Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach

TL;DR

This work introduces Statistical Causal Prompting (SCP), a framework that fuses large language model (LLM) knowledge with statistical causal discovery (SCD) to produce a prior knowledge matrix that guides causal graph learning. By sequentially deriving initial causal structures with SCD, extracting domain knowledge from LLMs via zero-shot prompting, and transforming LLM outputs into constraints for SCD (including edge presence, bootstrap probabilities, and causal coefficients), the method achieves mutual performance gains on benchmark datasets and a real health-screening dataset not seen by the LLM during training. The authors rigorously evaluate multiple SCD algorithms (PC, Exact Search, DirectLiNGAM) and several SCP patterns, analyzing robustness, computation time, and risk, and provide guidance for practical deployment with expert checks and domain customization. Overall, SCP enhances the statistical validity and plausibility of inferred causal graphs, while highlighting the need for careful handling of LLM hallucinatory risks and data-domain alignment in real-world applications such as healthcare. The work thus points to a promising direction for data-driven causal inference that leverages codified expert knowledge while maintaining a systematic, auditable workflow.

Abstract

In practical statistical causal discovery (SCD), embedding domain expert knowledge as constraints into the algorithm is important for reasonable causal models reflecting the broad knowledge of domain experts, despite the challenges in the systematic acquisition of background knowledge. To overcome these challenges, this paper proposes a novel method for causal inference, in which SCD and knowledge-based causal inference (KBCI) with a large language model (LLM) are synthesized through ``statistical causal prompting (SCP)'' for LLMs and prior knowledge augmentation for SCD. The experiments in this work have revealed that the results of LLM-KBCI and SCD augmented with LLM-KBCI approach the ground truths, more than the SCD result without prior knowledge. These experiments have also revealed that the SCD result can be further improved if the LLM undergoes SCP. Furthermore, with an unpublished real-world dataset, we have demonstrated that the background knowledge provided by the LLM can improve the SCD on this dataset, even if this dataset has never been included in the training data of the LLM. For future practical application of this proposed method across important domains such as healthcare, we also thoroughly discuss the limitations, risks of critical errors, expected improvement of techniques around LLMs, and realistic integration of expert checks of the results into this automatic process, with SCP simulations under various conditions both in successful and failure scenarios. The careful and appropriate application of the proposed approach in this work, with improvement and customization for each domain, can thus address challenges such as dataset biases and limitations, illustrating the potential of LLMs to improve data-driven causal inference across diverse scientific domains. The code used in this work is publicly available at: www.github.com/mas-takayama/LLM-and-SCD

Figures (19)

• Figure 1: Overall framework of the statistical causal prompt in a large language model (LLM) and statistical causal discovery (SCD) with LLM-based background knowledge.
• Figure 2: Results of DirectLiNGAM on the health-screening data. (a) Result without prior knowledge. (b) Result with prior knowledge, which is generated from GPT-4 with the SCP in Patterns 2 and 4. In this randomly selected subset, the DirectLiNGAM result without prior knowledge exhibits unnatural paths drawn in red in (a), which indicates that "Age" is influenced by "HbA1c." However, when the proposed method is applied, the unnatural behavior is clearly mitigated with the guidance of prior knowledge generated from GPT-4 with SCP, including the value of causal coefficients in (a) or the bootstrap probabilities of the emergence of directed edges.
• Figure 3: Framework of the simulations for assessing the robustness and vulnerabilities of the proposed method and the influence of SCP. In particular, the processes of Simulation A (for assessing the LLM's confidence in edges, where causal relationships are recognized as unreasonable considering domain knowledge) are exemplified, and the entire framework is almost the same as the proposed method illustrated in Figure \ref{['fig:main_idea']}.
• Figure 4: Results of Simulation A through the methodology illustrated in Figure \ref{['fig:reliability_test_1']}, with the pseudo-results based on the SCD results for the subsampled health-screening dataset, which is used in the experiment of Section \ref{['subsec: Results in the Health-Screening Dataset']}. Simulations were conducted on unrealistic edges "BMI" $\rightarrow$ "Age", "Waist" $\rightarrow$ "Age" and "HbA1c" $\rightarrow$ "Age." (a) Results for Pattern 2 (various values of causal coefficient $c$ are prompted with in Process B). (b) Results for Pattern 3 (various values of bootstrap probability $b$ are prompted with in Process B). Considering that the maximum values of the left vertical axes for these graphs are smaller than $1.0 \times 10^{-5}$, GPT-4's confidence probability in these unrealistic edges is fixed around 0.0, regardless of the causal coefficients or bootstrap probabilities in the pseudo-results of SCD.
• Figure 5: Example of pseudo-results of DirectLiNGAM in the entire health-screening dataset with 123151 for Simulation B. In this example, on the basis of the initial DirectLiNGAM results shown in Figure \ref{['DAG:health LiNGAM total']}, the causal coefficient and the bootstrap probability of the directed edge "Age" $\rightarrow$ "HbA1c" are replaced with the variables $c$ and $b$, respectively. (The value of the causal coefficient without replacement is 0.02, and the bootstrap probability is 1.0.) Because of the large number of data points in the entire health-screening dataset, some directed edges, including the ground truth bootstrap probabilities, are 1.0. In Simulation B, in addition to this example, the pseudo-results modulating the causal coefficients and bootstrap probabilities of "Age" $\rightarrow$ "BMI," "Age" $\rightarrow$ "SBP," and "Age" $\rightarrow$ "DBP," are also embedded similarly to Figure \ref{['fig:reliability_test_1']}.