Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach
Authors: MASAYUKI TAKAYAMA
Tadahisa OKUDA
Thong Pham
Tatsuyoshi Ikenoue
Shingo Fukuma
Shohei Shimizu
Akiyoshi Sannai
Venue: Accepted by TMLR ()

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Furthermore, with an unpublished real-world dataset, we have demonstrated that the background knowledge provided by the LLM can improve the SCD on this dataset, even if this dataset has never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: https://github.com/mas-takayama/LLM-and-SCD.

Published in Transactions on Machine Learning Research (05/2025)
Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach
Masayuki Takayama
Data Science and AI Innovation Research Promotion Center, Shiga University National Institute of Science and Technology Policy (NISTEP)
Tadahisa Okuda
Department of Health Data Science, Tokyo Medical University Graduate School of Medicine Humon Health Sciences, Kyoto University
Thong Pham
Data Science and Al Innovation Research Promotion Center, Shiga University Graduate School of Medicine Human Health Sciences, Kyoto University Center for Advanced Intellignnce Project, RIKEN
Tatsuyoshi Ikenoue
Data Science and Al Innovation Research Promotion Center, Shiga Universily Graduate School of Medicine Humon Health Sciences, Kyoto University
Shingo Fukuma
Graduate School of Medicine Human Health Sciences, Kyoto University Department of Epidemiology Infectious Disease Control and Prevention, Hiroshima University Groduate School of Biomedical and Health Sciences
Dala Science and Al Innovalion Research Promotion Center, Shiga Universily
Shohei Shimizu
shohei-shimiceu@dss.eettt osaka-u..saaauccc.
SANKEN, The University of Osaka
Faculty of Data Science, Shiga University Center for Advanced Intelligence Project, RIKEN
Graduate School of Medicine Human Health Sciences, Kyolo Universily Institate for the Advanced Study of Human Biology, Kyoto Universily National Institute of Science and Technology Policy (NISTEP)
Akiyoshi Sannai
aknnai.akigoshi, 7o@kyoto-waac.)
Deportment of Physics, Kyoto University
Data Science and Al Innovation Research Promotion Center, Shiga University Graduate School of Engineering, The University Tokyo Center for Advanced Intelligence Project, RIKEN
Research and Development Center for Large Language Models, National Institute of Informatics National Institute of Science and Technology Policy (NISTEP)
Reviewed on OpenReview: ht tps:: // en ew net /f or um Pt d- Re S8
Abstract
In practical statistical causal discovery (SCD), embedding domain expert knowledge 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 novel method for causal inference, which SCD and knowledge-based causal inference (KBCT) with large language model (LLM) are synthesized through "statistical causal prompting (SCP)" for L.LMs and prior knowledge augmentation for SCD. The experiments in this work have

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Published in Transactions on Machine Learning Research (05/2025)
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 datasel, even if this datasct has never been included 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
1 Introduction
1.1 Background
Understanding causal relationships is key to comprehending basic mechanisms in varions scientific fields. The stat ical causal inference framework, which is widely applied in areas such as medical science, economics, and environmental science, aids this understanding. However, traditional statistical causal inference methods generally rely on the assumed causal graph for determining the existence and strength of causal impacts. To overcome this challenge, data-driven algorithmic methods have been developed as statistical causal discovery
(SCD) methods (Spirtes et al.) 2000
Chickering 2002 Silander & Myllymäki
2006 (Shimizu et al. 2006
Hoyer et al. 2008 SShiiizu et al. 2011 Yuan & Malone 2013 Huang et al. 2018 Xie et al. |2200] Rolland
ct al.
2022 Tu et al. 2022). In addition, benchmark datasets have been published for the evaluation of SCD
methods Mooojj et al. 2016 Käding & Runge 2023
Despite advancements SCD algorithms, data-driven acquisition causal graphs without domain knowledge can be inaccurate. This generally attributed a mismatch between assumptions SCD and real-world phenomena (Reisach al.) 2001). Moreover, obtaining sufficient experimental and systematic datasets for causal inference is difficult, whereas obsorvational datascts, which are prone to selection bias and mcasurement errors, are more readily accessible (Abdullahi et al. 2020). Consequently, to obtain more persuasive and reasonable causal models supported by sufficient knowledge of domain experts, the augmentation with domain knowledge plays a critical role (Rohrer 2017). In addition, with respect to efficiency and precision in the SCD, the importance of incorporating constraints on trivial cansal relationships into the SCD algorithms has been highlighted (Tnazurni et al., 2010 Chowdhhry et al., (023). :
Causal learning software packages have been augmented with prior knowledge, as demonstrated in "causal-learn" and "LiNGAM" (Zheng et al.
2023b Ikeuchi et al. 2023).
Moreover, the systematic acquisition of domain expert knowledge is challenging task. Although several examples of constructing directed acyelic graphs (DAGs) by domain experts exist, as demonstrated in health services research (Rodrigues el. al.; 2022), practical methods for this process have not been proposed.
The scenario has recently changed with rapid progress the development of high-end large language models (LLMs). Owing to their high performance the application of their domain knowlodge acquired from vast amounts of data in the pretraining processes (OpenAl 2023: Touvron al.) 2023 Gemini Team, Google 2023), it is expected that LLMs also be applied to causal reasoning tasks. In fact, several studies have
https://github... wwwp:///mmmmmmaaaaaaaaaaaaaeaaaa and-SCD
https://github.. com/ whw.hhywwwuusshhhh learn https://github. cdt
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1st step: Data-Driven Causal Discovery (without constraints on the edges)
4th step: Retrying Causal Discovery (with the constraints determined In 3 step)
Input: Dataset
Input:
Dataset + constraints
Pollution
Smoker
Cancer
X-tay
Dysproee
Pollution
Smoker
Cancer
Xiny
Dyppnoea
Low
True
True
True
True
True
High
False
True
Fale
True
Constraints
Cancer X-aa: forced, Xray Cancer. forbidden, elc
Output: Causal Graph
SCD: statistical causal discovery
SCD: causal discovery
Output: Modified Graph
Smokal
Not so plausible from domain experts' point of view.
Polldion
Plausible both from domain experts' and statistical points of view!
Cancer
Pollution
Cancer
Smokar
Dysprooe
Xraay
Dysphoes
Transforming the probability matrix generated in 3 stop into background knowledge for the cousal discovery
2dd step: Knowledge Generation on Causal Relationships by the LLM with ZSCoT
3 step: Knowledge Integration and Evaluation of
the Probability of Causal Relationships with
with the LLM
Input: prompts
result causal discovery
Input: prompts with the dialog in 2nd step
According to the result shown above, the state of "cancar" Please
Considering objectively this discussion above, the state "cancer is changed, will have direct the state of "I-ray?
may direct impact state
wheth statsticclly steehyysheeeee
plausible with explanation that lvverpes
inowledga this caus ilsttoonshpp
Please
with <yes>
Output: response with the qualitative discussion on causal relationships in detail as domain experts
Output: <yes> or <no>
log probability
While it suggested that may not be a direct causal effect from state "Cancer" to the state of
Most likely response: Yes (log probability 0408) 2 most likely response: No (log probability: -.2119) 96%, 4%
LLM L
"Cray" toomsto be plauzible considernn
LLM
inowlodge...coooo explained below.....
Figure 1: Overall framework of the statistical causal prompt in large language model (LLM) and statistical causal discovery (SCD) with LLM-based background knowledge.
reported the trial results of LLM knowlodge-ben based causal inference" (LLM-KBCI) Jiang et al. 2023 Jin et al. 2024
Kiciman al.] 2024 Zéčević al. 2023 Jiralerspong et al. 2024 Zhang al. 2024), and in particular, the performance enhancement in nonparametric SCD with the guides by LLMs confirmed (Ban et al.) Vashishtha et al 2023 Khatibi et al. 2024 However, it remains unclear whether the enhancement in accuracy with background knowledge augmented by LLMs is robustly observed when the task of the
2023
SCD
SCD depends on closed data uncontained in the pretraining datasets of LLMs.
1.2
Central Idea of Our Research
On the basis of the rapidly evolving techniques in the context of causal inference with LLMs, novel methodology for SCD is proposed in this paper, in which the LLM prompted with the results of the SCD without background knowledge evaluates the probability of the causal relationships considering both the domain knowledge and the statistical characteristics suggested by SCD (Figure D
In the first step, an SCD is executed on dataset without prior knowledge, and the results of the statistical causal analysis are output. To maximize the usage of the expert knowledge acquired in the pretraining process of the LLM, the method of generated knowledge prompting (Liu et al. (2022) is adopted, and then, the process of utilizing the LLM includes the second step (knowledge generation) and the third step (knowledge integration). In the second step, knowledge of the causal relationships between all pairs of variables is generated detail from the domain knowledge the LLM based on the zero-shot chain-of-thought (ZSCoT) prompting technique (Kojima et al.] 2022p. Here, the LLM can be prompted with the results of the SCD supplemental information for LLM inference, expecting that the in-context learning (Brown al., 2020) of the SCD results can lead to better performance of the LLM-KBCT in terms of statistics. We define this
'In this context, the causal inference is used in different sense from its conventional meaning in standard statistical frameworks, which typically aims to quantify the causal effect between pair of variables. However, we inteutionally refer to our process with LLMs as LLM-KBCI (LLM knowledge-bass based causal inference), as it can also interpreted an upstream task for constructing candidate causal models with SCD, be used subsequent causal effect analyses.
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technique as "statistical causal prompting" (SCP). Thereafter, in the third step, the LLM judges whether causal relationships exist between all pairs of variables with "yes" or "no," thus objectively considering the dialogs of the second step. Here, the probabilities of the responses from the LLM are evaluated and transformed into the prior knowledge matrix. This matrix, the output of LLM-KBCI with SCP, is finally reapplied to SCD the fourth step.
1.3 Our Contribution
The contributions of the method proposed in this study are as follows:
(1) Realization of the Synthesis of LLM-KBCI and SCD in a Mutually Referential Manner We detail the practical method for realizing the proposed concept of Figure [I and propose the SCP method. Furthermore, we demonstrate experiments with several benchmark datasots, which are open and have been widely used for the evaluation of SCD algorithms. They all consist of contimuous variables.
(2) Mutual Performance Enhancement of SCD and LLM-KBCI We demonstrate that the aug- mentation by the LLM with SCP, improves the performance of several SCD algorithms in terms of domain expertisc and statistics, and the performance of the LLM-KBCI is also enhanced by the SCP including the initial SCD results.
(3) Improving the SCD results with the background knowledge provided by LLMs even if the dataset is uncontained in the pretraining materials We prepare a closed health-screening dataset. that is not included in the pretraining materials for LLMs, and demonstrate the experiment on sub-dataset that has been randomly sampled from the entire dataset. Through this experiment, it is confirmed that the proposed method can lead to more statistically valid causal models with established domain knowledge. This fact proves that the LLMs can indeed contribute to background knowledge augmentation for SCD algorithms in practical siluations, even if the dataset used for SCD is not memorized by LLMs.
(4) Discussion on the Reliability and Risks of Integrating LLMs as a "black-box" into SCD In addition, demonstrate some simulations of SCP in various conditions, confirm the existence of the patterns where SCP stably works intended, and discuss the technical and statistical limitations of the proposed method. We also discuss realistic strategies and directions for future practical applications, to overcome the limitations of the proposed method, and to effectively obtain appropriate causal models from both expert and statistical points of view, avoiding critical crrors.
2 Related Work and Originality in Our Work
Augmentation of SCD Algorithms with Background Knowledge As introduced in Section 1.1 several SCD algorithms can be systematically augmented with background knowledge. Morcover, their software packages are open. For example, as a nonparametri and the constraint based SCD method, the Peter-Clark (PC) algorithm (Spirtes et al. 2000) is augmented with background knowledge of the forced or forbidden directed edges in "causal-learn." "Causal-lean" also provides the Exact Search algorithm (Silander & Myllymäki] 2006 Yuan & Malone 2013) a score-based SCD method, which can be augmented with the background knowledge of the forbidden directed edges superstructure matrix. With respect to semiparametric approach, the DiMM (Shimizu et al. (211]] algorithm is augmented with prior knowledge of the causal order (Inazumi et al. 2010) in the "LiNGAM" project (Teuchi et al. 2023
'All of the algorithms adopted for the experiments in this paper can be used under the assumption of DAG and with hidden confounders.
On this context, "nonparametric"" indicates that neither the functional form characterizing the relationship between causo-effect pair of variables the distribution of variables is assumed during the discovery process. In this sense, the PC algorithm be classified as nonparametric SCD method. Converscly, DircetLiNGAM is semiparametric approach, it estimates cansal coefficients through regression analysis, although does not assume any specific distribution of variables other than non- Gaussianity.
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Causal Inference in Knowledge-Driven Approach with LLMs In addition to the study of causality detection from natural language texts via language models with additional training datasets (Khetan et al. 2022), the rapid growth of LLMs has made it possible to produce valuable works on causality, including causal inference using LLMs. Attempts have been made to use LLMs for causal inference among a set of variables, prompting with the metadata such as the names of variables, and without the SCD process with the benchmark datasets (Kiciman et al., 2024 Zéčević et al., 2023; Jiralerspong et al. 2024 Zhang et al. 2024). Adopting a similar approach, the concept of causal modeling agents, which improves the precision of causal graphs through iteration of hypothesis generation from LLMs and model fitting to real-world data, has also been proposed (Abdulaal et al. 2024).. There are also studies on incorporating LLMss in the process of SCD as an alternative tool for conditional independence tests in the PC algorithm (Cohrs et al. 2023). and for the identification of causal graphs beyond the Markov equivalent class (Long el al. 2023). In addition
studies have focused on the use of LLMs to improve the SCD results(Ban et al. 2023 Vashishtha et al. 2023
Khatibi ct al. 2024). However, all the experiments were conducted only on popular benchmark datascts, contained in the pretraining datasets of LLMs. Consequently, while acknowledging the valuable foundations laid by previous studies, it has remained uncertain whether the enhancements in SCD accuracy are truly driven by LLMs leveraging their vast knowledge for genuine causal inference, or merely by reproducing the memorized content of datasets (Vashishtha et al. 2023
Originality in Our Work In contrast to studies with similar focus on LLM-guided SCD (Ban et al., 2023 Vashishtha et al. 2023 Khatibi et al. 2024), this study also focuses on the construction of background knowledge in a quantitative manner based on the response probability of the LLM, which can reflect the credibility of the decision made by the LLM with SCP. Tn addition, the case of a semiparametric SCD method such as LiNGAM, we detail herein how to achieve both the statistically well-fitting causal model and reasonable interpretation with respect to domain knowledge, by prompting with the causal cocfficients and bootstrap probabilities of all the patterns of directed edges.
Moreover, we validate the proposed method on an unpublished dataset. For future practical applications, we also thoroughly discuss the limitations, risks of critical errors, expected improvement of techniques around LLMs, and the suggestion of realistic integration of domain expert checks of the results into this automatic methodology, with the simulations of SCP both successful and failing scenarios. These approaches have not only demonstrated the practical utility and robustnnss of our method for future applications in each domain, but also opened new avenues for supporting the validity and applicability of existing works (Ban
et al. 2023 Vashishtha et al. 2023 Khatibi et al. 2024).
3 Materials and Methods
In Section 3.1 we present an overview of the method in the form of an algorithm and explain the experimental conditions in detail. Furthermore, the prompting patterns used in the experiments are outlined in Section 3.1 Finally, the datasets used in the experiments are described in Section 3.3
3.1 Algorithms and Elements for LLM-Augmenter Causal Discovery
With respect to practicality, the method of Figure ! outlined as Algorithm [ Following the notation in Algorithm [ the input elements in the demonstration are explained below. First, the algorithms for SCD used in the first and fourth steps of Figure [ are introduced. Then, for the second and third steps involving GPT-4, we explain the experimental conditions, the prompt templates, and the method for measuring GPT-4's confidence probabilities in causal relationships. Furthermore, to clarify how the output of the third step is applied to SCD in the fourth step, we describe the conversion from the probability matrix to the prior knowledge matrix in detail. Finally, with respect to practical application, we supplement our discussion with the theoretical computation time and scalability of the proposed method.
Algorithms for Statistical Causal Discovery For the SCD method S, we adopted the PC algo- rithm (Spirtes et al. 2000) with Fisher's Z. test (A. 1921) the Exact. Search algorithm based on the A*
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Algorithm Background knowledge construction with the LLM prompted with the results of the SCD
Input 1: Data X with variables(211.....22
Input 2: SCD) method S (the one selected from PC, Exact Search, and DirecLLiNGAM)
Input 3: Function for bootstrap B
Input 4: Response of the domain expert (LLM) GLAM
Input 5: Log probability of the response L(ELLM)
Input 6: Prompt function for knowledge generation 0,7
Input 7: Prompt function for knowledge integration !
Input 8: Transformation from the probability matrix to prior knowledge T
Input 9: Number of times to measure the probability M
Output: Result of SCD with prior knowledge G on X
SCD result without prior knowledge Go S(X) bootstrap probability matrix P X)
for i = 1 to n do
for 1 to do
P.i = NaN
if i + then
prompt Pij Qij (Ii Fjj Go, P)
response dyj ELLM(
(1)
prompt gij Q (giz ais)
(2)
(2) (1)
for m = 1 to M do
(m) (m)) (cLLM (2) "yes")
end for
M
exp(Li (m))
mean probability Pij
M
end
end for end for probability matrix p (pij)
prior knowledge PK ( return Ô = S(X, PK)
algorithm! Yuan & Malone 2013), and the DirectLiGGAM algorithm Shimizu et al. 2011 which can all
be optionally augmented with prior knowledge, and are open in "causal-learn" (Zheng et al.) 2023b) and
"LiNGAM" (Teuchi et al. 2023).
Moreover, the form of Go, the SCD result without prior knowledge, is a DAG if S is Exact Search DirectLiGGAM, and is completed partially directed acyclic graph (CPDAG) if S is PC.
Furthermore, we also implement the bootstrap sampling function B of the SCD algorithm to investigate the statistical properties such as the bootstrap probabilities Pij of the emergence of the directed edges from Ij to Ze. our experiments, the number of bootstrap resamplings was fixed to 1000.
II particular, utilized the A Exact Search algorithm from "causal-learn" package (Zheng et employs the Bayes information criterion (BIC) (Schwarz) 1978) scoring metric.
2023b which

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Conditions of the LLM and Prompting To utilize the LLM the domain expert, we adopted GPT-4-1106-previeer developed by OpenAT; the temperature, hyperparameter for adjusting the probability distribution of the output, was fixed to 0.7.
(1) for knowledge generation is shown in Table This prompting template The template for the first prompt Kj
is based on the underlying principle of the ZSCoT technique [ (Kojima et al. 2022). which was reported as potential method to enhance the performance of the LLM generation tasks; enhancement is performed by guiding logical inference and eliciting the background knowledge acquired through the pretraining process from the LLM. Furthermore, expecting that the in- in-context learning (Brown et al. 2020) of the SCD results can lead to better performance of the LLM-KBCI in terms of statisties, the SCD results, e.g., the causal structure and bootstrap probabilities, can be included in (blank 5) and (blank 9), which are defined as "statistical causal prompting" (SCP). Because the information used in SCP partially dependent on the SCD algorithms, brief description of the patterns for constructing the contents of (blank 5) and (blank 9) is presented in Section
3.2
As shown in Table 2 the generated knowledge is integrated into the second prompt, and GPT-4 is required to judge the existence of the causal effect from 2j on 2₁, considering the discussion of the second step regarding causal relationships from another perspective. Because the response from GPT-4 is required with "yes" or "no," " it is simple to quantitatively evaluate the level of confidence of GPT-4 in the existence of a causal relationship based on both the SCD result and domain knowledge. The probability Pij of the assertion that there is a causal effect from Iy on 2; can be output from GPT-4 directly with the optional function of returning the pog-probabilities of the most likely tokens at cach token position Although Pij can be evaluated readily from the log probability of the GPT-4 response as "yes," there is slight. fluctuation in the log probability output from GPT-4 (Anrrishchenno et al. 2024). Thus, we adopted the mean probability Pij of the single-shot measurement M times for the decision of prior knowledge matrix PK, and we set M 5 5 in the experiments. The combination of these prompt techniques can contribute to minimizing the risk of hallucination, and a reliable probability of the response of the LLM for the causal relationship between a pair of variables is expected to be obtained.
Conversion from the Probability Matrix to the Prior Knowledge Matrix For the subsequent SCD with prior knowledge, the probability matrix p is transformed with T, as expressed by Algorithm 2 into the background knowledge matrix.
Here, if PK, Forbidden, the causal effect from Ty to z2 is forbidden from appearing in the SCD result. While only the existence of a directed edge from Ty to I; is forbidden in the case of the PC and Exact Search algorithms, setting the PK3 = Forbidden as prior knowledge in DirectLiNGAN prohibits all direct paths from 3ú to T;- However, if PKi, = Forced, the causal effect from Ij to 2; is forced to appear in the SCD resul For the decision of a forbidden or forced causal relationship from PKij, we prepare the probability
We recognize that various types of high-performance LLMs have been developed several institutes, and that it is valuable to demonstrate that including a broader range of LLMs could provide valuable insights into the generalizability and scalability of our method across various LLM architectures. From this recognition, in addition to the main exper- iments with GPT-4-1106-previerr, we have also demonstrated our approach with other LLMs, such as other GPT-series models ( GPT-3. 5-turboorr-61666 LLMs L1ama-3. 1..aa-...-70B-111 -Isttrctt gemms-2-27b-- 2-27b-it, and Quen2.5-7B-11 5-7B-Instruct, and have improved the performance of SCD, as described in Appendix H However, our goal in this work is to explore the effectiveness of integrating LLMs into SCD via the SCP, which requires trials and comparisons of varions SCP patterns and SCD algorithms, as described in Section [ To maintain consistency and control across these trials, it is also important to fix the LLM in the experiments, which has advanced capabilities and state-of-the-art status in various domains. Moreover, we should adopt the LLMs that satisfy specific conditions for our experiments, such as the maximum input taken capacity for the prompting processes, and the functionality to obtain the log- bog-probability of the output. For these strategic and technical reasons, we adopted CPT-4 in our thorough experiments.
57r-3.5-turb--0155 GPT-4-0125-prevtae
and 07740-20024-8-06- and other open-source
"The details of the adjustment of the wording in the prompt template explained in Appendix
10 "AAthoogh the quality of the LLM outputs can be further enhanced, e.g., by fine-tuning with several datasets containing fundamental knowledge for the discussion of causality
retrieval-uummented generation (RAG), we adopt the idea of the ZSCoa to establish low-coss and simple methods, which can be universally applied independent of the targeted fields of causal inference.
1he technical detail of this probability sampling is explained in Appendix D
12 Althougg these constraints can be systomatically adapted with the augmentation supported in "causal-lcarn" " Zheng all
2023b) and "LINGAM" [Teecchi et al. 2023). the detailed meanings of forced and forbidden causal effects are slightly different. among the SCD algorithms. The details are described Appendix
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Table 1: Prompt template of Q (z, Fij Go, P) used for the generation of expert knowledge of the causal effect from 2j 24. The "blanks" enclosed with ) are filled with description words The word for (blank 6) is selected from "a" or "no," depending on the content of (blank 5). Notations of the SCD result without prior knowledge Go and the bootstrap probability matrix P are the same as those in Algorithm
Prompt Template of 9. = Qi3 (1i, Lz Go. P)
We want to carry out causal inference on (blank 1. The theme), considering (blank 2. The description of all variables) as variables.
First, we have conducted the statistical causal discovery with (blank 3. The name of the SCD algorithm), using fully standardized dataset on (blank 4. Description of the dataset).
(blank 5, This includes the information of Co or P.The details of the contents depend on the prompting patterns.)
According the results shown above, it has been determined that there may be (blank 6. a a/no) direct impact of a change in (blank 7. The name of 22) on (blank 8. The name of æs) (blank 9. The value of causal coefficients or bootstrap probability).
Then, your task is to interpret this result from a domain knowledge perspective and determine whether this statistically suggested hypothesis is plansible the context of the domain.
Please provide an explanation that leverages your expert knowledge on the causal relationship between (blank 7. The name of 2,) and (blank 8. The name of zı), and assess the naturalness of this causal discovery result.
