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Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model
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Extends constraint-based and additive-noise-model causal discovery to missing data with weak self-masking missingness, yielding the SM-MVPC skeleton algorithm and the LCS-MD direction algorithm that identifies structure up to an IN-equivalent pattern.
Problem
Causal discovery from observational data where missingness depends on the missing values themselves (self-masking MNAR), which makes the original joint distribution unrecoverable and existing methods produce wrong conclusions.
Approach
Relaxes the no-self-masking assumption to weak self-masking (a missingness indicator caused only by its own variable), shows CI tests remain consistent after removing self-masking indicators, and uses ANM independence of residuals on the observed skeleton to orient edges up to an IN-equivalent pattern, plus orientation rules.
Key results
- SM-MVPC achieves the best skeleton F1 across sample sizes and numbers of weak self-masking variables, while MVPC degrades as self-masking variables increase.
- LCS-MD outperforms baselines in causal direction identification, with a larger gap than in skeleton learning.
- On the CFS real dataset, LCS-MD identifies pActivity, focusing, control and functioning as direct causes of fatigue, consistent with prior conclusions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SM-MVPC instead of MVPC and MissDAG for skeleton learning | Causal skeleton learning with weak self-masking missingness · Synthetic MNAR experiments | F1 | Helped |
| Increase the number of weak self-masking variables | SM-MVPC · Synthetic MNAR experiments | F1 | No clear effect |
| Increase the number of weak self-masking variables | MVPC · Synthetic MNAR experiments | F1 | Hurt |
| Use LCS-MD instead of baseline methods for causal structure learning | Causal structure learning with weak self-masking missingness · Synthetic MNAR experiments | F1 | Helped |
| Increase the number of weak self-masking variables | LCS-MD · Synthetic MNAR experiments | F1 | No clear effect |
Limitations
- Relies on strong assumptions: weak self-masking only, causal sufficiency, faithfulness, and a structural condition.
- Only applies to ANMs identifiable in complete data (e.g., LiNGAM, nonlinear ANM).
- Direction identification only yields an IN-equivalent pattern; some edges remain undirected.
Experimental setup
Datasets: Chronic Fatigue Syndrome (CFS) dataset synthetic MNAR data
Benchmarks: synthetic MNAR graphs (10 variables) Chronic Fatigue Syndrome (CFS) dataset
Metrics: SHD Precision Recall F1
Baselines: MVPC MissDAG
Builds on: MVPC MissDAG Additive noise model PC algorithm Meek's rules
Closest papers by meaning
- Optimal Transport for Structure Learning Under Missing Data (ICML 2024 · similarity 0.90)
- MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models (NeurIPS 2022 · similarity 0.90)
- Strong and Weak Identifiability of Optimization-based Causal Discovery in Non-linear Additive Noise Models (ICML 2025 · similarity 0.89)
- Learning Mixtures of Unknown Causal Interventions (NeurIPS 2024 · similarity 0.87)
- When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery (NeurIPS 2025 · similarity 0.87)
- A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery (ICLR 2025 · similarity 0.86)
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