# Improving constraint-based discovery with robust propagation and reliable LLM priors

arXiv: https://arxiv.org/abs/2509.23570 · HTML: https://mlsanity.com/paper/2509.23570/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 18 of 18)

- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Large Language Models Sensitivity to The Order of Options in Multiple-Choice Questions](https://mlsanity.com/paper/2308.11483/) (2023)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [R-Tuning: Instructing Large Language Models to Say `I Don't Know'](https://mlsanity.com/paper/2311.09677/) (2023)
- [Causal Order: The Key to Leveraging Imperfect Experts in Causal Inference](https://mlsanity.com/paper/2310.15117/) (2023)
- [Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach](https://mlsanity.com/paper/2402.01454/) (2024)
- [ALCM: Autonomous LLM-Augmented Causal Discovery Framework](https://mlsanity.com/paper/2405.01744/) (2024)
- [Fact-and-Reflection (FaR) Improves Confidence Calibration of Large Language Models](https://mlsanity.com/paper/2402.17124/) (2024)
- [Causal Structure Learning Supervised by Large Language Model](https://mlsanity.com/paper/2311.11689/) (2023)
- [Large Language Models for Constrained-Based Causal Discovery](https://mlsanity.com/paper/2406.07378/) (2024)
- [Improving Accuracy and Scalability of the PC Algorithm by Maximizing P-value](https://mlsanity.com/paper/1610.00378/) (2016)
- [Optimizing Data-driven Causal Discovery Using Knowledge-guided Search](https://mlsanity.com/paper/2304.05493/) (2023)
- [IGDA: Interactive Graph Discovery through Large Language Model Agents](https://mlsanity.com/paper/2502.17189/) (2025)

## Built on by (most cited first, 1 of 1)

- [Coupling Noisy Pairwise Knowledge to the DAG Posterior for Causal Discovery](https://mlsanity.com/paper/2610.04559/) (2026)

## Abstract (arXiv)

Learning causal structure from observational data is central to scientific modeling and decision-making. Constraint-based methods aim to recover conditional independence (CI) relations in a causal directed acyclic graph (DAG). Classical approaches such as PC and subsequent methods orient v-structures first and then propagate edge directions from these seeds, assuming perfect CI tests and exhaustive search of separating subsets -- assumptions often violated in practice, leading to cascading errors in the final graph. Recent work has explored using large language models (LLMs) as experts, prompting sets of nodes for edge directions, and could augment edge orientation when assumptions are not met. However, such methods implicitly assume perfect experts, which is unrealistic for hallucination-prone LLMs. We propose MosaCD, a causal discovery method that propagates edges from a high-confidence set of seeds derived from both CI tests and LLM annotations. To filter hallucinations, we introduce shuffled queries that exploit LLMs' positional bias, retaining only high-confidence seeds. We then apply a novel confidence-down propagation strategy that orients the most reliable edges first, and can be integrated with any skeleton-based discovery method. Across multiple real-world graphs, MosaCD achieves higher accuracy in final graph construction than existing constraint-based methods, largely due to the improved reliability of initial seeds and robust propagation strategies.