Your response should consider the relevant factors and provide reasoned explanation based your under- standing of the domain.
Table 2: Prompt template of 0 (Gig atz) used for the quantitative evaluation of the probability of GPT-4's assertion that there a cansal effect from By on 2z-
(1)
Prompt Template of d. 2.7 (e. ag)
An expert was asked the question below: (1);
(blank 10. 4iy
Then, the expert replied with its domain knowledge: (blank 11. a.y)
Considering objectively this discussion above, if (blank 12. The name of my) is modified, will have a direct indirect impact on (blank 13. The name of a:)? Please answer this question with (yes) or (no). No answers except these two responses are needed.
criterion for the forbidden path as an and that for the forced path as 02. our experiments, on is fixed 0.05, and 02 fixed at 0.95 for common settings
Furthermore, the differences in the constraints that can be adopted depending on the SCD algorithms should be considered In the Exact Search algorithm, the constraints of the forced edge cannot be applied. For the
13These heuristic thresholds follow the widely accepted conventions seen in statistical siguificance levels. Although the specific choice of threshold might influence the formation of the prior knowledge matrix, the probability outputs from LLMs for clear domain knowledge instances are either very high (close to 100 %) or very low (close to %), ensuring that the essential insights retained regardless of the threshold. In Appendix technical details of this sensitivity around these thresholds are described through the evaluation of the standard error of Pty, which be realized by repeating singlo-shot measurements of Pt M times. 14For this reason stated here, is certain that Algurithm which considers several SCD algorithms, becomns somewhat complex due to the case-by-cnse approach depending on which SCD algorithm adopted. Although it is ideal construct unified framework for the incorporation PK, this rase-by-case approach Algorithm 2 originates from the differences how prior knowledge be adopted in each SCD algorithm. Therefore, for simpler interpretation, from practical point of view,
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Algorithm Transformation from the probability matrix into the prior knowledge matrix
Input 1: probability matrix (Ptj)
Input 2: SCD) method S E { PC, Exact Search, DirectLiNGAM
Input 3: probability criterion for the forbidden causal relationship
Input 4: probability criterion for the forced causal relationship 02
Output: prior knowledge matrix PK- = (PKs))
for = to n do
for to do PK; :j Unknown
if j then
iK = Forbidden
else
if Pa < a₁ then
iK Forbidden
else if (Ptj 2 az) and (S * Exact Search) then
PK Forced
end if
end if end for end for if = DirectLLNGAM then
PK A(PKK (acyclic transformation) end if return PK
case of DirectLiNGAM, because prior knowledge used for the decision of the causal order in the algorithm, the prior knowledge matrix must be an "acyclic" adjacency matrix when it is represented in the form of a network graph. Thus, when S = DirectLiNGAM and PK is cyelic, additional transformation algorithm A is required. In addition, several acyclic transformation patterns can exist; only one acyclic matrix with some criteria should be selected. The algorithm for the transformation and the matrix selection criterion in this study are explained in Appendix
Theoretical Computation Time and Scalability is also valuable to discuss the computation time and scalability with respect to the number of variables, as our proposed method includes steps involving the LLM in addition to the calculations performed by the SCD algorithm. The total time required for machine processing T(SCD, LLM, n. N, PK) is expressed as follows:
T(SCD, LISCD,LLM, N, M, PK)
Tstep. EStep.(SCDD. (SCD, n, N), (LLM,n)
+Tstep.3 7 (LLM, M) step. (SCD, N. PK)
+TAcyelic (SCD,
(1)
The variable SCD can be one of the following algorithms: PC, ExactSearch, or DirectLiNGAM, The variable LLM refers to the model adopted in this process. Furthermore, n denotes the number of variables, and N represents the number of data points in the dataset. The computation time of the transformation algorithm A, described Appendix F is denoted as TAcyclie (SCD, PK). When SCD is PC or ExactSearch, this value is zero because no transformation process for adoptable PKis required.
The SCD computation time, Istep. n, N), has the same scalability as that of the SCD computation. Similarly, (SCD, n, N, PK) represents the computation time of the SCD algorithm under the constraints of PK. Because the constraints imposed by PKreduce the search space of the SCD algorithm, it is expected that (SCD, n, N, PK) < (Step.((SCD) n, N). Furthermore, the stronger constraints PKimposes, the smaller "Step..(SCD n,N, N, PK) becomes.
recommended that the SCD algorithm adopted in this methad be determined immediately after the dataset for analysis is determined.

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However, the LLM computation times Tstep. (LLM, n)) and 3 M) have different scalability compared to the SCD computation times I N) and Tstop.4 n, N, PK). Tf we represent. the time for a single cycle of reading the prompt q and generation by an LLM as f(LMM, q), because all the LLM's tasks in Steps 2 and 3 can be carried out independently, T (LLM, n) and Tstep.s (LLM, n, M) can be expressed as follows:
2 n) = Σ
t(LLM, g
(2)
Stop.3 (LLM, M) M (LLMM, )
(3)
ifj
(2) (1) and f(LLM, 9: can be considered approximately Furthermore, the computation times t(LLM, Gi
independent of the pair of variables, we have t(LLM, 9i
(2)) = (LLM)) and t(LLM, a = (LLMM). Therefore,
Eq. 2 (3 are approximately expressed as follows:
Tstep. (LLM, = N(N - (LLM) = O(N3)
(4)
Tstep. (LLM, n, M) = MN(N 1)T2(LLM) = O(MN2)
(5)
Consequently, when the computational costs in the steps involving the LLM are estimated, the scalability described in Eq.
5 should be considered.
Finally, when SCD DiAM and PK has cyelic structure, Tecycii PK) becomes non-zero value. Although do not further discuss the cost of this process, discussed in Appendix F with an increasing number of cycles in PK, Tecyolic (SCD, PK) may increase rapidly because of the complexity involved in removing cycles.
3.2 Experiment Patterns of SCP
Related to (blank 5) and (blank 9) in Table | we conducted experiments using several patterns of SCP. The notations of the prompting patterns in the experiments are presented with explanations below:
Pattern 0: without SCP This pattern corresponds to the reference for the comparison with the other patterns, including SCD results in their prompts. Because the prompt template shown in Table L is not adequate for this pattern, we prepare a different template for Pattern 0, which is shown in Appendix
Pattern 1:
With the list of edges that appcared in the first SCD Directed or undirocted odges between F2 and Fy that emerged in the SCD are listed.
Pattern 2: With the list of edges with their non-zero bootstrap probabilitics Directed undirected edges between 2, and I, that emerged in the bootstrap process are listed with their bootstrap probabilities.
Pattern 3: With the list of edges that emerged in the first SCD with the calculated causal coefficients (only for DIMA) On the basis of the property of DirectLiNGAM, which outputs the causal coefficients with the DAG discovered in the algorithm, this pattern is attempted to elucidate whether more information, such as causal coelficients, addition to Pattern 1, can improve the performance of LLM-KBCI and the subsequent SCD with prior knowledge.
Pattern 4: With the list of edges with their non-zero bootstrap probabilities and calculated causal coefficients for the full dataset (only for DirectLiNGAM) We also attempt this pattern with the most information of the 1st SCD as mixture of Patterns 2 and 3.
InIn the PC algorithm, since it is possible that all edge directions determined by the orientation rules, the default output CPDAG, and undirected edges that appear as a; 2j with respect causal relationships between "a; and æy" in which the direction cannot. be determined, can be detected. The prompt template for reflecting this difference from directed edges is shown in Appendix [
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3.3 Datasets for the Experiments
Although several widely open benchmark datasets with well-known ground truths exist, particularly for Bayesian network-based causal structure learning (Scutari & Denis 2014), several of them are fully or partially composed of categorical or discrete variables. However, considering Patterns 3 and 4 for the experiments in this study, because the basic structure causal model assumes the continuous properties of all the variables, it is more effective to adopt benchmark datasets fully composed of continuous variables.
Consequently, we select three benchmark datasets for the experiments, as follows: 1. Auto MPG data [Quinlan 1993) (five continuous variables) 2. Deutscher Wetterdienst. (DWD) climate data [Mooij et al.) 2016 (iix continuous variables).
3. Sachs protein data (Sachs et al. 2005 (eleven continuous variables).
Furthermore, to demonstrate that GPT-4 can aid SCD with its domain knowledge, even if the dataset used in the SCD process and analytics on the dataset are not contained in the pretraining data of GPT-4, the proposed methods are also applied to our dataset of -ereennn results, which has not been disclosed and therefore not lcarned by GPT-4. To demonstrate that the proposed methods can be applied when the dataset could contain biases, which may lead to highly inaccurate SCD results, the health-screening datasel. for this experiment was sampled, and we deliberately chose subset where certain biases could be still present. Basic information on these datasets, such the first SCD results and the ground truths is presented in Appendix
4 Results and Discussion
In this section, we first present the experimental results on benchmark datasets with known ground truths, which are evaluated via several metries, as described in Section [.1 In addition, Section 1.2 reports the experimental results on our impublished health-screening dataset, demonstrating that the assistance of GPT-4 with SCP can help the output of SCD align more closely with the ground truths. Furthermore, we discuss the reliability of our method in Section
4.3 including simulations to identify both successful and failure cases. 4.3 we also discuss potential ial improvements in the prompting methodology for stabilizing GPT-4's confidence probability measurements, as well as realistic strategies for overcoming these issues in practical applications of our proposed method.
Finally, at the end of Section
4.1 Results in Benchmark Datasets
For the interpretation of the experimental results, we evaluate PK (for measuring the performance of the LLM-K -BM-KBCI with the prompts, including the first SCD results) and the adjacency matrix obtained in SCD with PK for each pattern (for measuring the performance of the SCD augmented with the LLM-KBCT), with the structural hamming distance (SHD), false positive rate (FPR), false negative rate (FNR), precision, adjacenda
and the F1 score, using the ground truth adjacency matrix GT as a reference.
All of these metrics are frequently used to evaluate how the results of the causal structure learning are close to the ground truths, and can be calculated solely from the adjacency matrix and GT, as shown in Appendix F.3 In addition, this paper presents an evaluation of the comparative fit index (CFT) (Bentler 1990 root mean square error of approximation (RMSEA) (Steiger & Lind 1980) and BIC (Schwarz 1978h of the cansal structure obtained in SCD with PK, under the assumption of
data !7 to evaluate the results with respect to the statistical validity of the calculated causal models. To evaluate the effect.
Although datasets can generally exhibit various types of bias- as selection bias, sampling bias, label bias, confirmation bias, and measurement bias-it it is often challenging to identify the specific biases present. As explained in Section [12] we selected a subsample that is much smaller than the original one, with which DirectLiNGAM produces the unreasonable edges from the perspective of domain experts, although that subsample dataset is randomly selected from the original dataset. In this context, as a result, there could be biases associated with particular attribute, although there is no arbitral process in composing this subsample. However, the proposed method remains effective regardleas of the types of biases present in the dataset. Therefore, we do specify the exact type of bias here.
17 Although this ussumption of Gausain data for the calculation of the CFI, RMSEA, and BIC, does not match the assumption of non-Gaussian error distribution in LiNGAM, we adopt those indices uniformly evaluate and compare the results with respect the same statistical method based the typical analysis using the structural equation model with the Thear-Gausian assumption, irrespective of the difference in the SCD algorithms.
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of PK augmentation by the LLM, the baseline result is that without PK (Baseline A), as reference for comparison with the SCD results augmented with PK. In contrast, to evaluate the effect of the SCP, the results with the prompt in Pattern 0 become the baseline (Baseline B), for comparison with the results obtained in other SCP patterns. The indices for all patterns on the DWD, Auto MPG, and Sachs datascts are summarized Table
Enhancing the performance with prior knowledge augmentation by GPT-4 One of the character- istics in Table 3 is that, in most cases, the result of SCD augmented with PK is more similar to GT than the first SCD result without prior knowledge (Baseline A). This bohavior interpreted as the knowledge-basse basod improvement of the causal graph by GPT-4 as a domain expert, which is qualitatively consistent with other related researches LLM-guided causal inference (Ban et al., 2023 Vashishtha et al. 2023). Moreover, in many of the cases of Auto MPG and DWD data, the precision or Fl score are higher after the SCD augmented with PK than the pure PK, which are conclusions of LLM-KBCI, while they are almost comparable in the cases of Sachs data. This comparison implies that even if the LLM-KBCI is not optimal, the ground truths can be better approached by conducting SCD augmented with the LLM-KBCL. In addition, the BIC decreases in almost all the patterns from the SCD result without PK (Baseline A). The aforementioned properties suggest that knowledge- based augmentation from GPT-4 can improve the performance of SCD, indeed, in terms of consistency with respect to domain expert knowledge and the statistical causal structure. However, the amount of improvement can differ depending on the number of variables and the methods of SCD.
Dependence on the number of variables In the case of Auto MPG data with only five variables, the amount of improvement for each SCD method is almost constant among all the prompting patterns. One of the possible reasons is that, within relatively small numbers of variables, the amount of information in the SCP becomes small, and the difference in the inference performance of GPT-4 among the prompt patterns becomes subtle. Moreover, because the space for discovery also decreases as the network shrinks, the SCD algorithm may reach a single optimal solution, even if PK is different.
On the other hand, in the cases of DWD data with six variables and Sachs data with eleven variables, the difference in the amount of improvement becomes clearer depending on the prompting patterns. This implies that the threshold of the number of variables over which the quality of the PK and SCD results depend on the amount of information included. In the SCP for GPT-4, it is approximately five.
Moreover, in many cases of DWD and Sachs data, particularly for Exact Search or DirectLiNGAM, the precision and Fl score of PK in Pattern 0 (Baseline B) are usually smaller than those of any of the other patterns, in which GPT-4 experiences SCP. This finding supports the performance enhancement of LLM-IBCI by the SCP.
Prompting pattern dependence on SCD methods On the other hand, considering the output of the SCD augmented with PK, Pattern 0 (Baseline B) stably indicates relatively higher performance among all the patterns in terms of both domain knowledge and statistical model fitting. Furthermore, the results of Patterns 0 and 1 are almost the same when the PC or the Exact Search algorithm is adopted; in particular, the result of Pattern 0 with the PC algorithm on Sachs data is superior to that of Pattern 0.
Although it is difficult to explain this behavior, one of the possible reasons, if we focus only on the results on Sachs data, is that we adopted the ground truths partially determined by Bayesian network inference (Sachs let al. 2005). Indeed, the first SCD result in PC is already relatively close GT, as shown in Figure 12 (a), and we interpret that, in this situation, the performance of SCD with PK cannot be improved.
The scenario differs when NGAM is adopted. The performance of the SCD with PK either in Pattern or 2, remains overall superior to that of Pattern 0 (Baseline B) from both statistical and domain expert. points of view. This implies that the SCP can elfectively improve the performance of Direct L...A..
However, from the analysis of Patterns and 4, in which GPT-4 is prompted with the causal coefficients of the first SCD results, it is also revealed that prompting with a greater amount of statistical information does not always lead to improved SCD results. In particular, although PK in Pattern 4 is closer to the ground
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Table 3: Comparison of the SCD results in all the experimental patterns. While the SHD, FPR, FNR, precision, and the F1 score are compared to evaluate how close the results are to the ground truths, CFI, RMSEA, and BIC are compared to evaluate the statistical validity of the calculated causal models. Lower values are superior for the SHD, FPR, FNR, RMSEA, and BIC, and higher values for the precision, F1 score and CFI. The numbers in parentheses indicate the SHD, FPR, FNR, precision, and the F1 score of PK with ground truths, to evaluate the performance of LLM-KBCL. The values highlighted in bold are the optimal results among Patterns 0-4, if the dataset and the SCD algorithm are fixed. Baseline A is used for comparison with the SCD results with PK generated by the LLM, to evaluate the effect of PK augmentation by the LLM. Baseline B is used for comparison with the results obtained in other SCP patterns, to evaluate the effect of the SCP.
Auto MPG data with continuous variables
SCD algorithm
Pattern
SHD.
FPR.
FNR.
Precisiont
Flacoret
CFI:
RMSEA,
BICJ
wo PK (Baneiie A)
8
0:40
0.80
0.11
0.14
1.00
0.50
71.65
Pattern [Baseline B)
(5)
0.15 (0.25)
0.20 (0.20)
0.37 (0.41)
0.67 (0.57)
1.00
0.07
65.62
PC
Pattern I
4 (7)
0.15 (0.30)
0.20 (0.20)
0.57 (0.40)
0.67 (0.53)
1.00
0.00
59.71
Pattern 2
3 (6)
0.15 (0.30)
0.20 (0:20)
0.57 (0.40)
0.67 (0.53)
1.00
0.07
65.62
(Baselle A)
0.25
0.40
0.38
0.46
1.00
71.61
Exact Search
Pattern D [Baseline B)
(5)
0:20 (0:25)
0.20 (0:20)
0.50 (0.44)
0.62 (u.57)
1.00
0.03
71.59
Pattern 1
5 (5)
0.20 (0.20)
0.20 (0:20)
0.50 (0.50)
0.62 (0.62)
1.00
0.07
65.62
Pattern
(5)
0.20 (0.25)
0.20 (0:20)
0.50 (0.44)
(0.57)
1.00
0.09
71.59
Baseele
0.40
0.80
0.11
0.14
1.00
0.03
71.61
Pattern 0 [Buseline B3)
3 (5)
0.15 (0.25)
0.20 (0.20)
0.57 (0.44)
0.67 (0.57)
1.00
0.07
65.62
DirectLINGAM
Pattern 1
3 (3)
0.15 (0.30)
0.20 (0.20)
0.57 (0.40)
0.67 (0.5:)
1.00
0.07
65.62
Pattern 2
(G)
0.15 (0.25)
0.20 (0.20)
0.57 (0.44)
0.67 (0.37)
1.00
0.07
65.62
Pattern 3
(6) 0.20 (0.35)
0.20 (0.20)
0.50 (0.36)
0.62 (0.50)
1.00
0.00
71.65
Pattern 4
3 (7) 0.15 (0.30)
0:20 (0:20)
0.57 (0.40)
0.67 (0.53)
1.00
0.07
65.62
Although there are no significant differences in the metrics between the prompting patterns, it is clearly
observed that the SCD results augmented with PK are more similar to GT than the initial SCD results without prior knowledge (Baseline A).
2. DWD climate data with 6 continuous variables
SCD algorithm
Pattern
SHD.
FPR.
FNR
Precisiont
Flscoret
CFI:
RMSEA
BICL
(Baeelie A)
9
0.20
0.83
0.15
0.90
0.22
69.32
Pattern 0 [Baseline B)
5 (8)
0.03 (0.20)
0.67 (0.33)
0.67 (0.40)
0.44 (0.50)
0.71
0.36
32,70
PC
Patter I
5 (9)
0.03 (0.23)
0.67 (0.33)
0.67 (0:36)
0.44 (0.47)
0.71
0.36
32.70
Pattern 2
(8)
(0.20)
0.67 (0.33)
0.67 (0.40)
0.44 (0.50)
0.71
0.36
32,70
PK (Baseline A)
6
0:20
0.17
0.45
0.59
0.91
0.28
92.87
Exact Search
Pattern 0 (Baseline B))
5 (8)
0.10 (0.20)
0.33 (0.33)
0.57 (0.000
0.62 (0.54l
0.98
0.12
58.38
Pattern 1
(G)
0.10 (0.13)
0:33 (0.17)
0.57 (0.56)
0.62 (0.67)
0.91
0.19
57.73
Pattern 2
(9)
0.13 (0.23)
0.33 (0.33)
0.50 (0.36)
0.57 (0.47)
0.91
0.20
63.58
PK Paseeie A)
10
0.33
0.67
0.17
0.22
1.00
0.00
09.53
Pattern 0 [Buselite B))
(8)
0.07 (0.20)
0.33 (0.33)
0.67 (0.40)
0.67 (0.50)
1.00
0.00
52.67
DIGMM
Pattern
(8)
(0.10)
0.83 (0.83)
0.25 (0.25)
(0.20)
0.61
0.43
38.03
Pattern 2
4 (7)
0.03 (0.17)
0.50 (0.33)
0.75 (0.44)
0.60 (0.53)
0.98
0.09
40.80
Pattern 3
5 (6) 0.10 (0.13)
0.33 (0.33)
0.57 (0.50)
0.62 (0.57)
0.93
0.16
57.90
Pattern
(6)
(0.17)
(0.16)
0.57 (0.50)
0.62 (0.62)
0.92
0.18
57.80
It is confirmed that the outputs of LLM-KBCI in many of Patterns 1 4 are likely to approach the ground
truths more closely than those in Pattern 0. The performance of Exact Search in Pattern 1 (with the SCP) is
the similar in quality to that in Pattern 0. The output of DirectLiNGAM in Pattern 2 (with SCP) can be a
superior causal model than that in Pattern 0.
Sachs' protein data with 11 continuous variables
SCD algorithu
Pattern
SHD
FPR
FNR.
Precision
Flscoref
CFI1
RMSEAA
BIC
wo PK (Baseline A)
24
0.16
0.47
0.38
0.44
0.99
0.05
204, 15
PC
Pattern D [Baselite B)
15 (19)
0.04 (0.11)
0.58 (0.17)
0.67 (0.48)
0.52 (0.50)
0.89
0.16
166.91
Pattern 1
25 (43)
0.17 (0.53)
0.68 (0.16)
0.26 (0.23)
0.29 (0.36)
0.97
0.11
281.58
Patter 2
23 (23)
0.13 (0.24)
0.74 (0.32)
0.28 (0.35)
0.27 (0.46)
0.97
0.09
231.27
WO (Bsellie A)
31
0.26
0.68
0.18
0.23
0.59
0.07
374.35
Exact Search
Pattern [Bueeine B)
(19)
0.07 (0.11)
0.58 (0.47)
0.53 (0.48)
0.47 (0.50)
0.91
0.16
202.97
Pattern 1
17 (15)
0.05 (0.06)
0.68 (0.58)
0.55 (0.57)
0.40 (0.48)
0.87
0.20
158,26
Pattern 2
16 (14)
0.11 (0.14)
0.53 (0.32)
0.45 (0.48)
0-46 (0.57)
0.95
0.12
267 .53
wo (Bssellleee A)
29
0.25
0.47
0.28
0.36
1.00
0.01
410.23
Pattern (Baseline B)
17 (19)
0.07 (0.11)
0.53 (0.47)
0.56 (0.48)
0.51 (0.50)
0.91
0.16
203.02
DirectLINGAM
Pattern 1
15 (13)
0.07 (0.08)
0.47 (0.37)
0.59 (0.60)
0.56 (0.62)
0.88
0.18
2201.3
Pattern 2
22 (21)
0.14 (0.18)
0.63 (0.17)
0.33 (0.36)
0.35 (0.13)
0.70
0.31
269.76
Pattern 3
22 (23)
0.15 (0.18)
0.53 (0.63)
0.38 (0.33)
0.42 (0.39)
0.92
0.16
301.51
Pattern 4
20 (16)
0.12 (0.16)
0.53 (0.26)
0.43 (0.47)
0.45 (0.57)
0.59
0.19
264.97
Although the prompting patterns that lead to the best performance differ, a similar tendency to that observed in the DWD climate data is observed.
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(a) Without prior knowledge
(b) With prior knowledge generated from Pattern2 and 4
IlbAlc
LDL
0.30
Age
BMI
0.03
DM
0.08
0.05
0.17
0.90
0.34
0.29
0.10
Waist
-0.30
0.32
0.30
0.21
0.07
Age
DBP
Waist
SBP
0.79
0.10
0.75
The proposed method of generating prior knowledge with SCP in GPT-4
SBP
DRP
Figure 2: Results of DirecLLiNGAM 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" influenced by "HbAlc." 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.
truth matrix than that in Pattern O in the DWD or Sachs data 18 the final SCD result augmented with PK in Pattern 4 is inferior to that of Pattern 0. One of the possible reasons for this may be the pruning of the candidate edges suggested from PK in the SCD process. To elucidate this behavior, further research is required on what type and amount of information in SCP can truly maximize the performance of SCD.
