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Improving constraint-based discovery with robust propagation and LLM priors

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Identifiability with hidden confounders

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Proposes MosaCD, a constraint-based causal discovery method that seeds edge orientations from shuffled-order LLM queries (filtering hallucinations via positional bias) and propagates from high-confidence seeds, prioritizing non-collider evidence.

Problem

Constraint-based causal discovery accumulates orientation errors from noisy CI tests and v-structure seeding, and prior LLM-augmented methods assume LLM answers are reliable despite hallucination and positional bias.

Approach

Replace collider-based seeding with LLM-derived seeds retained only when answers are consistent across shuffled option orders, then propagate orientations confidence-first (non-collider evidence before collider evidence) and resolve leftovers by least-conflict orientation.

Key results

• On the PC skeleton, MosaCD achieves F1 0.81 vs 0.69 for the best baseline (ILS-CSL) on Win95pts and 0.72 vs 0.44 on Hepar2 (best baseline Hepar2 ILS-CSL 0.54).
• Averaged across skeletons, MosaCD's LLM seeding yields 1.69x the true seed ratio of PC with false-direction rate 4.8% vs 26.7%.
• MosaCD achieved best F1 on 9 of 10 datasets with the PC skeleton.

Surprising findings

• LLMs show strong positional bias, selecting the first option (forward direction) more often, which the shuffled-query design exploits.
• Under the stylized model, collider-first identification has expected false positive rates orders of magnitude higher than non-collider-first identification.

Limitations

• Gains depend on informative variable descriptions; performance declines as descriptions become uninformative.
• GPT-oss-120b backbone performed slightly weaker than others.
• Theoretical analysis relies on a stylized model with independent CI errors and a locally sparse graph.

Experimental setup

Datasets: BNLearn Cancer Asia Child Insurance Water Mildew Alarm Hailfinder Hepar2 Win95pts

Benchmarks: BNLearn Cancer Asia Child Insurance Water Mildew Alarm Hailfinder Hepar2 Win95pts

Metrics: F1 score for edge orientation true seed count false seed count

Baselines: PC PC-stable CPC Meek Shapley-PC ILS-CSL SCP

Builds on: PC algorithm CPC PC-stable Meek's rules ILS-CSL SCP

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