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Causal Order: The Key to Leveraging Imperfect Experts in Causal Inference
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Proposes causal order (instead of graphs) as the output interface for LLM or human experts and a triplet querying method with majority-vote ensembling to obtain more accurate, cycle-free causal orders.
Problem
Pairwise LLM or human queries about causal edges cannot separate direct from indirect effects, so the inferred graphs are unstable and pairwise answers from imperfect LLM experts produce cycles.
Approach
Elicit a causal (topological) order rather than a graph, and query experts with triplets of variables (each pair plus an auxiliary variable) enforcing acyclicity within the triplet, then aggregate by majority vote across triplets; a perfect expert's pairwise-derived order is provably correct even when the graph is not.
Key results
- Triplet method with GPT-3.5-turbo gets D_top=0 on Survey, Earthquake and Cancer, while base pairwise prompting yields cycles on Child (>>3k) and Asia-M (7 cycles).
- Triplet prompting with Phi-3 and Llama-3 8B yields lower SHD/D_top than pairwise GPT-4 on Asia, Alzheimers and Child (e.g., Child SHD 69 for Phi-3 vs 148 for pairwise GPT-4).
- With human annotators, the triplet method produced zero cycles across datasets where pairwise queries produced cycles, and consistently lower SHD.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace pairwise prompting with triplet prompting | GPT-3.5-turbo expert queries · Child | SHD: 177 -> 28 | Helped |
| Replace pairwise CoT prompting with triplet prompting | GPT-3.5-turbo expert queries · Neuropathic | SHD: 64 -> 24 | Helped |
| Replace pairwise CoT prompting with triplet prompting | GPT-3.5-turbo expert queries · Covid | SHD: 27 -> 30 | Hurt |
| Replace pairwise base prompting with pairwise Chain-of-Thought prompting (ablation) | GPT-3.5-turbo expert queries · Child | SHD: 177 -> 138 | Helped |
| Replace pairwise GPT-4 prompting with triplet prompting using Phi-3 | Causal order estimation · Asia | D_top: 1 -> 0 | Helped |
| Replace pairwise GPT-4 prompting with triplet prompting using Phi-3 | Causal order estimation · Child | SHD: 148 -> 69 | Helped |
| Add expert-provided causal order to PC discovery | Causal discovery · Earthquake, N=250 | D_top: 0.16$\pm$0.28 -> 0.00$\pm$0.00 | Helped |
| Add expert-provided causal order to CaMML | Causal discovery · Child, N=250 | D_top: 3.00$\pm$0.00 -> 3.53$\pm$0.45 | Helped |
| Add LLM-derived causal order to CaMML | Causal effect inference · Asia (smoke, dyspnoea) | ε_ACE: 0.05 \pm 0.00 -> 0.00 \pm 0.00 | Helped |
| Use a quadruplet prompt instead of a triplet prompt (ablation) | Prompting strategy · Causal order estimation | accuracy | No clear effect |
| Replace the triplet method with pairwise prompting | Human annotators · Survey | Cycles: 0 -> 0.67 | Hurt |
Surprising findings
- Upgrading pairwise prompting from GPT-3.5 to GPT-4 still yields many cycles on large graphs such as Child, indicating model upgrades alone do not fix cycles.
- Small open models (Phi-3, Llama-3 8B) with the triplet method outperform GPT-4 with pairwise prompting.
Limitations
- LLMs may not be useful for completely novel variables or relationships outside known knowledge.
- Causal order may not suffice for counterfactual estimation requiring full graph structure.
- Tie-breaking relies on a high-cost expert (GPT-4 or ground-truth oracle), adding cost.
Experimental setup
Datasets: Earthquake Cancer Survey Asia Asia-M Child Neuropathic Alzheimers Covid-19
Benchmarks: Earthquake Cancer Survey Asia Asia-M Child Neuropathic Alzheimers Covid-19
Metrics: D_top SHD cycles IN/TN ACE error
Baselines: Pairwise (Base) prompt Pairwise (CoT) prompt BFS BFS+Stats PC SCORE ICA-LiNGAM DirectLiNGAM NOTEARS CaMML
Builds on: pairwise LLM causal graph prompting topological divergence CaMML PC algorithm
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