4.2 Results for Selected Subsample of Health-Screening Data Excluded from the GPT-4 Pretraining Dataset
It is difficult to assert that this improvement is solely duc to the LLM's high performance in KBCI from the experimental results on open benchmark datasets, because it cannot be determined whether the improvement stems from the LLM's recall of the data obtained during the pretraining process on these datasets. Furthermore, assuming realistic situations, is also important to confirm the robust effectiveness of this method, even if the range of the available dataset for statistical causal inference is limited to observation data, which may be statistically biased, and trivial causal relationships are not apparent in SCD without prior knowledge. Therefore, we also apply the proposed methods to the sub-dataset of health-screening results, which has been sampled from the entire datase [9 and the natural ground truth is not presented in the SCD results without screening data from Japanese health insurance records.
PK. The original dataset consists of personal Owing to legal restrictions in Japan, the raw data are not publicly available. Anonymized data are used in a restricted environment, are not directly exposed to the Internet for analysis, and are not shared with third parties. On the basis of these properties, it is reasonable to conclude that our unpublished health-screening dataset was not included in the pretraining data of GPT-4, although it is impossible to strictly prove the absence of any overlap between our dataset and the pretraining data, as noted in Appendix C.4
In Figure aa), the result of DirM without PK is shown, and unnatural directed edges to " "Age" from other variables are suggested, although the parts of the ground truths from expert knowledge are reversed relationships from these odges, such as " assisted by PK generated from GPT-4 with the SCP in Pat 2 and 4, the causal graph becomes more natural: "Age" is not influenced by other variables, and the ground truth " "Age""""Hbal detected without PK in this randomly selected subset, appears in the causal graph, as shown in Figure 2()). Because this sub-dataset and the analysis results are not disclosed and have been completely excluded from the pretraining data for GPT-4, GPT-4 cannot respond to prompts asking for causal relationships merely by reproducing the knowledge acquired from the same data. On the basis of the above, is verified that the assistance of GPT-4 with SCP can cause the result of SCD to approach the ground truths to some extent,
However, when the causal discovery is
which cannot be
18This fact reinforces the reliability of our interpretation that the SCP enhances the performance of L.M--KRCT. 19The details of the sampling method for this experiment are presented in Appendix
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Table 4: Quantitative evaluation of the characteristic results of SCD in the proposed methods on the subset of health-screening data, which could contain certain biases. A: Elements of P generated in each prompting pattern for all the appropriate ground truth causal relationships in these variables. The values enclosed in parentheses the DirectLiNGAM algorithm without PK. It is suggested that the mean probabilities of the positive response on the causal relationships from GPT-4 are influenced by the results of SCD and bootstrap probabilities when they are included in SCP. Moreover, all the probabilities of reversed, unnatural causal relationships in which "age" is influenced by other factors are extremely close to zero.
the bootstrap probabilities of the directed edges in
B: CFI, RMSEA, and BIC were evaluated on the basis of model fitting with the structure discovered by DirectLiNGAM, under the assumption of linear-Gaussian data. The values enclosed in parentheses are the statistics of the structure calculated without PK.
It can be inferred that SCP with bootstrap probabilities in Patterns 2 and 4, enhances the confidence in "Age" "DD"" by GPT-4 and improves the BIC compared with Pattern 0.
Pattern
Pattern
Pattern 2
Pattern 3
Pattern
"Age" "rre""""Bie "BMI"
0.901
0.076
0.093
0.306
0.037
A. Probability of repro- ducing ground truth from GPT-4
(0.166)
0.626
0.302
0.207
0.235
0.795
(0.550)
"Age""** ""DB"" (0.308)
0.001
0.019
0.115
0.095
0.926
"Age" "HbAle"
0.986
0.170
0.723
0.046
0.176
(0.327)
B. Statistics of linear- Gaussian fitting with the results of DirecLLiNGAM
CFI1
(1.002)
0.999
0.992
0.995
0.986
0.995
RMSEAL
(0.000)
0.018
0.054
0.032
0.057
0.032
BIC
(124.332)
103.581
89.738
89.740
103.506
89.740
even when the dataset not learned by GPT-4 and could contain biases. This finding suggests that our proposed method can work well with the domain knowledge acquired by the LLM during training, even if the exact same data are not memorized by the LLM. Moreover, the effectiveness of the proposed method demonstrated on both open benchmark datasets and unpublished health-screening datasets, also supports the validily and applicability of existing works (Ban el al. 2023 Vashishtha et al. 2023 Khatibi et al. 2024), where knowledge-basc based improvements with LLMs of the causal graph on open benchmark datasets have been demonstrated via their own methods with unique originality. Our research, by showing versatility across both open and unpublished data, further enhances the validity of these existing works.
For further clarity regarding the behaviors of SCP, the mean probabilities of the positive response on the causal relationships from GPT-4 for ground truths in the health-screening data, in addition to the statistics of the fitting results with the structure suggested by DirectLiNGAM with the SCP, are presented in Table 4
Finally, it is also confirmed that the BIC decreases with the assistance of GPT-4 compared with that without PK. In particular, the values in Patterns 1, 2, and 4 are lower than those in Pattern 0. This suggests that SCP can contribute to the discovery of causal structures with more adequate statistical models.
4.3 Discussion of Reliability Evaluations from the Domain Knowledge and Prevention of Misuse Toward Practical Applications
However, from realistic point of view, it is also impossible to control the LLMs as perfectly as possible, for adequate output of the LLM-KBCI tasks. Therefore, for the practical application of the proposed method, it is important not only to confirm the effective points of view shown above, but also, to analyze the case of failed oulputs of the LLM-KBCL. In fact, as shown in Table 4 while the existence of "A "Age" le" is supported in the probabilities over 0.95 in Pattern without SCP, the probability decreases for other patterns with SCP. This behavior implics that while GPT-4 itself, without any prompting, accepts " "Agc">>"Hbi as one of the ground truths, the SCP, including the result that does not statistically support this edge, reduces the confidence of GPT-4 in this causal relationship.
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The primary cause of this behavior is reliance solely on the knowledge possessed by GPT-4, and the inherent performance limitations of GPT-4 itself may influence these results. Generally, it is challenging to comprehensively confirm what LLMs know or do not know. Although benchmark tests or equivalent performance measurements, as described in the development reports of each LLM, can confirm their knowlodge to some exlent, it is practically difficult. to exhaustively grasp all of their knowledge (Kaddour et al. 2023 Pezeshkpour 2023).
Morcover, although we have adopted several prompt techniques to reduce hallucinations much possible with our method, we cannot predict when and how hallucinations might occur during practical applications. Therefore, it is necessary to recognize this point and exercise cantion during deployment. Specifically, examining the impact of prompting patterns reveals that, while incorporating SCD results through the SCP tends toimprove outcomes overall compared with not including them, at a granular level such as each causal relationship between pair of variables, SCP might inadvertently guide LLMs' judgment in the wrong direction.
Recognizing these issues, mechanically applying method without considering potential countermeasures raises concerns, especially when reliable decisions are expected in critical domains such as healthcare. Therefore, in this section, we also proposc a simulation method to verify these issues and conduct experiments to discuss the two lypes of risk mentioned above.
In particular, on the basis of the discussion of causality in the realm of health-screening as a use case, we demonstrate that certain patterns exist where even for GPT-4, it is obvious that causal relationships cannot exist, and that false positives do not occur even if GPT-4 undergoes SCP with the wrong causal relationships suggested by SCD. In addition, identify patterns that are considered ground truth from domain knowledge but are not necessarily obvious to GPT-4, resulting in a risk of false negalives through SCP. Furthermore, the potential improvement of the prompt methodology for stabilizing the GPT-4 confidence probability measurement is also discussed. Finally, we discuss realistic strategies to overcome these problems when applying our proposed method.
Simulation Methods for the Assessment of Robustness and Vulnerabilities of the Proposed Method and the Influence of SCP
For the simulations mentioned above, we make a minor change in the method shown in Figure L and the overall process of these simulations is illustrated Figure 3 To investigate quantitatively the effect of SCP including the causal coefficients or bootstrap probabilities, on the confidence GPT-4 causal relationships, we focus on the case of DirectLiNGAM.
Process A is based on the first step in Figure D and "pseudo-results" of SCD is prepared for SCP. We prepare the SCD results from DireetLNGAAM, and find the edge that should obviously not appear, or should appear from the domain knowledge. By changing the causal coefficient e and bootstrap probability b of that edge from the DirectLiNGAM result, "pseudo-results" can be easily manufactured. Processes B and C correspond to the second and third steps Figure [ and we evaluate the average probability Pty b) of the output in Process C, as function of the input causal coefficient e and the bootstrap probability b.
To clearly examine the dependency of Pij on and b, consider the following prompt patterns from all the patterns shown in Section 3.2
Pattern 2: Prompting only with the bootstrap probabilities (without assigning causal coefficients).
In our simulations, Pij is taken in this pattern while varying b in increments of 0.1, from 0 to 1.
Pattern 3: Prompting only with the causal coefficients (without assigning bootstrap probabilitie)).n our simulations, Pij is taken in this pattern while varying e in increments of 0.05, from -2 to 2.
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Process A: Preparing Psuedo-Results Statistical Causal Discovery
Causal Graph Based LiectLiiNGA
Bootstrap Probabilities of Directed Edges
HbAle
LDL
0.30
CafectediCausee
BMI
Waist
SBP
HbAfc
Age
0.05
BMI
0.158
0.076
0.381
0.927
0.648
0.166
0.08
0.99
Waist
0.841
0.024
0.124
0.577
0.222
0.480
Whist
00.30
0.32
0.791
0.122
0.813
0.581
0.038
0.30
0.07
DBP
0.502
0.078
0.187
0.288
0.080
0.308
Age
DBP
HbAtc
0.000
0.000
0.000
0.000
0.033
0.327
0.10
0.75
0.139
0.014
0.000
0.003
0.026
0.001
SBP
0.457
0.385
0.448
0.296
0.025
Knowledge Generation on Causal Relationships by the LLM with ZSCOT for Varlous and b
Process C: Knowledge Integration and Evaluation of the Probability of Causal Relationship
Acsording the noulla cso abow,, il has bewn ditarmiredd that there may direct mpact a change in HbAfc on Age
with a bootstrp probobi by it and the confiiciet is lkety Then, your lask is to interpres not this resuit from domain knowladge perspoctivo and ceserminee whether this studitccalty sugpested typotheolc is plausible in the context of the domain.
Considering objectively this discussion above, IHbbAic changed, will have a direct impact on Ago? Please arswer this quidiio with or sno>
Plasss provide an expleradion leceragua your expert
kncel lege on catuaal retatiorani belewan HaAfe and Age. causal soovery result...
assess naturainess
Probability answering "Yes": Pyea(b.c) Probability answering "No": (b.
domain suggested the LINGAM results- thal relationahlo At (Hb/1 c) increase
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 almost the same as the proposed method illustrated Figure
Pattern Prompting with causal coefficients and bootstrap probabilities (assigning both). In our simulations, Ps is taken in this pattern while varying b in increments of 0.1, from 0.1 to 1 and varying in increments of 0.1, from -1 to 20
we adopted 1PT-4-1106-prevve set the temperature to 0.7, and use a single-shot measurement of repetition count of M = 5, calculating the average of piy(e, b) over five runs as pij(e, b).
In the simulation, following the experimental setup shown in Section 3.1
By examining the dependency of the average probability (ry b) on the coefficient. and bootstrap probability b, we analyze the performance of GPT-4 and the influence of SCP. If Pty consistently takes values close to 0 regardless of these parameters, it suggests that GPT-4 has firm domain knowledge for recognizing edge as extremely unnatural (in the case of 0) or natural (in the case of 1). Conversely, if Pty (c, b) changes depending on e or b, it indicates that GPT-4's knowledge about the existence of the edge is not firm, and that SCP can influence its judgment.
Simulation A: LLMs' Confidence in Edges Where Causal Relationships Are Recognized as Unnatural (Discussion on Firmly Successful Cases)
First, as in Simulation A, examine cases where obviously unnatural edges appear, such "HbA1c" "Age", and investigate whether changes in causal coefficients or bootstrap probabilities affect the confidence probabilities. We base this analysis on the DirectLiNGAM results from subsampled datasct of 1,000 instances where such edges actually appear, as shown in Figure a). Process A in Figure 3 clearly illustrates
20 Although the experimental range of in Pattern 3 2 for thorough investigation of the dependence input shrink this range in Pattern into <eS 1, for practical feasibility the experimenta in the two-dimensional parameter space
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(a)
(b)
Probability LLM-KBCI p
3.0x10"
1.0x10
Probability from LLM LLM-KBC) KBCI
BM -> Age
BMI >> Age
2.5
Waist
0.8
Waist
Age
Age
2.0
0.8
1.5
1.0
0.5
0.2
0.0
Input Causal Coeflicient
Input Bootstrap Probahility
Figure 4: Results of Simulation A through the methodology illustrated in Figure 3 with the pseudo-resules based on the SCD results for the subsampled health-screening dataset, which is used in the experiment of Section 4.2 Simulations were conducted on unrealistic edges "BMI" + "Age", "Waist" - "Age" and "HbAlc" + "Age." (a) Results for Pattern 2 (various values of causal coefficient c are prompted with Process B). (b) Results for Pattern 3 (various values of bootstrap probability are prompted with in Process B). Considering that the maximum values of the left vertical axes for these graphs are smaller than 1.0 10-5, GPT-4's confidence probability in these unrealistic edges is fixed around 0, regardless of the causal coefficients bootstrap probabilities in the pseudo-results of SCD.
Table 5: Results of linear regression of Pty with the causal coefficient and the bootstrap probability b, for the results of Simulation A on unrealistic edges "BMI" - "Age," "Waist" + "Age," and "HbAlc" + "Age." The values enclosed in parentheses are the root mcan squared error (RMSE) obtained through regression. Although we do not discuss whether these coefficients and constants are signíficantly different from at any significance level, obviously illustrated that Pij does not depend on e or for the directed edges above, since all the values are approximately (all of the absolute values are less than 10 10-6).
Causal Relationship
Variable of Regression
Pattern 2
Pattern 3
Pattern
7.7 10-3
1.0 x 10-
3.3 x 10
Constant
(+1.2 10-8)
(422.8 10-8)
(166.8 10-9)
"BMI" " "Age"
3..3 10-8
-9.8 x 10-9
Causal Coefficient e
(12.4 10-3)
(15.22 10-9)
-3.3 x 10-9
1.7 x 10
Bootstrap Probability b
(+2.1 x 10-5)
(+1.1 x 10
1.2 10
5.3 x 10
-1.5 x 10
Constant
(#7.4 x 10 9)
(+1.5 x 10 8)
(#3.0 x 10 9)
"Waist" + "Age"
-25 10
-2.1 10
Causal Coefficient
(+1.3 10-8)
(#2 x 10-8)
-9.4 x 10-9
7.9 10-8
Bootstrap Probability b
(+1.3 x 10-8)
(+4.8 x 10-8)
5.7 x 10-10
2.1 x 10
6.8 x 10
Constant
(15.7 x 10-9)
(18.5 10-9)
(L3.3 x 10-5)
"HbA1c" - "Age"
1.7 x 10
2.2 x 10-9
Causal Coefficient
(17.2 x 10-9)
(.2.5 x 10-8)
8.6 10-9
5.99 10-8
Bootstrap Probability b
(19.7 x 10-9)
(15.3 x 10-8)
how the causal graph and bootstrap probability matrix are modified and mounted in SCP, in the case of examining "HbAlc" - "Age". In addition, we also examine the cases of "Waist" " "Age" and "BMI" " "Age", all of which are similarly unnatural paths, since "Age" determined only by birthday and the passage of time.
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Figure 4 shows the values of Pij and its dependence on causal coefficients in (a) and on bootstrap probabilities in (b). These graphs confirm that, regardless of the values of or b, the confidence probabilities in causal relationships of "HbAlc" + "Age", "Waist" + "Age" and "BMI" + "Age" remain almost zero (below
1 x 10 9)).
Moreover, the results of the regression analysis are also shown in Table Here, the function for the regression set as follows:
Pu + ac
(pattern 2)
P.
Po + 33
(pattern 3)
(6)
Po + ac + 36 (pattern 4)
Here, a is the coefficient for с (the causal coefficient in the pseudo-results of SCD), 3 is the coefficient for (the bootstrap probability in the pscudo-results of SCD), and po the constant. From the regression results shown in Table [ it can be confirmed that Pij for the unnatural causal assumption "HbAlc" "Age," " "Waist" "Age," and "BMT" + "Age" is indeed independent of and staying around 0.
This finding suggests that, regardless of how the SCP is performed, the judge of GPT-4 is firm, and it can correctly judge that such unnatural edges as that Pij for unnatural causal assumptions "HbAlc" - "Age", "Waist" + "Age" and "BMT" + " "Age" should not appear. Therefore, it is possible to identify these unnatural causal hypotheses that even GPT-4 can reject regardless of SCP through the experiments above, and our method indeed effectively contributes to gencrating prior knowledge for SCD, which effectively avoids the risk of false positives. As result, the proposed method makes it possible to focus on truly possible causal relationships from the experts' point of view.
Simulation B: LLMs' Confidence in Edges Where Causal Relationships Should Be Recognized and the Influence of SCP (Discussion on Failure Cases)
On the other hand, it is also important to discuss how the LLMs are confident in the causal relationships that are widcly accepted as ground truths from an expert's point of view. To clarify this problem, we try Simulation B, the method of which is almost the same that of Simulation A shown in Figure except for the targeted edges in this simulation, and the base of the pseudo-results included in SCP.
Although the basic experimental processes of Simulation B are the same as those of Simulation A illustrated in Figure 3 there are two types of modifications from Simulation A to demonstrate the GPT-4's confidence test in ground truth directed edges as follows:
The basis of the pscudo-results generated in process A is replaced with the DirectLiNGAM results on "entire" health-screening data with 123151 points, as illustrated in Figure 5 Since this basis holds all the ground truth directed edges, the causal coefficients and bootstrap probabilities of these edges can be easily modulated in Process A.
The modulated directed edges are replaced with "Age" - "BMI," " "Age" "SBP," " and "Age" + "HbAle." (from "HbAle" + "Age," "Waist" + "Age," and "BMI" "Age")
"Age" + "DBP," "
The experimental results in the case of "Age" - "HbAlc" are graphically illustrated in Figure as examples, and the entire results of linear regression of Pij with causal coefficient c and the bootstrap probability b are shown in Table 6 From Figure t (a), although a large and irregular fluctuation of pij is clearly observed, the dependence of Pty on the causal coefficient e in the case of " "Age" + "HbAlc" is also confirmed: whereas 0 is satisfied, it becomes more stable and often approaches when c 0 is satisfied. Conversely, illustrated in Figure t (b), the dependence of Pty on the bootstrap probability b is more unstable than that on the causal cocfficient c. However, it is also clearly confirmed that Pij never becomes stable even when b approaches 0 or 1.
Pij is relatively unstable and rarely approaches when
2or more strict discussion, since the range of the confidence probability Pty is 0 Piy & is more natural introduce logistic function for fitting. However, simply understand the dependence of Pij on we tentatively adopt the lincar function for the regression in this paper.
22eThe causal graph and bootstrap probability matrix are shown in Appendix
C.44
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Pseudo-Results of SCD Simulation (Testing the Influence of SCP on GPT-4's Confidence Probability Ground Truth Edges)
Causal Graph Based on DirectLiNGAM for entire health dataset with 123151 points
Bootstrap Probabilities of Directed Edges
EffactediCause
BMI
Waist
SBP
DBP
HbA1c
LDL
Age
Age
0.000
0.000
1,000
1.000
1.000
1,000
Waist
1.000
1.000
1.000
1.000
1,000
SBP
1.000
0.000
1.000
0.723
0.724
1.000
HbAle
LDL
0.05
0.16
0.000
0.000
0.000
1.000
1.000
1,000
1,25
0.02
HbAfc
0.000
0.000
0.000
0.000
1.00x
b
LDL
0.000
0.000
0.000
0.000
0.000
0.000
11.00
DRP
Ago
0.000
0.000
0.000
0.000
0.000
0.000
0.28
1.10
DMI
1.05
0.37
0.04
2.39
Figure 5: Example of pseudo-results of Dire in the entire health-screening dataset with 123151 for Simulation B. In this example, the basis of the initial DirectLiNGAM results shown in Figure 13 the causal coefficient and the bootstrap probability of the directed edge "Age" + "HbAlc" are replaced with the variables с and b, respectively. (The value of the causal coefficient without replacement 0.02, and the bootstrap probability 1.000.) Because of the large number of data points the entire health-screening dataset, some directed edges, including the ground truth bootstrap probabilities, are 1.000. In Simulation B, in addition this example, the pseudo-results modulating the causal coefficients and bootstrap proba bilities of "Age" "BMI," "Age" + "SBP," and "Age" + "DBP," are also embedded similarly to Figure
Moreover, the results of linear regression of Piy with b are summarized in Table 6 for all the directed edges of "Age" + "BM1," "Age" + "SBP," "Age" "DBP, and "Age" + "HbAlc." In contrast to the results of Simulation A illustrated in Table 5 all the absolute values of the estimated coefficients and constants are greater than 0.01. In addition, many of the estimated values are considered statistically significant at the % lovel. These results suggest that GPT-4's confidence probabilitics of these dirccted edges, which have been accepted as ground truths by medical experts, can be somehow influenced by the incorporation into SCP. Moreover, the minus coefficients of are suggested in Pattern 2 of " "Age" + "SBP." From this result, it can be interpreted that the higher the bootstrap probability b, which indicates greater likelihood of statistical causal relationships, can sometimes lead to lower confidence probability of GPT-4, although the detailed mechanism is unknown. Therefore, it must be recognized that SCP can also induce the risk of false negatives, especially when LLMs are not absolutely confident in the judgment of causal relationships. Adopting those uncortain results as prior knowledge could lead to incorrect causal graph generation.
or
Missing true causal relationships critical, especially in important domains such as healthcare. Therefore, for practical applications of the proposed method, we discuss below how to mitigate this risk from both technical and operational perspectives.
Toward Stabilization of LLMs' Confidence Probability Measurement with Improvement Prompting Techniques
For more practical use, the origin of the large fluctuations of Pú illustrated in Figure G should also be discussed. The main causes of variation in confidence probability are considered as follows:
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(a)
(b)
1.0
1.0
Age - HbAtc
nitiing
Probability from LLM-KBCI
0.8
Probability from LLM KBCI p
0.8
p 0.486 0.14bb
0.6
0.8
Age HbA1c
filing resull
0.757 0.105
0.0
0.0
Input Causal Coefficient
Input Bootstrap Probability
Figure 6: Representative results of Simulation B through the methodology illustrated in Figure 3 with the pseudo-results based on the SCD results for the full health-screening dataset shown Figure 5 Simulations were conducted on unrealistic edges "Age" "BMI," " " "Age" + "SBP," " "Age" "DBP," and "Age" "HbA1c," " we representatively show the results "Age" " "HbAlc."
(a) Results for Pattern 2 (various values of causal coefficient are prompted with in Process B). although large and irregular fluctuation of Pij is observed, the dependence of Pij on the causal coefficient in the case of "Age" + "HbAlc" is also confirmed: while Pij is relatively unstable and rarely approaches when < 0 is satisfied, it becomes more stable and often approaches 1 when <> 0 is satisfied.
(b) Results for Pattern 3 (various values of bootstrap probability are prompted with Process B). The dependence of Pij on the bootstrap probability more unstable than that on the causal coefficient However, it is also clearly confirmed that Pij never becomes stable even when b approaches 0 or 1.
