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Learning Mixtures of Unknown Causal Interventions

NeurIPS 2024 · Probabilistic and scientific modeling › Causal discovery · approach: Interventional causal discovery · 0 citations (OpenAlex)

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Shows that mixtures of unknown soft/do interventions in Gaussian linear SEMs can be disentangled via Gaussian mixture learning, enabling causal graph recovery up to the I-MEC.

Problem

Causal discovery from data where interventional samples are noisy blends of intended and unintended interventional distributions, with unknown intervention targets and no known causal graph.

Approach

Treat a mixture of atomic soft/do interventions in a Gaussian linear SEM as a Gaussian mixture; prove a separation lower bound on covariance and mean differences under an effectiveness assumption so the mixture is identifiable, then pass the recovered components to UT-IGSP to get the I-MEC.

Key results

• On the Protein Signaling dataset, the mixture method recovers 4 components at cutoff 0.01 versus 6 true, with SHD 15 vs oracle UT-IGSP 19 at that cutoff.
• In simulations, parameter estimation error decreases with sample size from 2^10 to 2^17 in both 'all' and 'half' intervention settings.
• Average Jaccard similarity on the Protein Signaling data is only 0.03, close to the oracle's 0.05, indicating target identification is hard even with correct disentangling.

Measured effects reported in the paper

Surprising findings

• Even with correctly disentangled ground-truth components, UT-IGSP intervention-target identification on the Protein Signaling data is poor (Jaccard about 0.05).

Limitations

• Restricted to linear Gaussian SEMs with causal sufficiency; no latent confounders.
• Assumes the number of mixture components is fixed and known; the empirical number-of-components selection is heuristic.
• Non-perturbative settings are not covered by the cited efficient mixture algorithms.

Experimental setup

Datasets: Protein Signaling dataset (Sachs et al., flow cytometry) simulated linear Gaussian SEM data

Benchmarks: simulated linear Gaussian SEM mixtures Protein Signaling dataset

Metrics: parameter estimation error Jaccard similarity of intervention targets structural Hamming distance

Baselines: UT-IGSP (oracle, with separated ground-truth mixture)

Builds on: UT-IGSP Gaussian mixture model EM (scikit-learn) Learning mixtures of Gaussians (Moitra-Valiant style identifiability) I-faithfulness

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