recovers the direct causes and effects of a target variable under latent confounding, using MAG Markov blankets, m-separation, V-structures and stop rules.
Problem
Local learning of direct causes (parents) and effects (children) of a target variable from observational data when latent confounders may exist, since existing local methods assume causal sufficiency and global methods (FCI, RFCI) are costly.
Approach
Learn the MAG Markov blanket of the target and of nodes iteratively, use m-separation and V-structures within MMB+ to recover correct edges at the target, and apply stop rules (including a leaf-removal-based rule R3) so the local output matches global PAG-based results under causal Markov and faithfulness with infinite samples.
Key results
- On ANDES (RApp3 target, size 5000) MMB-by-MMB reaches F1 0.98 vs 0.34 for CMB and 0.39 for GraN-LCS, using about 4.6k CI tests vs 1.58M for FCI.
- On ALARM (LVEDVOLUME target, size 1000) MMB-by-MMB reaches F1 0.96 versus 0.77 for FCI and 0.57 for GraN-LCS.
- MMB-by-MMB uses far fewer conditional independence tests than FCI and RFCI, e.g. 392.95 vs 5032.70 (RFCI) on MILDEW at size 1000.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MMB-by-MMB instead of the strongest listed baseline | Local causal discovery with latent variables · MILDEW.Net targets dm-1 and dm-4, Size=1000 and Size=5000 | F1: dm-1: 0.83±0.27 -> 0.95±0.15; dm-1: 0.85±0.27 -> 0.97±0.13; dm-4: 0.72±0.20 -> 0.92±0.15; dm-4: 0.80±0.18 -> 0.98±0.08 | Helped |
| Use MMB-by-MMB instead of the strongest listed baseline | Local causal discovery with latent variables · ALARM.Net targets LVEDVOLUME and STROKEVOLUME, Size=1000 and Size=5000 | F1: LVEDVOLUME: 0.57±0.14 -> 0.96±0.12; LVEDVOLUME: 0.58±0.13 -> 0.98±0.09; STROKEVOLUME: 0.77±0.25 -> 0.95±0.16; STROKEVOLU | Helped |
| Use MMB-by-MMB instead of the strongest listed baseline | Local causal discovery with latent variables · WIN95PTS.Net targets Problem5 and HrglssDrtnAftrPrnt, Size=1000 and Size=5000 | F1: Problem5: 0.68±0.24 -> 0.89±0.20; Problem5: 0.76±0.27 -> 0.92±0.19; HrglssDrtnAftrPrnt: 0.80±0.24 -> 0.92±0.18; HrglssDr | Helped |
| Use MMB-by-MMB instead of the strongest listed baseline | Local causal discovery with latent variables · ANDES.Net targets RApp3(V5) and RApp4, Size=1000 and Size=5000 | F1: RApp3(V5): 0.68±0.24 -> 0.89±0.17; RApp3(V5): 0.79±0.24 -> 0.98±0.07; RApp4: 0.78±0.24 -> 0.91±0.21; RApp4: 0.84±0.24 -> | Helped |
Surprising findings
- Local methods designed for causal sufficiency (MB-by-MB, CMB, GraN-LCS) perform poorly under latent variables, often worse than global FCI/RFCI in accuracy.
Limitations
- Results are proven only with infinite samples and oracle conditional independence tests; finite-sample behavior is evaluated only empirically.
- Some edges remain undetermined from observational data with latent variables, needing background knowledge.
- Faithfulness violations may affect the method; the authors note reliance on faithfulness and suggest GES-based extensions as future work.
Experimental setup
Datasets: MILDEW ALARM WIN95PTS ANDES Arabidopsis thaliana gene expression data (33 genes, 118 conditions)
Benchmarks: MILDEW ALARM WIN95PTS ANDES Arabidopsis gene expression
Metrics: Precision Recall F1 Distance nTest
Baselines: PC-stable FCI RFCI MB-by-MB CMB GraN-LCS
Builds on: FCI RFCI TC (Total Conditioning) PC algorithm Zhang's orientation rules
Closest papers by meaning
- Local Identifying Causal Relations in the Presence of Latent Variables (ICML 2025 · similarity 0.94)
- Identification of Latent Confounders via Investigating the Tensor Ranks of the Nonlinear Observations (ICML 2025 · similarity 0.91)
- Differentiable Causal Discovery for Latent Hierarchical Causal Models (ICLR 2025 · similarity 0.91)
- Score-Based Causal Discovery of Latent Variable Causal Models (ICML 2024 · similarity 0.91)
- Learning Discrete Latent Variable Structures with Tensor Rank Conditions (NeurIPS 2024 · similarity 0.89)
- Local Causal Discovery Without Causal Sufficiency (AAAI 2025 · similarity 0.89)
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