The dependency of GPT-4's judgment in Process C of Figure 6
(Step 3 of Figure
2 on the content.
of the sentences generated in Process B (Step of Figure
Fluctuations in the log-probabilities in Process C (Step 3 of Figure 2 Section 3.1
itself (as already explained in
Although the latter can be mitigated by evaluating Pt obtained through multiple measurements. the former arises from the separation of GPT-4's judgment process into Processes and C (Steps 2 and in Figure 1
As explained in Sections 1.2 and 3.1 we have adopted the method of generated knowledge prompting (Liu) lt al. (022) to suppress hallucination. Therefore, each task of Processes B and (Steps 2 and in Figure 1 is relatively simple, and this separation also makes it possible to detect the tendency of the hallucination, which can further improve the performance of the LLM's causal reasoning with its domain knowledge. For example, if Pij generated in Process C (Step 3 in Figure 1 is completely different from the expectation of human experts, there may be a fatal defect in the factual statement or logic in the generated knowledge in Process B (Step in Figure D which leads to incorrect judgment in Process C (Step 3 in Figure D. In (Step 2 in Figure I from an expert's point of view can also be an effective process for improving the performance the proposed method. Moreover, this additional process with domain experts can lead to the discovery of new discussions on causal relationships, especially when there is no systematic understanding of the causality between pair of variables.
that case, checking the generated texts in Process
However, careful attention also required so that analysis of the long text generated Process B (Step in Figure [ is complicated, because all the tokens are randomly generated with the next token prediction on the basis of the probabilistic process. To illustrate this difficulty, analyze the fluctuation observed around
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Table 6: Results of linear regression of Pij with the causal coefficient с and the bootstrap probability b, for the results of the simulation on realistic edges "Age" + "BMI", "Age" "SBP", "Age" + "DBP" and "Age" "HbAle," which are strongly supported the medical domain and are interpreted as ground truths. The values enclosed in parcntheses the RMSEs obtained through regression. The asterisks *, **, and indicate that the coefficients or constants are significantly different from zero at the 10, 5, and 1 % levels, respectively.
Causal Relationship
Variable of Regression
Pattern 2
Pattern
Pattern
0.1347 (+ 0.0764)
0.6623
0.0558
Constant
(+ 0.0312)
(+ 0.0361)
"Age" "BMT"
-0.0491
-0.0661
Causal Coefficient
(1: 0.0267)
(4: 0.0276)
0.0243
0.6000 .*.
Bootstrap Probability b
0.1310)
(+ 0.0581)
0.7756 *.*
0,8106 ..*
0,8106 **.
Constant
(# 0.1180)
(#: 0.0255)
(# 0.0292)
"Age" "SBP"
-0.0553
-0.0114
Causal Coefficient
(#: 0.0218)
(+ 0.0223)
-0.8103
-0.0101
Bootstrap Probability b
(+ 0.2010)
(+ 0.0471)
0.5448
0.8058
0.3681
Constant
(# 0.1070)
(#: 0.0268)
(#: 0.0411)
"Age" "DBBP"
-0.0284
0.0548
Causal Coefficient
(+: 0.0229)
(+ 0.0314)
-0.3726
0.4405
Bootstrap Probability
(# 0.1830)
(+: 0. 0.0682)
01.4550
0.7570
0.1814
Constant
(+: 0.1330)
(+: 0.0247)
(+: 0.0393)
"Age" "HbAle"
0.1048
0.1915
Causal Coefficient
(1: 0.0211)
( 0.0300)
-0,1446
0,5272
Bootstrap Probability
(# 0.2270)
( 0.0633)
1.25 Figure G(a) in terms of the generated text in Process Whereas Pif becomes only 0.0493 when 1.25, Pij becomes 0.9833 when 1.30. To elucidate the origin of this sudden behavior, we compare the generated text in Process B for
1.25 illustrated in Table 7 with the text for = 1.30 illustrated in Table [ It is confirmed that both contents of the texts in these tables do not include critical errors, from the medical domain experts' points of view. However, although only the value e changed, the textual composition and the tones of generated knowledge in Process radically change as follows:
While the discussion is separated into the detailed aspects of the physiological factors of glucose metabolism in the generated text in Table 7 the text of Table g breaks down the issuc into the validity of statistical causal inference, not only from the medical point of view, but also from the perspective of statistical causal inference methodology.
While the statement in Table is based on the connection between variables, Table presents the discussion of causality more aggressively.
While the validity pseudo-result of the SCD is carcfully interpreted terms of the intorpretation of the magnitude of the causal coefficient Table 7 the discussion in Table g is positively stated including the ude interpretation and consistency with the previous studies.
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Table 7: Textual output in Process B of Simulation B in the case of "Age" + "HbAlc" when the causal
coofficient is modulated c 1.25 in SCP Pattern
Output in Process B for c 1.25 (Pattern 2)
The LiNGAM algorithm has suggested a direct causal relationship between age and hemoglobin Ale (HbAlc) with positive coefficient of 1.25. This implies that age increases, HbAle levels are also expected to increase, according to the model.
From the perspective HbAlc can be assessed for plausibility. Hemoglobin Alc is measure of the average blood glucose levels over the past two to three months and is used as an indicator blood sugar control in individuals with diabetes. It reflects the glycation of hemoglobin, process that is influenced by the concentration of glucose in the blood.
domain knowledge in medicine and epidemiology, the relationship between age and
As people age, several physiological changes can affect glucose metabolism:
1. Insulin Sensitivity: Aging is often associated with decrease in insulin sensitivity, which is also known as insulin resistance. This can lead to higher blood glucose levels because the body's cells are less effective at absorbing glucose from the bloodstream.
2. Pancreatic Function: Beta-cell function in the panereas may decline with age, leading to less insulin production. Insulin necessary for glucose uptake the cells, and a deficit can result in higher blood glucose levels.
Older adults may have changes in their lifestyle, such as decreased physical activity and altered dietary patterns, which can contribute poorer glycemic control.
3. Lifestyle Factors:
4. Comorbidities: With age, the prevalence of comorbid conditions that can impact glucose metabolism, such as obesity and chronic inflammation, tends to increase.
5. Hormonal Changes: Hormonal regulation changes with age and can affect glucose metabolism. For example, growth hormone levels and cortisol rhythms can influence blood sugar levels.
Given these factors, an increase HbAlc with age can be considered plansible from biological perspective. However, the coefficient of 1.25 is a standardized metric, and its interpretation depends on the scale of standardization. In nou-staudardize real- world setting, this coefficient would typically be much smaller, as the actual increase in HbAlc due to aging alone might be modest. But without the context of the units and the standard deviations of the age and HbAlc variables, it's difficult assess the magnitude this relationship's impact.
It's also important to note that while the causal relationship suggested by LiNGAM is statistically inferred, cansal claims should also be substantiated by domain knowledge and, possible, experimental or longitudinal studies. The plausibility of the relationship in this context is supported by domain knowledge, but other factors not included in the model could also be inftuencing both age and HbAle levels.
In conclusion, the statistical relationship discovered is consistent with domain knowledge about the physiology of aging and its effect on glucose metabolism. However, the strength and practical significance of this relationship would need further investigation, ideally through longitudinal studies and intervention trials, to confirm the causal pathways and to quantify the effect more precisely.
confidence probability generated in Process C: Prj = 0.0493
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Table 8: Textual output in Process B of Simulation B in the case of "Age" + "HbAlc" when the causal
coofficient is modulated as c 1.30 in SCP Pattern
Output in Process B for c 1.30 (Pattern 2)
The result from the LiNGAM analysis suggests that there is a direct causal effect of age on hemoglobin Alc (HbAlc) levels with coefficient of approximately 1.3. This implies that, in the structural causal model derived from your data, an increase in age associated with an increase in HbAlc levels. To interpret this finding from domain knowledge perspective, need to consider the biological relationship between age and HbAlc and whether the magnitude and direction of the effect make sense.
Hemoglobin Ale is a form of hemoglobin that is chemically linked to glucose. The HbAlc test measures the average blood gluense levels over the past 2 to 3 months. It is commonly used as an indicator of long-term glueose control individuals with diabetes and as a diagnostic tool for diabetes and prediabetes.
From a medical perspective, is known that as people age, they tend to experience various physiological changes that can affect glucose metabolism. This includes changes such as increased insulin resistance, decreased insulin secretion, and altered hormonal control blood glueose levels. These changes can contribute to higher blood glucose levels and therefore higher HbA1c levels in older adults.
The plausibility of the causal relationship suggested by the statistical analysis can be assessed by considering the following factors:
Biological Mechanism: There a clear biological mechanism by which aging can affect glucose metabolism and insulin function, leading to higher HbAle levels.
1.
2. Consistency with Previous Research: The direction of the effect is consistent with epidemiological studies that have found positive association between age and HbAle levels.
3. Magnitude of the Effect: The coefficient of 1.3 standardized coefficient, representing the change in standard deviations of HbAlc for each standard deviation change in age. The magnitude of this effect should be interpreted within the context of the data distribution and the units of measurement. In general, the magnitude seems large, and it would be important to compare it to existing literature to see if such change is reasonable.
4. Confounding Factors: The LINGAM analysis assumes that all relevant variables have been measured and included in the model. If there are unmeasured confounders that are associated with both age and HbAle, the estimated causal effect could be biased. For example, physical activity, diet, and other lifestyle factors can change with age and affect HbAle levels.
The analysis is based on working age adults (40 64 years old). The effect of age on HbAlc within this specific age range may differ from that in younger or older populations.
5. Population-Speeific Factors:
In conclusion, the statistically suggested hypothesis that age has a direct impact on HbAlc is biologically plausible and consistent with prior knowledge. However, further analysis should be conducted ensure that all relevant confounding factors have been accounted for, and the magnitude of the effect should be compared with existing research validate the results. Additionally, the clinical significance of this finding should be evaluated in the context of the overall health and management of individuals in the working-age population.
confidence probability generated in Process C: Pij 0.9833
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Consequently, it is inferred that these differences in aspects and tones lead to a significant gap in the confidence probabilities of GPT-4 at the same directed edge "Age" + "HbAlc." However, because the only difference in the SCP between Tables / and g is whether the causal coefficient of this edge is 1.25 or 1.30, the main factor of these gaps in aspects and tones is the complexity of sentence generation with a probabilistic process.
Therefore, considering the discussion above, it is practically challenging to quantitatively elucidate the tendencies of sentences generated in Process B (Step 2 in Figure [ including the analysis of reproducibility, the factual likelihood and the tone of the generated knowledge realistic evaluation of the fluctuation of GPT-4's confidence probability in Step 3 of the proposed method in this paper, other substitute prompt techniques should be considered.
long text. For the suppression and
For example, a more straightforward approach might. be to integrate Steps 2 and 3 in Figure [ applying the approach of ILLM-as-a-Judge (Zheng et al. 2023a; Yuan et al. 2021 Kocmi & Federmann, 2023 Under the condition of maintaining the measurement of GPT-4's confidence probability in causal relationships the proposed method, the position for the measurement of token generation probability and for the generation of "yes" or "no" in the generated text from GPT-4 must be fixed to the first or last one, from a practical point of view. Considering the limitations of ZSCoT and the property of the next generation of tokens from LLMs, fixing to the last token produces a better result than fixing to the first token, because the context generated before the token "yes" or "no" " is expected to suppress hallucination.
However, continuous caution will still be required for the reproducibility of the last token generation probability. In general, the probability of token generation wn is expressed by the conditional probability related to the prompt Q and the (W1, W2, 1n follows:
P(w, 1Q, Wi, W2 .... wa-1)
(7)
Therefore, the probability that the last generated token wt becomes "yes," " is calculated as follows:
L-1 P(wkQQ. w1, W2, ..., 1k-1) = =yes[Q, w1, W2, WL-1)
P(WL= = =cs) = -
W2....,
(8)
all
In contrast, the only probability that can be repeatedly measured from a practical point of view, is P(wL yes| w1, W2,,..,,
..., WL-1) in Eq. (8) Although it is possible to evaluate the mean value distribution of P(wr. = yesl W1, W2, ..., 1), which can be measured through repetitive measurements carried out in this paper, there is no guarantee that the true value of P(w,, = yes) can be obtained approximately, as it has not been clarified how 11/-1 P(wxlQ, W1, u...... wk-1) be measured. Therefore, the integration of Steps and 3 can hardly be considered fundamental solution, since the effective method for the stabilization of tones and aspects of the generated knowledge for judgment is still lacking.
Consequently, regardless of the integration or separation of Steps 2 and 3, the prompting technique for the stabilization of the generated knowledge expected to be constructed in detail. Although the discussion of this problem from this point forward requires further complex and careful examination beyond this paper, the possible aspects are as follows:
Appropriately enumerating the perspectives that need consideration, distinguishing between those that depend on the domain's inherent characteristics and those that do not This comprehensive listing of perspectives, and including them in the prompt can lead to appropriate domain-specific nuances, while maintaining the consistency of analytical knowledge generation and tone.
Confirmation of the characteristics of each variable and grouping, before the interpre- tation process following the listed perspectives as mentioned above
In the case of a health-screening dataset, for example, "SBP" and "DBP" are similar variables, that simultaneously measured in the health-screening process and share the same unit of measurement.
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Therefore, these two variables are expected to have similar causal relationships with other variables, and that "SBP" and 4DBP" are somehow correlated, although the detailed causal structure, including "SBP" and "DBP" has not been completely determined. However, as discussed earlier, the variable "Age" has a completely different characteristic from the other variables. This variable is mechanically determined from the birthday and the passage of time. Confirmation of LLMs' understanding of such properties of the variables expected to contribute to the suppression of hallucinations.
A careful examination of how the SCD results in the SCP are interpreted, particularly in handling anomalies that arise owing to limitations of the models for SCD
For example, the causal graph discovered through any SCD algorithm without prior knowledge, sometimes displays inappropriate directed edges with a large bootstrap probability, whose orientations are judged as obviously reversed from the experts' point of view, because of the strong statistical correlation between the pairs of variables. Since the SCP proposed in our method includes all the results of SCD, it is expected that the statistical information included in the prompts is handled effectively and appropriately, considering the tendency and limitations of SCD. Addressing these issues necessitates meticulous discussion to solidify a comprehensive understanding of the results, highlighting a significant. area for future research.
Transforming the standardized coefficients back to values in their original dimensions and including them into the prompts (for Patterns 2 and 4)
In the method proposed in this study, the causal coefficients are calculated via DirM with the datasels standardized before causal discovery, and without transforming them back to the values with original units. We have intentionally adopted the standardized causal coefficients, to ensure consistent scaling, which can lead to a relative comparison of the causal coefficients between different directed edges. However, as shown in Table 7 GPT-4 can insist, "without the context of the units and the standard deviations of the age and HbAlc variables, it is difficult. to assess the magnitude of this relationship's impact." Therefore, if it is expected that LLMs possess benchmarks or knowledge for judging the validity of prompted coefficients in some units, including the coefficients that are transformed back into the original dimensions into the prompt may enhance the capability of quantitative judgment.
Once this framework is in place, adopting the technique of few-shot prompting (Brown ct al. 2020) with accurate examples can further improve the stability and reliability of the model output. By providing the LLMs with ideal and correct exemplars, one can improve their ability to generate stabilized, consistent, and accurate responses, which contributes to the practical discussion of the reproducibility of LLM-KBCI.
To achieve even greater consistency in the oulputs, the instruction tuning (Wei et al. 2022 can also be adopted as an alternative to few-shot prompting. Instruction tuning involves fine-tuning the model via a dataset of instruction-respone pairs, aligning the model's behavior more closely with specific analytical requirements. However, this approach presents practical challenges: the cost of data generation for instruction tuning is much higher than that for few-shot prompting, and only fully open-source models (such as Llama2 Touvron et al. 2023) etc.) currently allow such fine-tuning. Therefore, although instruction tuning offers palential advantages in further stabilizing model oulpuls, its inplemenaation is limited by resource constraints and model availability.
Morcover, finc-tuning or employing RAG with some domain-spocific knowledge sources can be expected to enhance the domain knowledge of the LLM. These approaches could enable L.Mss to make more appropriate judgments between various pairs of variables. In particular, adopting RAG can also contribute to the stabilization of the tones of knowledge generation, because the range of information searches can be limited.
Toward Appropriate Application of the Proposed Method
As illustrated above, while GPT-4 has completely denied apparently unnatural directed edges from the domain knowledge such as "HbAlc" - " "Age" under any conditions, has not always been confidently judged in the ground truth edges where causal relationships should exist, such as "Age" + "HbAlc. Moreover, the SCP can sometimes unnecessarily decrease the confidence probability of ground truth edge in LLM-KBCI, although
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it is still unknown what kind of ground truth causal relationships are likely to be worsened. Therefore, using our proposed method as "black-box" may lead to unintended erroneous analysis results.
To mitigate this crucial risk as much as possible, first of all, although it is technically possible to connect all the steps shown in Figure ! and fully automate as described in Algorithm [ it is important to verify the validity of the output at each step. Recognizing this, we have carefully evaluated the results of all the steps throughout this work. In particular, to mitigate the risks arising from the use of LLMs, it is essential to assess the performance of the LLM-related processes, such as the second and third steps in Figure [ and to flexibly incorporate other optimal prompting techniques to improve the reliability the results.
Based on this premise, in addition to further technical clarification as discussed above, benchmarking the basic knowledge of LLMs in the domain in which the application of the proposed method is to be applied, is also important. Furthermore, before applying our method to construct data-driven causal models, especially when there are firm prior knowlodge edges that must be reflected, it is advisable to conduct preliminary experiments as performed in Simulations A and B. In addition, having experts review the actual results of the proposed method, including the textual output of Step 2, can be effective. Through these processes, it becomes possible to discuss what domain knowledge should be additionally learned by LLMs, for more precise and effective completion of the proposed method in each domain.
However, although high confidence can be achieved without critical errors through the approaches of adopting expert checks, especially when particularly focusing on small systems, the domain expert check becomes more impractical, as the number of variables increases, because the combinations of variable pairs increase quadratically. Because the strength of the proposed method in this paper lies in automating areas where expert verification becomes unmanageable owing to the large number of variables, premising expert checks in large-scale systems is counterproductive.
Therefore, continuing technical examinations, to overcome these issues, as discussed in this section, remain important, This ongoing effort is essential to enhance the reliability and practical applicability of our proposod method.
Finally, in terms of perfect realization of the expected role of the SCP, LLMs are also required to recognize the validity of the causal models prompted in the first step, and to point out the inadoquate part. To achieve these capabilities, accumulation of the modification process by domain experts as mentioned above, and structuring as a dataset for additional reinforcement learning of LLMs are also valuable. This framework can be interpreted as reinforcement learning with human feedback (RLHF) of causal graphs, and is expected to contribute to further suppression of hallucinations, toward the practical application of SCP in any domain. It also possible to introduce ensemble methods several LLMs, which have been intensively studied to mitigate hallucinations (Maksimov et al. 2024).
5 Conclusion
In this study, novel methodology for causal inference, in which SCD and LLM-KBCI are synthesized with SCP, and prior knowledge augmentation was developed and demonstrated.
It has been revealed that GPT-4 can cause the output of LLM-KBCI and the SCD result with prior knowledge from LLM-KBCI to approach the ground truth, and that the SCD result can be further improved, if GPT-4 undergoes SCP. Furthermore, with an unpublished real-world dataset, we have demonstrated that GPT-4 with SCP can assist SCD with respect to domain expertise and statistics, and that the proposed mothod is effective even if the dataset has never been included in the training data of the LLM and the sample size is not sufficiently large to obtain reasonable SCD results.
In addition, we have further simulated the SCP under various conditions, and confirmed both successful and failure cases on the basis of the SCD results on the health-screening dataset with LiNGAM. In successful cases, the existence of patterns where the SCP stably works as intended has been confirmed, especially when the hypothesis of the causal relationship (such as the hypothesis that " "Ago" is influenced by other factors) is apparently unnatural. In contrast, through the discussion of the failure cases, the technical limitations and risks of critical errors have been thoroughly discussed. Through these discussions, we have presented the
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expected improvements in techniques around LLMs, and the suggestion of realistic integration of domain expert checks of the results into this automatic methodology.
Technical Limitations of This Work
The details of the technical limitations and future directions for improving the proposed method in this paper are illustrated in Section 4.3 Here, we briefly discuss the general limitations and risks of adopting LLMs in causal inference tasks as the proposed method in this paper.
We fixed the LLM in our experiment to GPT-4 for its extensive general knowledge and capabilities in common-sense reasoning, and our experiments on several real-world datasets, typically, within the realm of common-sense reasoning, have illustrated the potential utility of the proposed method across various scientific domains. We expect that the proposed method will work even if other L.MSs are adopted, because the capability of LLM-KBCI has already been demonstrated in several models (Zečević ct al., 2023). Considering the continuous emergence of new LLMs and the rapid update of existing LLMss it is expected that the universal effectiveness of the proposed method across different LLMs will be verified.
Morcover, it is also important to recognize the risks of using current LLMs in our methods: hallucinations at Steps 2 and 3 in Figure
[ can worsen the results of LLM-KBCI and SCD. Considering that hallucinations arise from factors such as memorization of training data (McKenna et al. 2023 Carlini et al. 2023), statistical
biases (Jones & Steinhardt 2022 McMilin 2022), , and predictive uncertainty (Yang al. 2023 Lin et al.,
2024), it is essential to be especially careful when our method is applied in highly specialized academic domains (George & Stuhlmueller, 2023 Pal et al.) 2202).. To reduce these risks when the proposed method is applied in domains with deeper specificity in the future, it is necessary to further improve our method to avoid hallucinations more effectively. Although we have already introduced ZSCoT (Kojima et al.) 2022) and generated knowledge prompting (Tiu et al. 2022), employing optimal LLMs that are specifically pretrained with materials on specific domains is one of the possible solutions. Morcover, incorporating techniques such as fine-tuning and RAG could be necessary. Therefore, systematic research in the context of optimal LLM-KBCI is also required on the selection of the optimal LLMs for each domain and on the techniques for utilizing the LLMs.
Furthermore, for the generalization of the method we have proposed, we also note that although SCP is indeed likely to enhance the performance of SCD more than prompting without SCP, whether this improvement is observed can depend on the datasets used for SCD. Morcover, there remains a discussion on the potential for overfitting in SCP, especially with small or biased datasots. Although we have shown the effectiveness of the SCP on subsample of the health-screening dataset, which could contain biases, it is still an open question under what conditions the LLMs and prompt techniques can guarantee robustness for small or biased datasets. In terms of the more reliable application of the proposed method, further basic research on the effects of causal coefficients or bootstrap probabilities on the results of the LLM-KBCI is required.
Broader Impact Statement
This paper proposed a novel approach that integrates SCD methods with LLMs. This research has the potential to contribute to more accurate causal inference in fields where understanding causality is crucial, such as healthcare, economics, and environmental science. However, the use of LLMs such as GPT-4 necessitates the extensive consideration of data privacy and biases. Moreover, it should also be noted that incorrect causal inference, caused by hallucinations, biased training data, or inappropriate use of LLMs,, could lead to significant consequences for society. In particular, these risks arise when the proposed method used for completely "black-box" decision making. To prevent these risks, the transparency and interpretability of the whole system should be clarified.
This study highlights the responsible use of artificial intelligence, considering ethical implications and societal impacts. With appropriate guidelines and ethical standards, the proposed methodology can advance scientific understanding and provide extensive widespread benefits to society.
To mitigate the risk of data privacy and security properly, we have designed the method to avoid providing LLMs with the raw dataset, which could directly lead to the leakage of personally identifiable information. Tn
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the proposed method, the SCD processes with the raw dataset and LLM processes are completely separated, and only statistical results such as causal coefficients and bootstrap probabilities are used in the processes with LLMs. Therefore, even when the raw dataset contains highly confidential information, analysis through the proposed method should not raise privacy and sccurity concerns.
Acknowledgements
We sincerely appreciate Dr. Hitoshi Koshiba for his invaluable assistance in shaping the overall structure of this paper and for engaging in fruitful discussions. This work was supported by the Japan Science and Technology Agency (JST) under CREST Grant Number JPMJCR22D2 and PRESTO Grant Number JPMJPR2123, and by the Japan Society for the Promotion of Science (JSPS) under KAKENHI Grant Numbers JP20K03743, JJP3300484 and JP24K20741.
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A Ethics Review
Ethical Considerations in Methodology and AI Use This paper proposes a novel approach that integrates SCD with LLMs. We have thoroughly considered the issues of data privacy and biases associated with the use LLMs. The proposed methodology enhances the accuracy and efficiency of causal discovery; however, does not introduce explicit ethical implications beyond those generally applicable to machine learning. We are committed to the responsible use of AI and welcome the scrutiny of the ethics review committee.
Institutional Review and Consent Compliance for Hcalth-Screening Data The institutional review board of Kyoto University approved this study. As we only analyzed anonymized data from the database, the need for informed consent was waived.
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B Details of the Contents in Each Prompting Pattern
In this section, the details of the prompting in each pattern are presented. For Pattern 0, another prompting template is detailed instead of the sentences shown in Table | contents filled in (blank 5) and (blank 9) of the prompt template for the SCP shown in Table | are described.
Moreover, for Patterns 1, 2, 3, and 4, the
For Pattern 0 Compared with other patterns of SCP; Pattern 0 does not include any results of SCD without prior knowledge. As a result, the prompt template in Table 1 is not suitable for Pattern 0, as it includes blanks filled with descriptions of the datasct and the SCD result. Thus, we prepare another prompt template for Pattern 0, which completely independent of the SCD result, and requires GPT-4 to generate the response solely from its domain knowledge. Table presents the prompt template in Pattern 0, which is composed mainly of the ZSCoT concept. Because it does not include information on the SCD method and relies solely on domain knowledge in GPT-4, the probability matrix obtained from GPT-4 in Paltern 0 is applied independently of the SCD method.
Table 9:
The prompt template of Qij (1)) for Pattern 0 for the generation of expert knowledge of the causal effect from Ij on 24. The "blanks" enclosed with ( are filled with description words of the theme of the causal inference and variable names.
Prompt Template of d, ( (z), in Pattern (for all SCD methods)
We want to carry out causal inference on (blank 1. The theme), considering (blank 2. The description of all variables) as variables.
If (blank 7. The name of my) is modified, will it have direct impact on (blank 8, The name of w;)?
Please provide an explanation that leverages your expert knowledge on the causal relationship between (blank 7. The name of æ₁) and (blank 8. The name of z.). Your response should consider the relevant factors and provide a reasoned explanation based on your under- standing of the domain.
For Patterns 1 (in the case of Exact Search and DirectLiNGAM) Following the concept of each SCP pattern, the contents filled in (blank 5) shown in Table I are summarized in Table 10 In this table, the names of the causes and effected variables are represented as cause ) and effect i ), respectively, and the bootstrap probability of this causal relationship in SCD P. and the causal coefficient of LiNGAM by can be included in Patterns 2-4. In Patterns 2 and 4, only the causal relationships with P, + 0 are listed in ( blank 5 ). In Pattern 3, the causal relationships with b, o are listed in blank 5 >
The contents of (blank 6) and (blank 9) also depend on the SCP patterns, and are shown in Table 11 Here, we define the bootstrap probability of x, + x, as P.j. We also define the causal coefficient of x, + xy in LINGAM as by, because the structural equation of LiNGAM is usually defined as 23
34 Σ bij + +
Prompt template in the case of the PC algorithm Although the causal relationships are ultimately represented only as directed edges in Exact Search and DireeLLiNGAM, the situation changes slightly when we adopt the PC algorithm along with the codes in "causal-learn." This because the PC algorithm can also output undirected edges, when the causal direction between a pair of variables cannot be determined. Therefore, we have tentatively decided include not only directed edges but also undirected edges in SCP. Additionally, we have prepared another prompt template for SCP in the case of PC, shown in Table T2
23 Here, the error distribution function eç also assumed be non- Gaussian.
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Table 10: Contents filled in (blank 5) shown in Table [ when Exact Search or DirectLiNGAM is adopted for the SCD process.
SCP Pattern
Content in (blank 5)
All of the edges suggested by the statistical causal discovery are below: cause 7 effect 1
Pattern 1 Directed edges
cause 2 + effect 2
All of the edges with non-zero bootstrap probabilities
suggested by the statistical causal discovery are below:
Pattern 2 Bootstrap probabilities of directed edges
cause + effect 1 } (bootstrap probability = Pt) cause
effect 2 (bootstrap probability Pb)
All of the edges and their coefficients of the structural causal model suggested by the statistical causal discovery are below:
Pattern 3 (Only for DirectLiNGAM) Non-zero causal coefficients of directed edges
cause { effect 1 (coefficient = b1) effect 2 (coefficient b2)
cause
All of the edges with non-zero bootstrap probabilitics and their coefficients of the structural causal model suggested by the statistical causal discovery are below: cause cause - effect (coefficient d2, bootstrap probability Pa)
Pattern 4 (Only for DirectLiNGAM) Non-zero causal coefficients and bootstrap probabilities of directed edges
effect (coefficient = 61, bootstrap probability P1)
Table 11:
Contents filled in (blank 6) and (blank 9) shown in Table is adopted for the SCD process.
when Exact Search or DirectLiNGAM
SCP Pattern
Case Classification
(blank 6)
Content in (blank 9)
Pattern 1 Directed edges
2j + x; emerged
(No values are filled in)
J + #; not emerged
no
(No values are filled in)
Pattern Bootstrap probabilities of directed edges
Pi *
with bootstrap probability of Ps
Pi 0
(No values are filled in)
Pattern 3 (Ouly for DirectLiNGAM)
bi * 0
with a causal coefficient of bij
Non-zero causal coefficients of directed edges
big 0
no
(No values are filled in) with a bootstrap probability of Pa: and the coufficient likely to be by with bootstrap probability of Pag but the coefficient is likely to be 0
Pattern 4 (Ouly for LinecLL)NGAM) Non-zero causal coefficients and bootstrap probabilities of directed edges
Piy * 0 and bıy * O
a
Piş A 0 and biy =
Pij = 0
no
(No values are filled in)
This template is slightly modified from the one in Table D The description for ( blaan 5 ) in each SCP pattern is augmented by Table 13 and the description for ( blank 6)) ) is similarly augmented by Table 14
As shown in Table 13 the directed and undirected edges are separately listed and clearly distinguished by the edge symbols
for directed edges and " for undirected edges. These are then filled in (blank 5 ). The pairs of variables connected by undirected edges are represented as ( cause or effect i-1 ) and ( cauuse or effect i-2 ), and the bootstrap probability of the emergence of these relationships is represented as PR. On the other hand, the bootstrap probability of ( causs i) + effeett i ) is represented as p.d.
The division of descriptions in ( blank 6) ) is shown in Table 14 The bootstrap probabilities of the appearance of Æ + Ij and x,- 24 are represented as pt and P. respectively.
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Table 12:
The prompt template of Q (,,, Go, pd. pu) in the case of the PC algorithm. The "blanks" enclosed with ) are filled with descriptive words considering the theme of the causal inference, variable names, and the SCD result with the PC algorithm.
Prompt Template of d.
(1) xy, Go, pd pa) for PC
We want to carry out causal inference on (blank 1. The theme), considering (blank 2. The description variables) as variables.
First, we have conducted the statistical causal discovery with the PC (Peter-Clark) algorithm, using fully standardized dataset on (blank 4. The description of the dataset).
(blank 5. This includes the information of Go (for Pattern 1), or pd and pa (for Pattern 2). The details of the contents depend on the prompting patterns, both for directed and undirected edges.)
According to the results shown above, it has been determined that (blank The details of the interpretation of whether there a causal relationship between I, and from the result shown in blank 5).
Then, your task is to interpret this result from a domain knowledge perspective and determine whether this statistically suggested hypothesis is plausible in the context of the domain.
Please provide explanation that leverages your expert knowledge the causal relationship between (blank 7. The name of æz) and (blank 8. The name of æi), and assess the naturalness of this causal discovery result.
Your response should consider the relevant factors and provide a reasoned explanation based on your under- standing of the domain.
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Table 13: Contents filled (blank 5) shown in Table 12
SCP Pattern
Content in (blank 5)
All of the edges suggested by the statistical causal discovery are below: { cause + effect 1
( cause
effect
Pattern 1
In addition to the directed edges above, all of the undirected edges
Directed and undirected edges
suggested by the statistical causal discovery are below:
( cause or effect 1-1 ) - cause or effect 1-2
( cause or effect 2-1
cause or effect 2-2
All of the edges with non-zero hootstrap probabilities
suggested by the statistical causal discovery are below:
{ cause ) effect 1 (bootstrap probability pd) effect (bootstrap probability P2)
{ cause
Pattern Bootstrap probabilities of directed and undirected edges
In addition to the directed edges above, all of the undirected edges suggested by the statistical causal discovery are below:
cause effect 1-1 cause effect 1-1 (bootstrap probability (
effect 2-1 cause effect 2-2 (bootstrap probability PT
Table 14: Contents filled in (blank 6) shown in Table 12
SCP Patteru
Case Classification
Coutent in (blank
there may be direct impaact a change in (blank 7. The name of 2,) on (blank 8. The name of ax)
Pattern 1
2y +
Directed undirected edges
theme may be betweeu (blank 7. The name of 2y) and (blank 8, The of ax),
cansal relationship
xy
although the direction has not been determined
there may no direet impart
no edge between i, and i
change (blank 7. The name of xz) (blank 8. The of there may be direet impact of
change (blank 7. The name of zy) on (blank 8. The name ..)
with bootstrap probability of pd In addition. it has also been shown above that there may be direet causal relationship between (blank with bootstrap probubility of po ulthough the direction his not been deternined
Pi A 0 and Pa of
Pattern 2
Bootstrag probubiiiies of directed and undirected edges
name 2y) (blank name at)
there may be direct impact
rt, * and 17j =
change (blank 7. The with a bootstrap probability of pd there may be diress cansal relationship
zy) (blank 8. The
between (blank The name ay) (blank 8. name
p = 0 and Py o
with bootstrap probability of Pa.
although the direction has not been deternined
there may be no direct imppett
ng D and 1o
chango (hlank 7. The name xy) (blank 8. The
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C Details of Datasets used in Demonstrations
In this section, the details of the dataset used in the main body and the appendix are clarified. The ground truths set for the evaluation of the SCD and LLM-KBCI results for each dataset are presented.
C.1 Auto MPG data
Auto MPG data were originally open in the UCI Machine Learning Repository Quinlan 1993), and used as a. benchmark dataset for causal inference (Spirtes et al. 2010 Mooij et al. 2016). This dataset consists of variables related to the fuel consumption cars. We adopt five variables: "Weight", "Displacement" "Horsepower", "Acceleration" and "Mpg" (miles per gallon). Morcover, the number of points of this dataset in the experiment is 392. The ground truth of the causal relationships we adopt in this paper is shown in Figure 7 the original has been shown differences from the original study (Spirtes et al. 2010 are presented below:
example of the kPC algorithm (Spirtes et al. 2010 The
1 Loss of "Cylinders" Although there is also discrete variable of "Cylinders" in the original data (Quin an
1993
it is omitted the experiments to focus solcly on the continuous variables.
(2) Directed edge from "Weight" to "Displacement" The "Weight" and "Displacement" are connected with an undirected edge, which indicates that the direction cannot be determined in the kPC algorithm, although causal relationship between these two variables is suggested. However, it is empirically acknowledged that large and heavy vehicles use engines with larger displacements to provide sufficient power to match their size. Thus, we temporally set the direction of the edge between these two variables as "Weight" "Displacement."
We also recognize that another ground truth was interpreted in the process reconstructing the Tübingen database for causo-offoct pairs (Mooij et al. 2016) 24] and "Mpg" and "Acccleration" were interpreted effected variables from other elements. This ground truth seems to be reliable, if do significantly discriminate between direct and indirect causal effects and target the identification of cause and effect from pair of variables. However, we adopt the ground truth based on the result from the kPC algorithm, because our target is to approach the true causal graph, including multistep causal relationships.
Weight
Displacement
Horsepower
Acceleration
Mpg
Figure 7: Causal graph of the ground truth adopted for the Auto MPG data in this study.
In Figure g the results of basic causal structure analysis via the PC, Exact Search, and DirocLLINGAM algorithms without prior knowledge are presented. Several reversed edges from ground truths such as MMpg" "Weight" are observed.
24 https://webbaa http//ewwwv.uuubingnn..me www.ingen..gg...e...... -ffeceeeeeceeeefeeee//////
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(A) PC
BB) Exact Search
(C) DirectLiNGAM
Displacement
Mpg
-0881
Mpg
Acceleration
Weight
Mpg
0.75
Horsepower
-0.23
-1.20
Displacement
Weight
0.28
Weight
0.08
0.70
Horsepower
0.40
Acceleration
Displacement
0.34
Acceleration
Horsepower
Figure 8: Results of SCD Auto MPG data with (A) PC, (B) Exact Search, and (C) DirectLiNGAM.
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C.2 DWD climate data
The DWD climate data were originally provided by the DWD and several of the original datasets were merged and reconstructed as a component of the üibingen database for causal-effect pairs (Mooij et al.) 2016). This dataset consists six variables: "Altitude", "Latitude", "Longitude", "Sunshine" (duration), "Temperature" and "Precipitation". The number of points of this dataset is 349, which corresponds to the number of weather stations Germany without missing data.
Because there is no ground truth this dataset advocated, except for that in the übingen database for causal-effect pairs [Mooij al. 2016 we adopt it temporally in this experiment, shown in Figure
Latitude
Longitude
Altitude
Temperature
Precipitation
Sunshine
Figure 9: Causal graph of the ground truth adopted for the DWD climate data in this study,
In Figure 10 the results of basic causal structure analysis via the PC, Exact Search, and DirectLiNGAN algorithms without prior knowledge are presented. In all the causal graphs in Figure I0 several unnatural behaviors are observed, such as "Altitude" being affected by other climate variables, which we interpret as reversed causal relationships from the ground truths.
(A) PC
(B) Exact Search
(C) DirectLiNGAM
Longitade
Temperature
Sunshine
Longitade
0.24
-0.30
Temperature
0.24
Longitude
Latitude
Latitade
Precipitation
0.73
Precipitaiion
-0.15
Sunshine
0.09
Altitude
Altitude
Precipitation
Temperature
Aitinude
Figure 10: Results of SCD on DWD climate data with (A) PC, (B) Exact Search, and (C) DirectLiNGAM.
https:///wer dww..dddddd///////dd
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C.3 Sachs protein data
This dataset consists of variables related to the phosphorylation levels of proteins and lipids in primary human immune cells, which were originally constructed and analyzed with the nouparametric causal structure learning algorithm by Sachs et al. (2005). contains 11 continuous variables: "raf", "mek", "plc", "pip2", "pip3", "erk", "akt", "pka", "pkc", "p38" and "jnk". The number of points in this dataset is 7466.
The ground truth adopted in this study is almost the same as the interpretation shown in the study by [aachs] et al. (2005). The differences from the causal graph visually displayed in the original paper are presented below:
(1) Reversed edge between "pip3" and "ple" Although the directed edge "plc" - "pip3" was detected in the original study, it was denoted as "reversed," which may be the reversed direction from the expected edge. Thus, we adopt the causal relationship of "pip3" - "plc" which Sachs et al. anticipated as true from an expert point of view.
(2) Three missed edges in the original study In the study by Sachs et al, "pip2" + "pkc', "ple" "pke," " and "pip3" - "akt" did not appear in the Bayesian network inference result, although they were expected to be direct causal relationships from the domain knowledge. We adopt these three edges for the ground truth, considering that they may not appear under certain SCD conditions and assumptions.
pip3
plc
pip2
pkc
raf
pka
mek
p38
Y
erk
Figure 11:
Causal graph of the ground truth adopted for Sachs protein data in this study.
In Figure 12 the results of the basic causal structure analysis via the PC, Exact Search, and DirectLiNGAM algorithms without prior knowledge are shown.
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(A) PC
(C) DirectLiNGAM
61
94
622
(B) Exact Search
100
400
Figure 12: Results of SCD on Sachs data with (A) PC, (B) Exact Search, and (C) DirectLiNGAM.
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C.4 health-screening data (closed data and not included in GPT-4's pretraining materials)
To confirm that GPT-4 can adequately judge the existence of causal relationships with SCP, even if the dataset used in SCD is not included in the pretraining dataset of GPT-4, we have additionally prepared a health-screening dataset of workers in engineering and construction contractors, which is not disclosed because of its sensitive nature regarding personal handling and other private concerns. It contains seven continuous variables: body mass index ("BMT"), waist circumference ("Waist"), Systolic blood pressure ("SBP"), Diastolic blood pressure (*DBP"), hemoglobin Ale ("HbAlc"), low density lipoprotein cholesterol ("LDL"), and age ("Age"). The number of total points of this dataset is 123 151.
Although the causal relationships between all pairs of variables are not completely determined, we set two types of ground truths.
(1) Directed edges interpreted as ground truths ground truths.
We empirically set four directed edges below as
Age"-"BNai Clarke et al.
2008 Alley et al. 2008
Gordon-Larsen et al.
2010 Yang et al. 2021
at least one of " "Age" "SSBP and "Age" > "DBP" Gurven et al. 2012
" "Age" "HHA1c" Pani et al.
2008:
RaviKumar et al. 2011
Dubowitz et al.
2014
(2) Variable interpreted as parent for all other variables "Age" is an unmodifiable background factor. Furthermore, numerous medical studies have clearly demonstrated that aging affects "BMI," " "SBP," "DBP," and "HBAle." On the basis of this specialized knowledge, we interpret " "Age" as a parent for all other variables.
The ground truths introducod above also appear in the result of DirectLINGAM without prior knowlodge, shown in Figure 13 Although "Age"""HbAl is confirmed in this result, the causal coefficient of this edge is relatively small. Thus, depending on the number of data points or the bias of the dataset, it is possible that this edge does not appear in all SCD methods without prior knowledge, For the experiment, to confirm that GPT-4 can supply SCD with adequate prior knowledge, even if a direct edge of the ground truth is not apparent, we repeated the sampling of 1000 points from the entire dataset, until we obtained a subset. on which PC, Exact Search, and DirectLiNGAM cannot discern the causal relationship "Age" "HbAlc without prior knowledge.
The results of the SCD on the subset are shown in Figure 14 and this subset is adopted to confirm the effectiveness of the proposed method. All the SCD results confirm that "Age" > "HbAlc" does not appear, and " "Age" is directly influenced by other variables, which we interpret as an unnatural behavior from the domain knowledge.
(3) Limitations in the strict proof of the absence of any overlap with the pretraining data of GPT-4 As explained in Section 4.2 we conclude that our unpublished health-screening dataset was not included in the pretraining data of GPT-4. This conclusion is based circumstantial evidence such as the following:
the original dataset consists of personal health-screening data from Japanese health insurance records
the legal restrictions in Japan prohibiting the public use of the raw data
our past usage, which does not involve direct exposure to the Internet or sharing with third parties, and has complied with the scope of data use agreed upon by the data providers and approved by the institutc's ethics review board
For more rigorous validation, it idcally recommended technically confirm whether there any overlap between our dataset and the pretraining data of GPT-4, Indeed, various methods have been proposed detect potential data leakage into pretraining datasets of LLMss, or to estimate whether specific data are
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Age
0.02
HbA1c
LDL
0.16
-0.05
1.25
0.02
1.65
DBP
0.28
0.10
0.10
0.37
1.05
0.30
0.04
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00.01
Waist
Figure 13: Causal graph suggested by DirActLiNGAM using full points of the health-screening data.
(A) PC
(B) Exact Search
(C) DirectLiNGAM
HbAlc
LDL
0.30
0.11
Waist
LDL
HbAlc
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0.89
BMI
Waist
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Age
Age
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SHP
Age
0.775
Figure 14: Results SCD on the randomly selected subsample the health-screening dataset with (A) a PC, (B) Exact Search, and (C) DirectLiNGAM.
included in them, such n-gram matching (Singh et al.) 2024), membership inference attacks (MIAs) Duan et al. 2024), and the dataset inference method (Maini et al. 2024h. However, there still both technical and
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ethical limitations in the technical confirmation of the absence of any overlap between our health-screening dataset and the pretraining data of GPT-4.
First, since neither the model nor the pretraining dataset of GPT-4 has been disclosed, it is impossible to verify any overlap with our health-screening dataset via techniques such as n-gram matching. Moreover, it must be carefully assessed whether applying other verification methods to our actual dataset, could itself pose a risk of data leakage, which would raise social and ethical concerns. Ensuring sufficiently robust and secure environment for such validation would also require additional layer of safeguards. In addition, even if these technical concerns were addressed, further issues remain regarding the scope of data use agreed upon by the data providers. It would also be necessary to confirm compliance with legal restrictions, particularly concerning the use of personal records contained in our dataset.
Although the above challenges are highly relevant to the practical analysis of datasets containing confidential information via LLMs, addressing them requires thorough discussion of legal restrictions as well as technical demonstrations under carefully prepared conditions -both of which are far beyond the scope and the aim of our work. Consequently, from practical standpoint, it is reasonable conclude that our health-screening dataset not included in the pretraining data of GPT-4, based on circumstantial evidence.
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D Token Generation Probabilities as Confidence of LLMs and Sensitivity Analysis
In this section, we provide a supplemental explanation of the properties of the mean probability Pij, that the LLM generates the token "yes" as the response to the prompt asking for confidence in the causal relationship from 2 to 24, highlighting the properties of the token generation process Transformer-basee LLMs. We also discuss the mean probability Tij that the LLM generates the token "no," and explain the symmetric behavior of Pay and Fiy arising from the empirical relationship Psy + Fij = 1, under the assumption of the "faithfulness" of the LLM to the prompt. Moreover, quantitatively evaluate the fluctuation of Púj with the standard error (E())) indices of the sensitivity reliability of these probabilities measured in our experiments, through regression analysis with phenomenological distribution function SE(),)) = ap bp - 0.5)². Finally, the precision of the classification of forbidden causal paths is evaluated through numerical simulations.
The discussion in this section not only contributes to the evaluation of the LLM's confidence in the causal relationship between pairs of variables, but also supports the reliability of the LLM outputs.
D.1 Details of Token Generation Probability Calculations
As explained Section 3.1 we quantitatively evaluate the generation probability of the token "yes" from GPT-4, as the confidence of GPT-4 regarding the existence of the causal relationship. Although the details of GPT-4's architecture have not been disclosed, it is naturally assumed that GPT-4 employs a temnperalure-adjustedd softmax function for token generation, considering the following facts:
The previous GPT models developod by OpenAl are basod on the Transformer architecture (Radford
et al. 2019 Brown al., 2020
The temperature hyperparameter can be optionally set
The log-probabilities of the most likely tokens at each token position can be obtained
In the process of text generation in Transformer, the model first calculates the logit 26 for token ca (0 < k < K, where K' is the number of candidate tokens) as likelihood score for all candidate tokens on the basis of the prompted text X. Then, the conditional probability distribution of the emergence of token Co with the logit Za, (c,,/X), is calculated through the temperature-adjjster softmax function as follows Tuustall et al. 2022):
exp(za/ (Tp(2a/T)
P(c, (X,T)
(10)
Ex exp(2x/7))
Here, is a lemperature ure hyperparameter that adjusts the conditional probability distribution. Finally, the next token is sampled based on the conditional probability distribution above.
In this work, T was fixed to 0.7. In the third step, the log- log-probability Limi = (Im) (EGPTI(A))) = "yes") shown in Algorithm D is directly sampled M times via the optional function of GPT-4. Considering that the token generation probability represented by Eq. (10 we have calculated the mean probability Pij follows:
(T) A== exp( (m))
ΣM p(m) ("yes"|a (2) ,T)
Pij
(11)
M
M
We have interpreted Pij calculated above the confidence of GPT-4 in the existence of the causal effect. from Tj Zz.
Althuuhh it is suggested that this interpretation is valid in common-sense reasoning from experiments, notably, this probability simply represents the likelihood that the LLM selected the expected token the answer to the prompt. In this sense, this "coufidence" can be biased under of the LLM. Therefore, as discussed in Section reliably, especially for applications in highly specialized academic domains.
conditions since it depends on the architecture and the pretraining datascts necessary to further improve our method to avoid hallucinations more
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(a)
(b)
Regression Resull
0.14
Regression 0.002
5 1. 1,002p, 0. 0.990
SE(rg) 0.933SE(o,)
0.8
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SEir
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0.0
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1.0
0.00
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Pij
SE(P:)
Figure 15: (a) Relationship between Pij and Fiz. The red line is the result of least squares regression with Tij aPr + 3. The estimated values (= the standard errors) of the coefficients are = -1.002 + 0.002(= -1) and 3 = 0.990 = 0.001(~ 1). (b) Relationship between SE and SE(Fg). The red line is the result of The estimated values (# the standard errors) of the coefficients are 7 0.933 + 0.011(= 1) and 8 0.0015 + (=0002 0).
lcast squarcs regression with SE(ri)) = SSE()))
D.2 Confidence in the Absence of the Causal Relationship
Although the generation probability of the token "no" is not evaluated in the main text, it is valuable to discuss the idcal behavior of this probability for the subsequent discussion of the stability of Piz. In the same context as Ply, the mean probability of generating the token "no", Fiy, is calculated as follows:
ΣM p(m) ("no"la 14
(12)
M
Since GPT-4 is required answer only with "ves" or "no," under the assumption that the response from GPT-4
is faithful to the prompt explained in Table 2 it is expected that p(m) ("yes" (2) (T)+ +pm))()))((()) ("mm)(""""la"" (2)
4ij .)) = 1.
In this section, we define this property as "faithfulness." Therefore, from Eqs. 11 and 12 the ideal
relationship between Piy and rij is expressed as follows:
Pij +
(13)
is also expressed in a symmetrical form such as Fij - 0.5 - - 0.5), this property is expected to contribute to clearer quantitative interpretation of the stability Pij- This is particularly important for validating the latter discussion on the fluctuation of pij-
Since Eqq.
13
D.3 Stability of Token Generation Probabilities
For the quantitative evaluation the stability of Pty. we compare Py and Fıy, along with their standard errors (SE(p)) and SE(r,))) estimated through trials conducted M = times. We temporarily concatenato the results of LLM-KBCI on the datasets of AutoMPG, DWD, and Sachs (for all the prompting patterns and for all the SCD algorithms), and on the health-screening data (for all the prompting patterns with
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(a)
0.20
(b)
0.20
Regression Result
Regression Result
SE(p,) 0.069 0.278 0.5)
sFirg)
a 069 778(, 05
0.15
0.15
SE(P))
SEGO
0.10
0.10
0.05
0.05
0.00
0.00
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Pij
Fij
Figure 16: (a) Relationship between the mean probability Pij and the standard error SE(p:)). The red line is the result of least squares regression with SE(P:) ap - (P - 0.5) The estimated values (= standard errors) of the coefficients are a₂ = 0.0694 + 0.0007 and b, = 0.2783 + 0.0030. (b) Relationship between the mcan probability Tij and the standard crror SE(r,y). The red line is the result of least squares regression with SE(r)) a, - b, (Tij 0.5)². The estimated values (#: standard errors) of the coefficients are a, 0.0692 0.0007 and b, 0.2780 = 0.0032.
DirecLLiNGAM), under the assumption that the relations among Pıj. Tay, SE(pg) and SE(ny) are almost independent of the domains. This holds even if the SCP is conducted within the realm of common-sense reasoning. The number of points of the concatenated data is 1650.
Figure 15 (a) shows the relation between Pij and Fij, and the red line indicates the result of least squares
regression with riy = opi + 3. Considering that the estimated values of the causal coefficients (a = - 1.000, 3 = 0.990) exhibit similar behavior to Eq. 13), it can be inferred that the assumption of the "faithfulness" of the LLM gencration the prompts is valid our experiments. Therefore, it scems approximately valid assume the symmetrical relation Fij 0.5 (P 0.5).
Moreover, Figure 15 (b) shows the relationship between SE(PT) and SE(TT) where the red line indicates the result of least squares regression with SE(r,) = SPE))) + 8. Given the estimated values of the causal coefficients (y = 0.933, = 0.002), it can be inferred that the approximation SE ~ SE holds truc. This fact provides further evidence for the approximately symmctric behavior expressed as Tij 0.5 = (p.j 0.5).
Figure 16 shows the relationship between Ptj and SE(p)) in (a) and the relationship between Tīy and SE(ry) in (b). These two graphs exhibit mutually related characteristics follows:
In the limit of Pyj or Fij + 0, both SE(pG) and SE(ri)) approach 0, indicating that Pij and Tij become highly stable when confidence in the presence of the causal effect from æy to æ; is very high.
In the limit of p. + or Ty + 1, both SE(p)) and SE(y) approach 0, indicating that Pij and Ty become highly stable when confidence in the absence the causal effect from v, to I; very high.
Furthermore, the entire form of the Púj - SE(p)) distribution is quantitatively similar the Fij SE((r))))))) distribution. From this fact, it is expected that the functional form of SF(p))) explained with pij is
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approximately the same as that of SE(r)) explained with Tay- Therefore, to interpret the stability of the probability easily and clearly, we assume common distribution function between the Pij SF(())) and rij SB(r))) distributions, as well as the symmetric behavior shown in Eq. 113, and regress the Pij SE(())) distribution with a phenomenological function as follows:
SE(pg) = Up - (p 0.5)
(14)
In the same context, the Poj (r())) distribution is regressed with a phenomenological function as follows:
SE(rg) ar -,,7
(15)
Idcally, the symmetrical bohavior holds true, the relationship (ap, bp) = (a,,b,) ) is expected. From the analysis results of the least squares regression, the coefficients of Eqs. (14) and 115 are estimated as (ap: bp) = (0.0694, 0.2783) and (ar, = 0...6,99,.2780 Thus, it confirmed that (ap. bp) (ar, by) holds true.
From the results above, the standard error of Pij becomes the maximum value (expected to be 0.062) when 0.5. In our experiments, the fluctuation becomes critical at the criteria on and 02 explained in Section
Pij
3.1 From the phenomenological analysis shown above, the expected standard errors of pij at the criteria
a 0.05 and a2 = 0.95 in our experiments) are estimated through Eq. (14) to be approximately 0.013. Therefore, when Pij is near the threshold of 0.05 or 0.95, the probability fluctuation around this standard error can lead to a different PK matrix.
D.4 Effect on the Decision of the Prior Knowledge Matrix
For more detailed analysis of the effect of the fluctuation on the determination of PK, we focus on two indices of sensitivity: (A) the statistically estimated probability that the true value Ps (pi satisfies the inequality pizue On, and (B) the area under the curve (AUC) calculated through Monte Carlo simulation.
(A) Statistically Estimated Probability of True Confidence
For a simple simulation, we assume that SE(py) is calculated with Eq. [44 and that (ap. bp) = (0.0694, 0.2783), estimated through the regression analysis in Appendix DD3] Moreover, assume that the distribution of pipu is expressed with Gaussian distribution, with mean value Pij and standard deviation SE(Pi)), described in Eq. (16..
exp (- (-W-- (P-Pps) Pcj Poj)
Spicue (pig, (Pig, SF(ps).)) V2TSE(pT))
(16)
2SE (PT))
Under the assumptions above, P(ytrue e < an), the probability that the true confidence probability plgue is below the forbidden edge threshold a1, is calculated as follows:
P(P true <a1) = /0a0 nan
dpf (PT. SE(PG) p))
(17)
Then, P(ptrue < a1) is numerically calculated via Eq. 17 and the result is shown in Fig. 17 (a). When Pi S 0.04, ptpue almost certainly below the threshold on = 0.05, and when Púj 2 0.08, Ply almost certainly above 0.05. However, between 0.04 S P. S 0.08 (approxinately 0.05), P(y
a1) decreases with increasing Pty. Although it is confirmed that the width of the region of this decreasing P(p < an) is similar in the order of SE(P)) ~ 0.013 around P, 0.05, the slope of the decrease is gentler in the region of Pij 2 0.05 than in the region of P.j < 0.05. This asymmetric property originates from the phenomenological nonlinear function of SE(;)) as described in Eq. (14). If the threshold of the forbidden edge an is decreased, it is possible to shrink the region of decreasing P P
Tuee ue < a1) and the asymmetric slope. However, although we tentatively set a₁ to 0.05, the optimal threshold is expected to be discussed future rescarch from a practical point of view. Notably, lower aj leads to a PK matrix, which includes more uncertain elements from domain expert knowledge and can be less effective in the fourth step in Fig. [ than expected.
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(a)
1.0
(b)
1.0
Threshold for Setting Forbidden Fdges
AUC: 0.899
0.8
( = 0 05)
TPR (True Positive Rate)
0.8
P(Py <..05)
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Mean Probability (py)
FPR (False Positive Rate)
(b) ROC curve estimated through Monte Carlo simulation based on Eq. 16 The AUC calculated with this ROC curve is 0.899.
Figure 17: (a) Relationship between the calculated P(p < <ai) and Pij based Eq. 17
(B) ROC and AUC Estimated through Monte Carlo Simulation
Because p.j frue cannot be known in experiments, it is impossible to construct the receiver operating characteristic (ROC) curve directly with the probability data obtained in experiments. Instead, we have conducted Monte Carlo simulation, through which p/zue is randomly generated via the distribution described Eq. (6). Furthermore, for the calculation of the ROC and AUC, we define the conditions for true positive (TP), false positive (FP), true negative (TN), and false negative (FN), in the context of judging whether the causal path from &j to 2; forbidden, as follows:
TP: generated pirue satisfics piyue < a1, and experimentally fixed Pij satisfics Pij
FP: generated Pij true satisfies true 2 on, and experimentally fixed py satisfies Pij < on- p
TN: generated p satisfics
pij true 2 an, and experimentally fixed Ps satisfics Púj a1
FN: generated ph satisfies ptze < αı and experimentally fixed Pij satisfies Pij a1
The practical Monte Carlo simulation was conducted 1000 times for each Piy value, varying Pij from 0.032 to 0.10827 in increments of 0.001, and the calculated ROC through this simulation shown Fig. 17 The AUC is estimated to be 0.899, indicating excellent discrimination of the forbidden direct causal path (Hosmer & Lemeshow 2000). From this analysis, it is inferred that in the realm of common-senas reasoning, the decision process of PK from the confidence of GPT-4 at the third step in Fig. according to the interpretation obtained in the second step, is statistically valid.
27 this region, P(pfrue < an) satisfies 0.001 P(p < a1) < 0.999. Therefore, for the practical calculation of the ROC and AUC, we assume that when Pzz satisfies Paj < 0.032, p is under on and is always classified as TP, and that when Ptj satisfies Pi > 0.108, true is 2 on and is always classified as TN.
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D.5 Stability of SCD Results with PK
Although it is demonstrated that SCD results with PK are generated through LLM processes in Section 1.1 considering the stability of PK discussed in Appendix D.4, it is also important to evaluate the stability of the SCD results with PK against fluctuations in the LLM's confidence probability matrix, P.
For the supplemental experiment confirming the problem above, we first randomly generate the p. assuming that each component is independently determined with the distribution function expressed in Eq. (T6), repeated Naampling times for sufficiently large Naampling Then, we conduct the transformation from p to PK and perform SCD analysis with PK for all the generated of variables, we statistically analyze the sampling results of the SCD outcomes and evaluate the stability of causal edge emergence or causal coefficients (in the case of DiroctLiNGAM), Through this process, it is possible to assess the stability of the results of the SCD with PK against the fluctuation of the LLM's confidence probability matrix.
Finally, for all the patterns of pairs
We Naumpling 10,000, and for the simulation from real- woal-world data, we adopt DWD climate data. To evaluate the stability of both the edge emergence and the causal coelficients for all the pairs of variables, we adopt DirectLiNGAM as the SCD algorithm. We also select the p generated through Pattern 2 (prompting with causal bootstrap probabilitie)), since it realizes the best improvement in the LINGAM results, especially in precision, as shown in Table 8 The measured p and standard error matrix E obtained through M = 5 single-shot measurements are as follows:
0.000
0.000
0.000
0.000
0.000
0.000
0.997
0.000
0.007
0.000
0.999
0.989
0.739
0.999
0.000
0.000
0.000
0.384
p
(18)
0.000
0.000
0.000
0.000
0.000
0.000
0.874
0.010
0.976
0.000
0.000
0.981
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.006
0.000
0.000
0.004
0.140
0.000
0.000
0.000
0.000
0.144
SE
(19)
0.000
0.000
0.000
0.000
0.000
0.000
0.066
0.002
0.011
0.000
0.000
0.026
0.000
0.000
0.000
0.000
0.000
0.000
The histograms of causal coefficients for all the randomly regenerated p across all pairs of variables are summarized in Table [8 The causal coefficients clearly exhibit minimal fluctuations, with each histogram resembling delta function. This observation suggests that fluctuations in the probability matrix generated by the LLM do not degrade the stability of the SCD results.
There are two primary reasons for the stability of the SCD results with PK:
Robustness in the extreme values of LLM confidence probabilities: As discussed in Section D.3. the standard error decreases when confidence probabilities approach 0 1. This behavior may contribute to the stability of PK.
Numerical datasets as the main factor in structure determination: In DireMLL causal coefficients are determined through regression analysis with LASSO on the dataset. This suggests that the numerical propertics of the datasct play a significant role in structure determination.
D.6 Limitations in the Sensitivity Analysis of Token Generation Probabilities
Although we have discussed the sensitivity of the token generation probabilities as the confidence of GPT-4 above, there several limitations in elucidating the entire properties of the fluctuations induced by the
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Terperra.g Aildd
Predpaako Albse
Longhtk - Adbd
Sundhia ABi44
Lakade W23do
407
300
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01
43
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Lengude LeBido
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Figure 18: Histograms for all pairs variables obtained from the DirectLiNGAM analysis Neampling 10,000 randomly regenerated probability matrices for DWD climate data.
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randomness of the LLMs. For further research to improve methods, we introduce several additional points related to the measurement. stability in the third step in Fig. 1
Sensitivity in the Explanation Obtained in Step 2
Pij and SE(Py) can by (g a.y). Because it is practically impossible to evaluate the fluctuation of di at Step 2 quantitatively, we have discussed the token generation probability and its sensitivity with a fixed az-
Although we have evaluated the probability fluctuation emergent in Step 3 of Fig.
also depend on dij, the output in Step 2, on the basis of the relationship of 4ij (2)
Furthermore, we have not discussed this work the validity of aij, as this expected to be debated within the domain of research specific LLMs, which is outside the scope of our study. However, although our method has proven to be effective in many cases through this research, it may be negatively impacted if an LLM makes biased judgments. Therefore, ongoing efforts to eliminate biases in LLMs and prevent hallucinations are required. Additionally, considering the future applications of this method, careful consideration and judgment will continue to be necessary.
Imperfect Satisfaction of the Condition of "Faithfulness"
In work, "faithfulness" is almost confirmed, shown in Fig. 15
However, several points obviously deviate from the regression line, from Eq. (13). Specifically, out of total of 1650 points in the case of our analysis in this section, approximately 1400 points satisfy the relationship 0.99 < Ptj + Fiy < 1. In contrast, for approximatoly 80 points, Pij + Fay < 0.95, indicating clear violations of "faithfulncss."
The break of this "faithfulness" means that there a generation probability of the token that neither "yes" nor "no," " a level that cannot be ignored. One possible explanation for this case that GPT-4 cannot completely asscrt "yos" or "no" on the existence of the causal effect from zj to x; with the knowledge obtained in Step 2. In more anthropomorphic terms, this could suggest that GPT-4 sometimes struggles with its decision-making.
For further rigid handling in the application of our method, it is required to prevent the break of ffatthfulness," " or to extend our quantitative handling of the token generation probability to the one that permits the possibility of this behavior.
Temperature Dependence of the Fluctuation and "Faithfulness"
As described in Eq. (10), the probability distribution depends on the temperature parameter. Because a higher temperature leads to a higher generation probability of the token, unexpected at lower temperatures, it is possible that this parameter can also affect the fluctuations of pú and "faithfulness." Although we have fixed this parameter at 0.7 in all the experiments in this work, further discussion on the optimal temperature for this task is expected.
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E
Composition of Adjacency Matrices Representing Causal Structure and Evaluation
E.1
Composition of Prior Knowledge Matrices
As shown in Algorithm 2 the composition rule of PK depends on the type of SCD method adopted, and the decision criteria of forced and forbidden edges are tentatively set at 0.95 and 0.05, respectively. Although PC and N can be augmented with constraints for both forced and forbidden directed edges or paths, Exact Search can only be augmented with constraints for forbidden directed edges. In this scction, the composition rule for PK is described in detail for all the SCD algorithms have adopted in this work.
For PC For the matrix representation of PK, the values of the matrix elements are determined as follows:
Case 1. Tf x2 + my is forced (i.., Ptj 2 0.95), then PK oj is set to 1.
Case 2. If x; > zy is forbidden (i.e., Pij 0.05), then PKuj is set to O.
Case 3. If the existence of x2 + Iy cannot be determined immediately from the domain knowledge generated by GPT-4 (i.e., 0.05 S Pij 0.95), then P is set to -1
This ternary matrix composition is based on the constraints of the prior knowledge matrix DirectLiNGAM, which will be explained later, to apply the generated PK to DirectLiNGAM as quickly possible. Although prior knowledge is represented and forbidden edges can be set, and the possibility of other unknown edges can be explored. This property, which is similar to that of DirectLiNGAM, means that the prior knowledge for this PC algorithm can be represented in a ternary matrix, if we need to do so. Therefore, the composition rule of PK for PC is set to be the same as that for DirMctLiNGAM in this work, to treat it as consistently as possible.
matrix in the PC algorithm widely open in "causal-learn," both forced
For DIGMM Although the criteria for setting the values in PK are the same as those for PC, the definitions of the values slightly differ. Although the prior knowledge for the PC algorithm in the "causal-learn" package corresponds to the existence of directed edges between pairs of variables, the prior knowledge for AMM is determined with the knowledge of directed paths. The values of the matrix elements are determined as follows:
Case 1. If the directed path from I, to zÿ is forced (i.e., Pij 2 0.95), then PKij is set to 1.
Case 2. If the directed path from F, to zy is forbidden (i.e., Pyy 0.05), then PKij is set to 0.
Case 3. If the existence of the directed path from x; to æy cannot be determined immediately from the domain knowledge generated by GPT-4 (i..., 0.05 < P.j 0.95), then PKij is set to -1.
This ternary matrix composition, which uses 0 and -1, is indeed implemented in the software package "LNGAM..
For Exact Search While PK in cases of PC and DireM is a ternary matrix, one must. be careful that PK in Exact Search is a binary matrix. The values of the matrix elements are determined as follows:
Case 4. If H, + xy is forbidden (i.e., P.j < 0.05), then PK is set to 0.
Case 5. If + xy is foreed, or if the existence of this causal relationship cannot be determined immediately from the domain knowledge generated by GPT-4 (i.e., 0.05 S Pij). then PK;j is set to 1.
Notably, although the definition of PK = 0 in Case 4 for Exact Search is exactly the same as that in Case for PC and DirectLiNGAM, the definition of PKgj = in Case for Exact Search encompasses both Case and Case 3 for PC and DirectLiNGAM. This difference must be considered when evaluating PK in comparison with the ground truths, to interpret the results in a unified manner regardless of the SCD methods used.
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E.2 Composition of the Ground Truth Matrix
The representation of ground truths in matrix form can be simply realized via binary matrix, provided that it is determined whether directed edge exists for every possible pair of variables in the system. The composition rule for the ground truth matrix GT is as follows:
If 2j - 2y exists, then GT i is set
If 2 + 2y does not exist, then GT ig is set 0.
The matrix representations of the ground truths of the benchmark datasets of Auto MPG, DWD, and Sachs shown in Appendix C are expressed as follows:
0
0
0
1
GT AutoMPG
0
0
(20)
0
0
0
1
0
0
0
0
0
GT GTwWD
(21)
0
0
0
0
0
0
1
0
0
0
0
0
0
0
GT Sachs
0
0
1
(22)
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
E.3 Calculation of Metrics for the Evaluation of Structural Consistency with Ground Truths (SHD, FPR, FNR, Precision, F1 Score)
Structural metrics such as the SHD, FPR, FNR, precision, and the Fl score are commonly calculated for performance evaluation in various machine learning and classification contexts, and are compared with the ground truth data. In similar context, the causal structures inferred by LLM-KBCT and SCD, especially for benchmark datasets with known ground truths, can also be evaluated via these metrics.
For the practical evaluation of the SCD results in this study, we use the ground truth matrices defined for the benchmark datasets in Fq.(20) 20 21 and (22) as references, and we measure these metrics via the adjacency matrices that are calculated directly the SCD algorithms or casily transformed from the output causal graphs. Similarly, the calculation of these metrics for evaluating the LLM-KBCI outputs is carried out via PK.
However, it must be noted that there can be some arguments on the definition of metrics for PK on the basis of GT, because the definition of the matrix elements of PK shown in Appendix E. is partially different from that of GT described in Appendix E.2 In particular, although GT, a binary variable that is completely for PC and DiroctLiNGAM and for
determined by whether 24 + x, exists or not, PK; i3 can be set Exact Search, when it not impossible to definitively assert the presence or absence of 2, + De from the domain knowledge.
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Therefore, although reasonable extension of the definitions of these metrics may be required for the above case, in this study, we evaluate these metrics from |PK], in which both i = 1 and iK -1 are interpreted as "tentative assertions of the presence of zj - x;" and are treated identically. This processing of PK can also be interpreted as that temporarily adopting the composition rule of PK for Exact Scarch as it is for the evaluation the SHD, FPR, FNR, precision, and the F1 score, for all the SCD methods. With this processing, PK is handled in a unified manner regardless of the SCD methods used. We believe that this approach the best way to maintain the original concept of composing PK, while aiming for consistent. discussion across all SCD methods.
Calculation of SHD According to the original concept of the structural hamming distance (SHD), this metric is represented as the total number edge additions, deletions, or reversals that are needed convert. the estimatod graph G' into its ground truth graph G (Zheng al.) 2018 Cheng al., 2022. Hasan al., 2023). As in our study, if network graphs G and G' are represented by binary matrices G and G', respectively, where all the elements are either 0 or 1, then the total number of edge additions (A), deletions (D), and reversals (R) can be simply calculated as follows:
A(G', EIG,) 1)
(23)
id
D(G = Σ
1 ICC 1)
(24)
R(
G) Σ 1(G)) -
(25)
Here, we introduce the indicator function 1(r), expressed as follows:
(x) = {1 if = O,
(26)
0 otherwisc (x + 0).
As the SHD is defined SHD = A+ D R, it is easily evaluated as follows:
SHD(G', G) =
Σ{
IG 1) + ICC 1) + 1(G)) - 1)1(G, 1), } 1
(27)
For the evaluation of the SHD of LLM-KBCI outputs, SHD(IPK), GT) is calculated with Eq.
27
Calculation FPR, FNR, Precision, and F1 score In a similar context to the SHD, for the calculation of metrics such as the false positive rate (FPR) and the false negative rate (FNR), we prepare the equation for evaluating the number of true positive (TP), false positive (FP), true negative (TN), and false negative (FN) edges follows:
TP(G', = Σ 1(G 1)1(G' 1)
(28)
i.j
FP(G', G) = Σ
(G - 1)
(29)
i.j
TN(G', G) Σ [((G)))(GG))
(30)
FN(G", G) = Σ 1 1)
(31)
i.j
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Then, using Eq.
28
31
the definition of the FPR, FNR, precision, and the F1 score can be expressed
follows:
FP(G', G) TN(G' G)+ FP(G', G)
FPR(G',
(32)
FN(G", G)
FNR(G", TP(G',G) FN G)
(33)
TP(G', + G)
Precision CaniiionnG",,C ,G,
(34)
2 TP''', G) F Piscore(G',o 2 TP(G', G) FN(G', G) FP(G',
(35)
For the evaluation of structural metrics such as the FPR of TIM-KBCT outputs, FPR( PK|, GT);
FNR PK), GT), P GT') and [KK GT) are calculated with Eq.
332
35
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F Algorithm A for Transformation of Cyclic PK into Acyclic Adjacency Matrices and Selection of the Optimal Matrix
As briefly described in Section 3.1 for the case of DirecLLiNGAM,, an acyclicity of PK is also required. Thus, if the PK directly calculated from the probability matrix is cyclic, must be transformed into an acyclic form. One possible method is to delete the minimum number of edges inchuded in cycles to transform PK into acyelic matrix. However, several solutions may be transformed from the same PK with the minimum manipulation of deleting edges. Therefore, we have decided to carry out causal discovery with DiGMM for every possible acyelic prior knowledge matrix to select the best acyclic prior knowledge matrix PK A in terms statistical modeling. The dataset is again fitted with a structural equation model under the constraint of the causal structure explored with DirM assuming Kinear-Gausse data, and the BIC calculated. After this process repeated, the acyclic prior knowledge matrix with which the BIC becomes the lowest. is selected РK
The overall transformation process is described in Algorithm However, in the practical application of this method, completing the list of acyclic prior knowledge matrices A incurs significant computational costs. Hence, as the number of variables increases, completing this calculation algorithm in a realistic time frame becomes more challenging.
For the future generalization and application of our inference method via DirectLiNGAM, the development of more efficient algorithms for transforming cyclic matrix into acyclic matrix is anticipated.
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Algorithm 3 Transformation of Cyclic PK into Acyelic Adjacency Matrices and Selection of the Optimal
Matrix
Input 1: Cyclic prior knowledge matrix PKc
Input 2: Data X with variables Zn.
Input 3: DirectLiNGAM Algorithm L(X, PK)
Output: Optimal acyclic matrix PK A Initialize the temporal set for matrices T + {PKc}
Initialize the temporal for the number of cycles N 0 Initialize the temporal for acyclic matrices A + 0 repeat
for matrix Tm E T do
Count the number of cycles in Tm as Nm
Add Nm to N end for
IN,, E N Nm = then
Detect all Tm, which satisfies N, 0 and add them to A clse
Initialize the temporal set for modified matrices T" <- ! for Tm E ' do
Initialize the set for edges included in cycles Fm + θ Initialize the set for edges to be removed Fm + {} Detect all cycles in Tm For each detected cycle, identify all the edges that form the cycle Add these edges to set of edges to be removed Em Detect the most frequent edges "Ia 2," in Em as (i,j)s (f)) add (if to F.. for jir, E Fm do
Th: = Tm
Th, (fy:jr) + 0 Add TV to T end for end for
Replace T with T" end if until A is not empty Initialize the optimal BIC value B None
Initialize the optimal acyclic matrix for prior knowledge in DirectLiNGAM Aoptimal BIC None
for Am E A do
Calculate the adjacency matrix (with components) of the causal discovery result Adj L(X, PK Am)
Fit X with the structural causal equation model represented in Adj assuming linear- Gaussian data Calculate the BIC with Adj and as Bremp
B > Bremp or B = None then
B Bremp
Aoptimal BIC Am end if
end for return Aoptimal BIC as PK
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G Details of LLM-KBCI Results
It is also valuable to examine the details of the probability matrices generated by LLM-KBCI, both for the basic discussion of whether LLMs can generate valid interpretation of causality from domain expert's point of view, and for understanding the characteristies of SCP. In this section, the probability matrices generated by GPT-4 for Auto MPG data and DWD climate data, which are relatively casy to interpret within common daily knowledge, are shown and brielly interpreted. For comparison among various SCP patterns (Patterns 1-4) using the same SCD method as much as possible, the probability matrices generated by GPT-4 with SCP are shown only for DiroctLiNGAM. We also bricfly present the probability matrices of LLM-KBCI for the sampled sub-dataset of health-screening results.
G.1 LLM-KBCI for Auto MPG data
In Table 15 the probabilities of the causal relationships of pairs of variables in the Auto MPG data are shown. The cells highlighted in green are those in which the directed edges are expected to appear from the ground truths shown in Figure 7
For all the prompting patterns, although the probability of as one of the ground truth directed edges, is O, the probability of reversed edge "= is non-zero and over 0.95 in Patterns 1-4. To understand this behavior and elucidate the true causal relationship between these two variables, further discussion is required, including the possibility of the hidden common causes that are excluded from the datasct we have used.
which is interpreted
In addition, although we do not believe the existence of the directed edge of "Displacement" "= Acceleration," " the probability of this causal relationship is greater than 0.85 for all the prompting patterns. This may be due to the property of the prompt for evaluating the probability. As shown in Table 2 GPT-4 is allowed to judge the existence of both direct and indirect causal relationships, to acquire a positive answer even if any intervening variables are not included in the datasct. However, for example, considering that the and
probabilities of both "Displacement" """oreent"""""rpooooooe the ground truths, are relatively high, it is also possible that GPT-4 supports the hypothesis of some impact. from "Displacement" on " "Acceleration" partially due to confidence in the indirect causal relationship of "= ""Horspowor"" - "cccllrratio"" If one wants to distinguish the direct and indirect causal
=*"cppow
which are part of
"Displacement" > relationships in the interpretation of the probability matrix, investigating the response from LLMs for the first prompt may lead to further understanding.
Some differences that can be related to the prompting patterns can also be observed. For example, the in Pattern 1 is much smaller than that in the other patterns. Moreover,
probability of "Horsepower"=""Mp" the probabilities of "Horsopower" "Acollaattion" in Patterns and 3 are smaller than those of the other patterns, in which the probability of this edge is almost 1. A possible explanation for these behaviors is that the decision-making of GPT-4 is unsettled with the SCP, in which the causal structure inferred by DirectLiNGAM shown in Figure (c) is included. As neither "Horsepower" "cceleration"" "ccollrrto"""""aataaatttoo nor "Horsepower" "Pg""
appears in Figure (c), despite the confidence in the existence these edges only from the domain knowledge,
the mecision of GPT-4 may become more careful, considering the result SCD. In future work, the
types of decision-making of LLMs that are likely to be affected by the SCP should be investigated.
G.2 LLM-KBCI for DWD climate data
In Table 16 the probabilities of the causal relationships of pairs of variables in the DWD climate data are shown. The cells highlighted in green are those in which the directed edges are expected to appear from the ground truths shown in Figure g
For all the prompting patterns, it is confirmed that all of the probabilities of the causal effects on "Altitude," " "Longitude," " and "Latitude" from other variables are 0. As these three variables are geographically given and fixed, the interpretation by GPT-4 that they act as parent variables that are not influenced by other factors is completely reasonable. Although " "Altitude" and "Latitude" are somehow influenced according the result of LiGMM without prior knowledge as shown in Figure 10 (c), the SCP, including these
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Table 15: Probabilities the causal relationships suggested by GPT-4 in Auto MPG data. The cells in which the directed edges are expected appear from the ground truths, as shown in Figure 7 are highlighted in green.
Pattern 0
EFFECTED CAUSE CAUSE
"Displacement"
"Mpg"
"Horsepower"
"Weight."
"Acceleration"
"Displacement"
0.000
0.000
0,000
0,000
"Mpg"
0.999
0.997
1.000
1.000
"Horsepower"
0.999
0.000
0.000
0.000
"Weight"
0.635
0.000
0.000
0.000
"Acceleration"
0.996
0.023
0.998
0.998
Pattern 1 "Mpg"
EFFECTED,CATIO CAUSE
"Displacement"
"Horsepower"
"Weight."
"Acceleration"
"Displacement"
0.000
0.000
0.000
0.000
"Mpg" "
1.000
0.128
0.484
0.058
"Horsepower"
1.000
0.056
0.001
0.000
"Weight"
0.994
0.000
0.000
0,000
"Acceleration"
0.859
0.000
0.828
0.998
Pattern 2
EFFECTED CAUSE
"Displacement"
"Mpg"
"Horsepower"
"Weight."
"Acceleration"
"Displacement"
0.000
0.000
0.000
0.000
"Mpg"
1.000
0.999
1.000
0.984
"Horsepower"
1.000
0.000
0.000
0.000
"Weight"
0.997
0,000
0.000
0,000
"Acceleration"
0.995
0.002
0.996
0.999
Pattern 3
EFFECTED CAUSE
"Displacement"
"Mpg"
"Horsepower"
"Weight:"
"Acceleration"
"Displacement"
0.000
0.000
0.000
0.000
"Mpg"
0.977
0.969
0.754
0.547
"Horsepower"
1.000
0.051
0.696
0.010
"Weight"
0.954
0.000
0.000
0,000
"Acceleration"
0.981
0.000
0.435
0.809
Pattern 4 "Mpg"
EFFECTED CAUSE CAUSE
"Displacement"
"Horsepower"
"Weight."
"Acceleration"
"Displacement"
0.000
0.000
0.000
0.000
"Mpg"
0.995
0.994
0.997
0.940
"Horsepower" 0.999
0.999
0.314
0.006
0.000
"Weight"
0.000
0.012
0.000
" "Acceleration"
0.964
0.000
0.989
0.814
unnatural results, has not affected the decision-making of GPT-4. From this behavior, inferred that the response regarding axiomatic and self-evident malters from GPT-4 is robust and unlikely to be affected by the SCP, even if the SCD result clearly exhibits unnatural behaviors.
which is assumed to be a ground truth, is unlikely to be asserted by GPT-4, "Temperature" "Precppptaaaio which is not expected to be a ground truth, is likely to be asserted by GPT-4, across all the prompting patterns. For further interpretation of these unexpected behaviors from our ground truths, investigation of the response generated in the first prompting process is recommended. Interestingly, although the probabilities of 0 0-2, they become non-zero finite values in Patterns and 4, in which the causal coefficient of this directed
In addition, although
""Prcipttt""trrppaaaaatttt are 0 in Patterns
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edge calculated with DirectLiNGAM is inchuded in the SCP. This behavior may indicate that the SCP assist the decision-making of GPT-4 even if it generates incomplete response on causal relationships with its background knowledge.
Table 16: Probabilities of the causal relationships suggested by GPT-4 in DWD climate data. The cells which the directed edges are expected appear from the ground truths as shown in Figure are highlightod in green.
Pattern
EFFECTED,CAUSS "Altitude"
"Temperature"
"Precipitation"
"Longitude"
"Sunshine"
"Latitude"
"Altitude"
0.000
0.000
"Temperature"
1.000
0.891
0.000
1.000
1.000
"Precipitation"
1.000
0.999
0.000
0.001
0.995
"Longitude"
0.000
0.000
0.000
0.000
0.000
"Sunshine"
1.000
0.000
0.998
0.000
1,000
"Latitude"
0.000
0.000
0.000
Pattern
SFFECTED,CAUSE "Altitude"
" "Precipitation" "Temperature"
"Longitude"
"Sunshine" "
"Latitude"
"Altitude"
0.000
0.000
0.000
0.000
0.000
"Temperature"
0.384
0.034
0.000
0.856
0.011
"Precipitation"
0.025
0.999
0.000
0.036
0.026
"Longitude"
0.000
0.000
0.000
0.000
0,000
"Sunshine"
0.006
0.011
0.008
0.000
0.596
"Latitude"
0.000
0.000
0.000
0.000
0.000
Pattern 2
EFFECTED,CAUSE
"Altitude"
"Precipitation" "Temperature"
"Longitude"
"Sunshine" " "Latitude""
"Altitude"
0.000
0.000
0.000
0.000
0.000
"Temperature"
0.997
0.007
0.000
0.999
0.989
"Precipitation"
0.739
0.999
0.000
0.000
0.384
"Longitude"
0.000
0.000
0.000
"Sunshine"
0.874
0.010
0.976
0.000
0.981
"Latitude"
0.000
0.000
0.000
0.000
0.000
Pattern
EFFECTED.CAUST "Altitude"
"Temperature"
"Precipitation"
"Longitude"
"Sunshine"
"Latitude"
"Altitude"
0.000
0.000
0.000
0.000
0.000
"Temperature"
0.919
0.016
0.003
0.615
0.973
"Precipitation"
0.008
"Longitude"
0.000
0.000
0.000
0.000
0.000
"Sunshine"
0.039
0.000
0.001
0.875
0.199
"Latitude"
0.000
0.000
0.000
0.000
0.000
Pattern
EFFECTED:CAN
"Altitude"
"P "Precipitation" "Temperature"
"Longitude"
"Sunshine"
"Latitude"
"Altitude"
0.000
0.000
0.000
0.000
0.000
"Temperature"
0.982
0.023
0.958
"Precipitation"
0.826
0.987
0.927
0.010
0.797
"Longitude"
0.000
0.000
0.000
0.000
0.000
"Sunshine"
0.534
0.021
0.387
0.013
0.638
"Latitude"
0.000
0.000
0.000
0.000
0.000
G.3 LLM-KBCI for Dataset of health Results
In Table 17 the probabilities of the causal relationships of pairs of variables in our sampled sub-dataset of
bealth-screening results are shown. The cells highlighted in red are those which the directed edges are expected to appear, as described Appendix C.4] In contrast, since " "Age" an unmodifiable background factor, it can be concluded that it not a descendant of any other variables. Therefore, the probabilities in the cells highlighted in blue expected to be O.
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Across all the prompting patterns, it is confirmed that all the probabilities of the causal effects on "Age" from other variables are indeed 0. From this fact, it is likely to be regarded by GPT-4 as axiomatic and self-evident that "Age" cannot be affected by other variables, and the judgment of causal relationships is not influenced by the SCP, even the SCD result clearly exhibits unnatural behaviors as shown in Figure
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Table 17: Probabilities of the causal relationships suggested by GPT-4 in the sampled sub-dataset health- screening results. The cells which the directed edges are expected to appear from the ground truths are highlighted red. In contrast, the probabilities in the cells highlighted blue, are expected to be zero, since "Age" is expected to be parent variable for all other variables.
Pattern 0
SRRECTED,CAUSS
"BMI"
"Waist"
"SBP"
"DBP"
"HbAlc"
"LDL"
"Age"
"BMI"
0.994
0,000
0.000
0.000
0.000
0.901
"Waist"
1.000
0.000
0.000
0.000
0.000
0.353
"SBP"
0.999
0.962
0.998
0.987
0.000
0.626
"DBP"
0.998
0.995
0.993
0.000
0.000
0.001
"HbAle"
0.998
0.998
0.000
0.000
0.000
0.986
"LDL" "
0.988
0.967
0.000
0.000
0.000
0.002
"Age"
0.000
0.000
0.000
0.000
0.000
0.000
Pattern 1
EFFECTED CAUSE
"BMI"
" "Waist"
"SBP"
"DBP"
"HbAlc"
"LDL" T
"Age"
"BMI"
0.312
0.000
0.000
0.014
0.000
0.076
"Waist"
1.000
0.000
0.000
0.023
0.000
0.043
"SBP"
0.999
0.912
0.999
0.997
0.000
0.302
"DBP"
0.998
0.421
0.050
0.000
0.000
0.019
"HbA1c"
0.517
0.503
0.101
0.000
0.000
0.170
"LDL"
0.008
0.527
0.000
0.000
0.000
0.517
"Age"
0.000
0.000
0.000
0.000
0.000
0.000
Pattern
EFFECTED CAUSE
"BMI"
"Waist"
"SBP"
"DBP"
"HbA1c"
"LDL"
"Age"
"BM
0.998
0.001
0.001
0.996
0.000
0.093
"Waist"
0.999
0.000
0.003
0.959
0.007
0.099
"SBP"
0.998
0.994
0.983
0.994
0.040
0.207
"DBP"
0.997
0.975
0.984
0.983
0.002
0.115
"HbA1c"
0.982
0.608
0.002
0.000
0.000
0.723
"LDL"
0.994
0.946
0.000
0.000
0.452
0.171
"Age"
0.000
0.000
0.000
0.000
0.000
0.000
Pattern 3
SEFECTED.CAUSS
"BMI"
"Waist"
"SBP"
"DBP"
"HbA1e"
"LDL"
"Age"
"BMI"
0.003
0.000
0.000
0.868
0.923
0.306
"Waist"
1.000
0.000
0.000
0.983
0.000
0.076
"SBP"
1.000
0.855
0.959
0.999
0.000
0.235
"DBP"
1.000
0.032
0.140
0.021
0.000
0.095
"HbA1c"
0.967
0.634
0.000
0.000
0.000
0.046
"LDL" "
0.562
0.165
0.000
0.000
0.085
0.013
"Age"
0.000
0.000
0.000
0.000
0.000
0.000
Pattern 4
EFFECTED'S
CAUSE CAUSE
"BMI"
"Waist"
"SBP"
"DBP"
"HbA1c"
"LDL"
" "Age"
"BMI"
0.993
0.000
0.000
0.024
0.006
0.037
"Waist"
1.000
0.000
0.000
0.957
0.000
0.395
"SBP"
0.999
0.982
0.001
0.998
0.000
0.795
"DBP"
0.994
0.204
0.985
0.408
0.000
0.926
"HbAlc"
0.824
0.391
0.000
0.000
0.000
0.176
"LDL."
0.485
0.403
0.000
0.000
0.000
0.027
"Age"
0.000
0.000
0.000
0.000
0.000
0.000
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H Applicability of the Proposed Method Across Various LLMs
In the main body of this paper, we fix the LLM to GPT-4-1106-preview to maintain consistency and control across the trials with several kinds of datasets. In this section, however, to confirm the universal applicability of the proposed method, we conduct the same experiment of the proposed method with several LLMs, and confirm that adapting the results of LLM-KBCI as prior knowledge SCD indeed further enhances the performance of SCD with various LLMs.
H.1 Independently Assigning GPTs for Steps 2 and
For this supplemental experiment, in addition to GPT-4-1106-previeee we have adopted 577-3.5-turbo-012,, GPT-4-0125-preview and GPT-40-2024-00-06 Although these LLMs are mutually different in architecture and generation, the format of the input and output, and the API settings (including the log-pre pog-prbbablityy extraction) are standardized across the models. Therefore, the technical setup is standardized within this range of comparison, and it is easy to compare the performance of these LLMs in the proposed method.
As explained in Sections 1 and 3 LLMs are utilized both in Steps 2 and 3. Therefore, we choose the LLMs for these two steps independently, and confirmed every combination of LLMs in these steps. Furthermore, we adopt the prompting Pattern 0 (prompting without the results of SCD) for comparison, since the purpose of this experiment is to demonstrate that various LLMs can improve the SCD by providing prior knowledge. We also fix the dataset to DWD climate data, for the comparison of performance.
The experimental results are summarized in Table 18 In the same manner as Table evaluate the final SCD results obtained in Step 4, with the SHD, FPR, FNR, precision, and the Fl score, using the ground truth adjacency matrix GT as a reference. Furthermore, we also evaluate the CFT, RMSEA, and BIC of the causal structure obtained after Step 4, under the assumption of linear-Gaussian data; to evaluate the results with respect to the statistical validity of the calculated causal models. To evaluate the effect. of PK augmentation by the LLMs in Pattern 0, the baseline result is that without PK (Baseline A).
3 in Section
we
It is clearly observed that in any combination of LLMs in Steps 2 and 3, the SHD, FPR, FNR, and BIC after Step 4 become equal to or under the values of Baseline A (without PK). and that the precision and F1 score after Step 4 become larger than those of Baseline A. These facts clearly suggest. that the proposed method in this paper indeed improves the SCD results regardless of the LLMs adopted in Steps 2 and 3.
However, it is not clear from this table what types of LLMs can further improve the SCD results. For example, although the GPT-4 series has been reported to perform better than the GPT-3.5 series in many tasks (OpenAl 2023). this tendency is not observed in Table 18 Morcover, although SPT-3.5-turbo-oe and 1PP-4-0125-previee are updated models of
and GPT-4-0125-previeen respec- tively, the improvement related to these updates is not observed in Table [8 Therefore, for the optimal selection of the LLMs for practical application of this method across various domains, further research is needed on the relationship between the LLM properties and the performance on causal reasoning tasks in each domain, including the possibility of adopting RAG or fine-tuning.
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Table 18: Comparison of the SCD results after Step in Pattern O (prompting without any SCD results) across various GPT models, on the DWD climate datasct. While the SHD, FPR, FNR, precision, and the F1 score are compared to evaluate how close the results are to the ground truths, CFI, RMSEA, and BIC are compared evaluate the statistical validity of the calculated causal models. Lower values are superior for the SHD, FPR, FNR, RMSEA and BIC, and higher values for the precision, F1 score and CFI. The underlined values are the same those in Table which are obtained only with GPT-4-1106-preváaee Baseline A is used for the comparison with the SCD results augmented with PK generated by the LLM, to evaluate the effect of PK augmentation by the LLM. It is suggested that the proposed method in this paper indeed improves the SCD results regardless of the combination LLMs adopted in Steps and 3.
LLM for Step 2
LLM for Step 3 SHDI
FPR.
FNR
Precisiont
Fiscoref
CFI
RMSEAL
BIC
PK PBaasclie A)
0.33
0.67
0.17
0.22
1.00
0.00
99.53
gpt-3.5-turbo-111
0.07
0.33
0.67
0.93
51.98
gpt-3.5-turbo-0125
0.07
0.33
0.67
0.93
51.98
gpt-3.5-turbo-
gpt-4-1106-previeww
0.07
0.17
0.71
0.77
0.93
0.16
57.90 57.90
spt-4-0125-preview
0.07
0.33
0.67
0.67
0.93
0.16
51.98
gpl-4o-2024-08--0
0.07
0.50
0.60
0.55
1.00
0.00
46.81
spt-3.5-turbo-1100
0.03
0.50
0.75
0.60
0.98
0.09
40.80
spt-3.3-turbo-01255
0.07
0.33
0.67
0.67
0.93
0.16
51.98
gpt-3.5-turbo-0125
gpt-4-1108ppreview
0.07
0.50
0.35
1.00
46.81
gpt-4-0125-prvview
0.07
0.50
0.55
1.00
46.81
gpt-to-2U24-US-UU
0.07
0.33
0.67
1.00
67
spt-9.5-turb-11166
0.07
0.33
0.67
0.67
1.00
0.00
52.67
xpt-3.5-tuuro-01255
0.07
0.33
0.67
0.67
1.00
0.00
52.67
115-4-1106-previee
spo-4-1108-preview
0.07
0.33
0.67
0.67
1.00
0.00
52.67
spt-4-0125-previeew
0.07
0.33
0.67
0.67
1.00
0.00
52.67
gpt-4o-2024-08-66
0.07
0.33
0.67
0.67
1.00
0.00
52.67
gpt-3.5-turbo-1106
0.07
0.50
0.55
1.00
46.81
gpt-3.5-turbo-0122
0.07
0.33
0.67
0.67
0.93
0.16
51.98
gpt-4-0125 25-eeee
gpt-4-1106-preview
0.07
0.50
0.60
0.55
1.00
0.00
46.81
spt-4-0125-preview
0.07
0.50
0.60
0.35
1.00
0.00
46.81
gpt-4o-2024-08-00
0.07
0.50
0.60
0.55
1.00
0.00
46.81
spt-3.3-turbo-1106
0.03
0.50
0.75
0.60
0.98
0.09
40.80
gpt-3.3-turbo-01255
0.07
0.33
0.67
0.67
1.00
0.00
52.67
gpt-4o-2024-08-06
gpt-4-1106-preview
0.07
0.50
0.35
1.00
46.81
gpt---0125-prvview
0.50
0.55
1.00
46.81
gpt-4o-2024-06
0.10
0.67
0.40
0.36
0.51
0.53
42.85
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H.2 Evaluation with Open- Source LLMs
To validate the universal elfectiveness of the proposed method in this work across various LLMs, including open-source LLMs, we conducted the same experiments using several open-source LLMs. Specifically, we selected three reprosentative open-source LLMs: Llama-3. 3. 1-----.------------ Instrutttt
28 team 2024), 22-2b-t
Team 2024) and Qwen2. 5-32B-Instruct 30 Team 2024 Yang et al. 2024p. In these experiments, the
same L.T.M was used in both Step and Step 3. The parameter settings and prompts were consistent with
those described in Section 3.1
The results with three types of open-source LLMs are summarized in Table 19 It is clearly confirmed that the SHD, FPR, FNR, and BIC after Step 4 are lower than those of Baseline A (without PK) across all open-source LLMs adopted in this experiment. This result clearly supports the fact that the improvement with SCP does not merely comes from GPT-series models, but comes from the proposed method, which integrates LLMs into SCD.
htte:s//huungiaarrrr/.////////// Instruct
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Table Comparison of the SCD results in Paltern (prompting without any SCD results) with the DWD climate dataset we have conducted across several open-source LLMs. The underlined values are the same those in Table 3 which are obtained only with 6PT-4-1106-previe with the SCD results augmented with PK generated by the LLM, to evaluate the effect of PK augmentation by the LLM. Tt is suggested that the proposed method in this paper indeed improves the SCD results with various open-source LLMs, even those outside the GPT series.
Baseline A is used for the comparison
LLM for Steps and
SHD,
FPR.
FNR.
Precision
F1scoret
CFT1
RMSEA
BIC,
PK (Baseline A)
0.33
0.67
0.17
0.22
1.00
0.00
99.53
Llama-3. Instrucctt
0.07
0.33
0.67
0.67
1.00
0.00
52.67
getuma--2222 2-27b-it
0.10
0.50
0.50
0.50
0.92
0.17
51.92
9wen2.5-7B-Insteee
0.10
0.50
0.50
0.50
0.73
0.43
50.46
gpt 4- 106 10evvve (used in the main body)
0.07
0.33
0.67
0.67
1.00
0.00
52.67
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Prompt Template Adjustment for Estimating LLM Confidence in Causal Relationships
To fix the prompt templates described in Tables and 12 we also considered the sensitivity of LLM responses to the prompts (Sclar et. al. 2024; Cao el al. 2024 Although many functions and tools have been developed and released by the community for optimizing prompts, carefully focused on how to ask LLMs about the causal relationship from 2j to z₁. In this section, we provide supplementary explanation of how we decided to adopt the following question: "If xy is modified, will it have direct or indirect impact on x;?"
(2) as the core sentence of the prompt template 95j in Table
First we prepared 20 types of templates for asking LLMs about the causal relationship from Ty to o. summarized in Table 20 These templates were generated the GPT-3. 5-t.rb...........
Table 20: List of prompt templates Qn(r;, xz) for asking LLMs about the causal relationship from Tÿ to xe.
(z)),,zz)) highlighted in bold is the original form of the adopted template.
Number n
Template Qn (nt,
Does 2j lead to 2;?
Can Ty be attributed the cause of m;?
3
Is there a causal relationship between zy and x;?
4
If xt is modified, will it have an impact on x;?
5
We believe that 2j is responsible for z,. Is this assertion valid?
6
Is influenced by xzz
7
Can changes in Ij result in changes in .;?
8
Is there evidence to suggest, that Tÿ is the cause of x;?
9
Does Zy have a direct effect on 2;?
10
If 2 manipulated, will z; be affected?
11
Is there connection between Ty and F4, where Øj is the cause and x, the effect?
12
Can Zj bring about x;?
13
Will change if xy is altered?
14
Is there a correlation between 2ÿ and Hı, indicating a causal relationship?
15
Is 2y a determining factor for x;?
16
Can Tj be considered potential cause of x;?
17
If xj controlled, will it impact 2;?
18
Is there link between æy and 24, suggesting a causal association?
19
Does æÿ play role in causing x;?
20
Is there causal-effect relationship between æÿ and x;?
Next, we prepared brief benchmark test to evaluate the templates shown in Table 20 We adopted the ground truth relationships among the variables "hour of day," "temperature, " and "electricity load," which are included in the Tübingen database for cause-effect pairs (Mooij et al. 2016). Figure 19 illustrates the benchmark ground truths used in this evaluation. On the basis of these ground truths, we created variable name pairs, as shown in Table 21 and filled them into the templates to construct six questions.
Under the conditions described above, we evaluated the templates via zero-shot prompting, and generated knowledge prompting [Liu et al.) (2022). All the experiments were conducted using UPT-3.5-ture with the temperature fixed at 0.7. For all the questions, repeated the same prompting 50 times, and calculated the accuracy for all the prompt templates in Table 20
1.1 Results of Zero-Shot Prompting
To obtain the answer in the form of yes or no, We simply used the prompting template shown in Table with the question templates in Table 20 and variable the name lists in Table 21
22
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hour of day
temperature
x
x
electricity load
Figure 19: The benchmark ground truths based on the Tübingen database for causo-effect pairs Mooij ct al, 2016
Table 21: Variable name pairs filled into the templates (x),) for constructing questions and the correct.
answers the basis of Figure 19
Question Number
3i the temperature the electricity load the electricity load the hour of day the hour of day the temperature
Fj
Correct Answer
the hour of day the hour of day the lemperature the temperature the electricity load
Yes
2
Yes
3
Yes
4
No
5
No
6
the electricity load
No
Table 22: Prompt template for zero-shol prompting experiments.
Template for Zero-shot Prompting Experiments
Let's discuss the problem of causation on energy consumption related with climates.
(1))))
Please answer with <yes> or <no>>.
No except these two responses needed.
The top four and worst four templates, which are based on overall accuracy under zero-shot prompting, are summarized in Table 23 Although the template (z), shows the best performance when n = 4, 5, 12, 19, the performance becomes poor when n = 3, 14, 18.20, under the prompt condition of zcro-shot.
1.2 Results of Generated Knowledge Prompting
To obtain the knowledge used in the prompting process described later, utilized the ChatGPT plugin's functionality to connect to Wikipedia, using the prompt shown in Table 24 for the three variables. We then integrated all of the generated knowledge into a unified form, as shown in Table 25 Finally, the generated knowledge prompting (Liu et al. 2022) was performed using the template described in Table 26 in combination with the question templates from Table 20 and the variable name pairs from Table
The top three and worst three templates, based on overall accuracy under generated knowledge prompt, are summarized in Table 23 Although the template (m(,) shows the best performance when 4, 12, 19, the performance becomes poor when 14, 8,5, under the prompting condition of generated knowledge prompting.
In terms of the universality of the proposed method, it is ideal to adopt a prompt template that performs well in both zero-shot prompting and generated knowledge prompting. From this perspective, and on the basis of the results shown in Table 23 and Table 27 the prompt templates with n = 4 and n 19 appear be the most effective. As shown Table 20. both templates are simple and easy to modify if needed. However, whereas the template with 19 (*Does vj play role in causing x,?") treats æ; phenomenon, the
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Table 23: Summary of the experimental results of zero-shot prompting.
Top in Overall Accuracy
Template
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Overall Accuracy
Q19(1; m3)
0.14
0.70
0.98
0.98
0.64
0.62
0.68
Q1(2i, 45)
0.14
0.68
0.96
0.98
0.72
0.54
0.67
@z(2s, Zy)
0.12
0.70
1.00
0.94
0.64
0.60
0.67
Q12(12, 2g))
0.10
0.72
0.98
0.96
0.64
0.58
0.66
Worst 4 in Overall Accuracy
Template
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Overall Accuracy
Q20(1;, Tj)
0.16
0.64
0.92
0.00
0.42
0.48
0).4
Qs(Ti, zz}
0.16
0.64
0.94
0.08
0.32
0.46
0.43
Qia(1e, F5)
0.20
0.66
1.00
0.02
0.30
0.40
0.43
Q1a(1r, mT))
0.08
0.56
0.96
0.08
0.42
0.42
0.42
Table 24: Prompt Used for Knowledge Acquisition. in the blank of ø4, "the hour of day, "the temperature, or "the electricity load" is filled.
Template for Knowledge Acquisition
In the context of the relation between the climate and the energy consumption, please provide the knowledgge of i; in detail as much as possible.
template with 4 (fIf zy is modified, will it have an impact on xr)?") treats Ty variable. TTherefore, considering that our focus is on improving SCD using datasets composed of continuous variables, we judged that the template of n the best for our purpose.
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Table 25: Integrated knowledge for "the hour of day, "the temperature, " and "the electricity load."
Integrated Knowledge
1. about the hour of day:
Early Morning (12:00 AM 6:00 AM)
Lower Finergy Demand: Most people asleep, leading lower energy consumption for lighting, appliances, and electronies. Heating/Cooling: Depending on the scason and climate, heating or cooling systems may be in use, but generally at lower scttings. Industrial Use: Some factorics and industrics operate 24/T, contributing baseline level of energy consumption.
Morning (6:00 AM - 9:00 AM)
Peak in Energy Demand: People wake up, turn on lights, and use appliances, leading surge in energy demand. Heating/Cooling In colder climates, heating systems may be turned up as people prepare for the day. In hotter climates, cooling systems may be activated.
Transport: Increased use of public and private tramsportation, contributing to fuel consumption.
Midday (9:00 AM 3:00 PM)
Stable Demand: Energy demand stahilizes but remains high due to industrial and commercial activities.
Solar Energy: Peak hours for solar energy production, which can offset some fossil fuel consumption.
Air Conditioning: hot climates, the demand for cooling can be very high, especially commercial buildings.
Afteruoon to Early Evening (3:00 PM - 7:00 PM)
Peak Demand: Another surge often
people return home and use appliances, electronics, and lighting.
Heating/Cooliig:: Depending on the season, heating or cooling systems may be turned up again.
Solar Energy: Solar energy production
to decline the sun sets.
Late Evening (7:00 PM 12:00 AM)
Declining Demand: Energy demand gradually decreases as people go to bed.
Coating/Coolingg Systems may still use generally lower settings,
Off Peak: Some utilities use this time to generate energy at lower costs, sometimes using less efficient but cheaper power plants.
2. about the lemperature:
Heating and Cooling Heating in Cold Climates: In colder climates, a significant amount of energy is consumed for heating buildings. This is often done through natural gas electric heating systems. The colder the climate, the energy required maintain comfortable indoor temperature.
Cooling in Hot Climates: Conversely, in hot climates, air conditioning is used extensively, which also consumees a large amount of electricity.
Seasonal Variations
Winter: Energy consumption often spikes during the winter months in colder climates due heating needs.
Summer: In hot elimates, the opposite is true; energy consumption can be highest the summer due to air conditioning.
3. about the electricity load:
Scusonal Variations
Summer: Hot weather often leads to increased electricity consumption due to the use of air conditioning and cooling systems.
Winter: Cold weather also lead to high electricity demand for heating, although in many places, heating more commonly fueled by natural gas oil.
Time of Day
afternoon and carly evening. Off-Peak Hours: These are times when clectricity demand is lower, typically late at night and early in the morning.
Peak Hours: These are the times when electricity demand highest, often
Climate Change
Changing Patterns: Climate change could lead to more extreme weather events, affecting electricity load patterns.
Adaptation: As the climate changes, patterns of electricity consumption may emerge, requiring adaptive strategies.
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Table 26: Prompt Used for Knowledge Acquisition. in the blank of 24, "the hour of day, "the temperature, "the electricity load is filled.
Template for Knowledge Acquisition
Here is the basic kuowledge of the hour of day, the lemperature, and the electricity load, in the context of the relation between the climate and the energy consumption.
(domain knowledge shown in Table 25
Using this knowledge, let's discuss the problem of causation energy consumption related with climates.
Ir)
Please answer with <yes>> <no>> No answers except these two responses needed.
Table 27: Summary of the experimental results of generated knowledge prompting.
Top in Overall Accuracy
Template
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Overall Accuracy
Q+(1, 25)
0.00
1.00
1.00
1.00
1.00
1.00
0.83
Q12(2, mT)
0.00
1.00
1.00
1.00
1.00
1.00
0.83
(19(1;,7;)
0.00
1.00
1.00
1.00
1.00
1.00
0.83
Worst 3 in Overall Accuracy
Template
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Overall Accuracy
Qus(z, I,)
0.00
0.92
1.00
0.00
1.00
1.00
0.65
0.00
0.14
0.36
1.00
1.00
1.00
0.58
(g(
0.00
0.00
0.12
1.00
1.00
1.00
0.52
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J Other Potential Applications of the LLM-Generated Probability Matrix for Causal Inference
While the L.M-generated probability mairix is used as the basis for constructing the prior knowledge matrix improve SCD performance, careful understanding of the assumptions behind this matrix contributes to recognizing both its limitations and its potential for other applications. As previously explained in Appendix D.1 the (i.j) component of the LLM-generated probability matrix is theoretically expressed follows:
P(c = "yes"lo.s (2) exp(=<c= = "ycs=(c="ycs"
"9rs"",9;"11
(2) )/T
(36)
(2) Etor all exp(=(c, 01j )/T)
(2) is the prompt, the template of which is shown in Table 2 and T is the temperature parameter. Here, 96 Moreover, =(c, ) denotes the logit of the occurrence of token given the prompt ". Notably, the (2) conditional probability P(c= "yes" (2) T is determined solely by 43z T, and the internal properties of the LLM that produce the logit. z(c, 0ij Therefore, interpret this token generation probability as the LLM's confidence in the existence of a causal relationship from 2j to I;. Therefore, this probability is fundamentally different from the probability distributions used in conventional statistical causal inference, which are derived from observational data and vary with the values of the variables. Understanding this difference is key to recognizing both the limitations and the potential for applications of the probability matrix discussed in this work.
Limitations in the Application to Conventional Causal Inference Frameworks
For example, within the potential outcomes framework, the probability- average causal effect (ACE) from the intervened variable zÿ (fixed at 1 or 0) to the affected variable z; is expressed as follows:
TaCE(2: + m3) = P(zi(do(2,, = 1)) - P(x:ldo(2; = 0))
(37)
However, since the LLM's confidence probability expressed in Eq. 36 is independent of the actual variables, and not a probability distribution that reflects real-world data, it cannot be directly applied to the statistical causal inference framework.
Potential for Applying Probarilitttaaaaaee Causal Graph Discovery
Nevertheless, a study has also been reported on causal graph discovery and causal identification under the condition probabilistic uncertainties at the edges of a causal graph(Akbar) et al.) 2023). In this research, the probability of an acyclic directed mixed graph (ADMG) can be expressed as follows:
P(G)
II Pe [I eEg
(38)
egg
Here, Pe denotes the probability of the existence of edge e. If the probability in Eq. (36 is assumed to be equal to Pe, becomes possible to identify the causal graph, which has the highest likelihood according the domain expert knowledge in the LLM, by computing arg maxP(G). This idea may offer an alternative approach to reasonable causal inference by selecting the most likely causal graph based on domain expert knowledge the structural basis for further analysis, which then leads to the step of conventional statistical causal inference.
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Reviews:
[{"review_id": "iOiOhnUwBr", "reviewer": "Reviewer_VFiT", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "__Strengths__:\n- flexible approach (with respect to both the causal discovery method and the LLM used)\n- the idea and implementation of SCP is an important contribution to the growing literature on integrating LLMs and causality\n\n__Weaknesses__:\n- writing could be improved (grammar, organization, main text vs appendix)\n- formal details and rigor are missing, resulting in unjustified claims", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposed a new method for leveraging LLMs for causal discovery, with the main contribution being \"statistical causal prompting (SCP)\" to extract a measure of uncertainty about specify edges in a causal graph. The paper also experiments on an unpublished (and hence unseen by the LLM) dataset, which it claims hasn't been done before.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "__Essential__:\n- The paper needs careful proofreading and editing for tense and active vs. passive sentence construction, especially in the abstract and contributions, to make it more what this paper contributes compared to what others have done. \nFor example, the abstract has sentences \"It has been revealed...\" then \"Experiments have reaveled...\" followed by \"... we have demonstrated...\". I can't tell if the first two passive sentences are supposed to be describing related work or specific results in this paper. I suspect the latter, but there's a similarly confusing active vs passive pattern in Section 1.3, so it's not as clear as it should be.\n\n- There are several formal sounding but vague words and phrases that need to either be made more formal and explicit, or clarified somehow, or removed:\n  - end of page 2: \"more statistically valid causal models\"\n  - Section 1.3 (4): \"clearly confirmed... robustly leads to more statistically valid causal models with natural ground truths\"; this is an experiment on a single data set, so I don't find such a strong claim (\"clearly confirmed\" and \"robustly\") to be justified; also what is a \"natural\" ground truth?\n  - second to last paragraph on page 4: \"we detail herein how to achieve both statistical validity and natural interpretation with respect to domain knowledge at a maximally high level\"; this needs proof and formal definitions for \"statistical validity\" and \"maximally high\" and more clarification what \"natural interpretation\" means.\n  - third paragraph of page 6: \"from an objective point of view\"; what does this mean?\n  - \"naturalness\" and \"objectively\" in Tables 1 and 2, respectively\n  - \"unnatural\" in Figure 3 caption\n  - \"bias\" is mentioned throughout the paper, but it's never clear to me exactly what this means: selection bias in causal modeling comes to mind, as does biased statistical estimation, but these are specific, formal ideas whereas the paper seems to be using \"bias\" in a more vague and undefined way\n\n- Important details of the causal discovery methods used are missing or seem incorrect:\n  - top of page 4: \"non-parametric and score-based SCD method\"; scores often make parametric assumptions---which specific score is used here?\n  - bottom of page 5: which CI test is used for PC? If I'm not mistaken, the original A* algorithm paper uses a parametric score---which do you use?\n  - Algorithm 1: how are the different SCD results used? (thinking of DAG vs CPDAG)\n  - last paragraph of page 6: \"if $PK_ij$ = Forbidden, the causal effect from $x_j$ to $x_i$ is forbidden from appearing in the SCD result\"; more precisely, do you mean an ancestral graphical relation is forbidden, or a parental one?\n  - footnote 10, page 9: you earlier claimed to use a non-parametric score-based method, so why not use that score instead of the Gaussian BIC?\n  - need more clear distinction between casual discovery and causal inference: these seem to sometimes but not always be used interchangably in the paper, but that's confusing compared to the causality literature where these are often different tasks; I don't really see any causal inference in this paper\n  \n__Suggested__:\n- First sentence in Section 1.3 (5) is missing a verb in the last phrase \", and the technical...\"\n- Top of page 4: should be \"Clark\" not \"Clerk\"\n- add some discussion about or even experiment with a more naive SCD/LLM integration approach, like engineering a prompt to get the LLM to just directly tell you the DAG and associated edge confidences\n- streamline the main text by moving many of the LLM prompting details to the appendix; just as many of the causal discovery details are moved to the appendix, since the paper is about trying to be general/agnostic to the particular algorithm used, so should much of the GPT-4 details and prompting patterns etc.\n- emphasize the \"common sense causal model based on broad/vast knowledge\" aspect more in the abstract and intro", "broader_impact_concerns": "The paper ends with reasonable statements about technical limitations and broader impact of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "RIiqXnnJyQ", "reviewer": "Reviewer_8HhM", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n- The integration of SCD with LLM-generated knowledge is an interesting approach that attempts to bridge statistical inference and domain expertise.\n- The paper evaluates the approach on a dataset excluded from the LLM's pretraining, which strengthens claims of robustness.\n- The authors provide a detailed discussion of failure cases, limitations, and areas for future improvements.\n\nWeaknesses:\n\n- The paper does not address scalability concerns; it remains unclear how well the method would perform on datasets with a larger number of variables.\n- The sensitivity of SCP to different prompt wording and hyperparameters (such as temperature settings) is not extensively explored.\n- The probabilistic transformation of LLM outputs into structured prior knowledge is heuristic, and its reliability across diverse domains remains uncertain.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a novel method for knowledge-based causal inference that integrates LLMs with traditional statistical causal discovery (SCD) through a self-critique-type prompting strategy called Statistical Causal Prompting (SCP). The approach involves (1) zero-shot synthesis of a causal graph by an LLM, (2) prompting the LLM to critique its own response, (3) converting the dialogue consisting of critiques into probabilities of whether an edge exists in the causal graph, and (4) finally, incorporating these probabilities to update the graph. The authors validate their method on benchmark datasets and a closed health screening dataset, demonstrating that LLM-assisted SCD better aligns with ground truths than standard SCD. The paper also discusses the reliability, risks, and limitations of the approach.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I would appreciate the following updates to secure my recommendation for acceptance:\n- Clarifying the scalability of the approach would help understand how it would handle high-dimensional causal graphs.\n- Highlighting key takeaways from large tables of results (e.g. table 3) would improve clarity and presentation. \n\nI believe the following changes would greatly improve the impact and quality of the paper, although they are not critical for my recommendation:\n- Exploring the impact of different prompt wording/formats and LLM hyperparameter settings on causal discovery results would be very informative.\n- The LLM-log-probability-based prior knowledge used to update causal graphs imposes certain assumptions on the LLM's output distributions given an input dataset. These can be formalized under existing causal inference frameworks (e.g. potential outcomes) and doing so would make the assumptions and limitations of the method much clearer, especially to the causal inference community.", "broader_impact_concerns": "The paper discusses ethical implications, including risks related to biases in pretraining data of LLMs and concerns about transparency and interpretability of black-box models in high-stakes fields like healthcare.\n\nWhile the paper discusses failure cases, more explicit strategies for mitigating these risks in practical applications would be valuable.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "sHHeK3AgF5", "reviewer": "Reviewer_zBLS", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\n1. The paper leverages LLMs to provide domain knowledge that enhances causal modeling, trying to address the challenge of systematically acquiring background knowledge for SCD, making this research interesting.\n2. The proposed SCP is well-articulated, detailing a 4-step process, and it offers the possibility of automating labor-intensive tasks like variable selection or hypothesis generation as it could streamline causal analysis pipelines.\n3. The experiments cover a range of datasets from distinct areas, including benchmark datasets with ground truths (e.g., Auto MPG ground truth at Cause-Effect Pairs, DWD climate data at DWD), demonstrating the effectiveness of the proposed SCP.\n\n### Weaknesses\n1. SCP’s performance depends largely on the LLMs, and the role of LLMs in causality discovery is not transparent, thus, incorporating the black-box LLMs can heart the high explainability of pure SCD algorithms.\n2. The LLMs employed in this paper are all not open-source (all are GPT series, no other close- or open-source models), as knowledge generation, and integration are way more prompt engineering (shown in Tables 1,2,9, and 12) and LLMs are limited, the results of single-source LLMs cannot be that convincible and generalizable.\n3. The authors mentioned that “this dataset has never been included in the LLM”, how can it be detected? Have the authors checked the similarity between the proposed data and LLM training data with n-gram or other metrics? There is no introduction about that.\n4. Since using LLM-generated prior knowledge based on initial SCD results might lead to overfitting, especially if the intermediate results are not robust. This paper lacks experiments for classic SCD methods with intermediate results of knowledge generation and integration, which can illustrate the error propagation and help interpret the role of SCP components.\n5. Introducing LLMs into SCD can take more computation than conventional approaches, this work didn’t discuss the time or computation costs.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "As illustrated in the title, this paper integrates LLMs into statistic causality (SCD) by presenting a statistical causal prompting (SCP) approach, aiming to identify cause-and-effect relationships from data from different fields. The proposed SCP employs LLMs to generate prior knowledge based on initial SCD results, which are then used to refine the causal models. Experiments on benchmark datasets and a real-world health screening dataset, not included in the LLM's training data (not well-supported), show the improved performance of SCP under various metrics.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. The process of transforming LLM probabilities into prior knowledge matrices (Algorithm 2, Section 3.2) could be more clearly explained, especially for SCD algorithms with varying requirements. For instance, the paper notes constraints for Exact Search (binary, 0 forbidden, 1 otherwise, Appendix E) and DirectLiNGAM (acyclic transformation via BIC, Appendix F), but a unified framework would enhance clarity.\n2. The paper mentioned the risk of false negatives in LLM judgments (Section 4.3, Simulation B), but more detailed strategies, such as ensemble methods or expert validation, could mitigate this. This is crucial for applications in healthcare, where missing true causal relationships could have significant consequences.\n3. More LLMs should be employed to validate the effectiveness of the SCP, the improvement of current experiments may merely come from GPT-series models instead of the proposed pipeline.\n4. Current metrics (SHD, FPR, FNR, precision, F1 score, CFI, RMSEA, BIC) are good but could be supplemented with metrics assessing the directionality and strength of causal relationships, such as causal effect sizes or sensitivity analyses beyond those in Appendix D.\n5. Contributions 2 and 3 in the Introduction section share quite similar meanings, both are SCP benefiting SCD, no need to restate.", "broader_impact_concerns": "As API providers may collect the input data, employing LLMs with sensitive data in practice, such as personal health data, can raise privacy and security concerns that need addressing.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper makes some relevant contributions; i) the proposed approach lokks flexible (with respect to both the causal discovery method and the LLM used), ii)  the idea and implementation of SCP is an interesting contribution to the growing literature on integrating LLMs and causality, iii) the paper evaluates the approach on a dataset excluded from the LLM's pretraining, which strengthens claims of robustness, iv) the authors provide a detailed discussion of failure cases, limitations, and areas for future improvements, v) the proposed SCP is well-articulated, detailing a 4-step process, and it offers the possibility of automating labor-intensive tasks like variable selection or hypothesis generation as it could streamline causal analysis pipelines, vI) numerical experimentes are extremely rich by including benchmark datasets with ground truths.
Decision: Accept (poster)