Consistency Guaranteed Causal Graph Recovery with Large Language Models

We appreciate your comments. Actually, your concern about the incomplete metrics for OUR method does not undermine the soundness of our paper, since the information we provide is equivalent to what you mentioned, i.e., the full metrics for LACR 2 and the final recovered DAGs. We provide the details as follows. For the baseline methods, we cannot report the full metrics due to no accessibility to their codes and result causal graphs.

We response to your comments as follows.

(1) We did not run the code of baseline methods due to no access to the codes and full prompting of existing works. Therefore, we only record the reported metrics. The papers do not provide the constructed causal graphs, and hence we could not have both the precision and recall to compute the F1 score.

(2) We surveyed recent LLM-based causal discovery papers (list in Appendix E.2) and select the two methods with the highest performances. We do not use the same method for both datasets because most of the surveyed papers do not use both datasets for evaluation. By our comparison, we show that our method beats all LLM-based causal discovery methods that we surveyed.

(3) As we described in our experiment results, for both evaluation ground truths and all parameter settings of both datasets, the accuracy of orientation (LACR 2) is $100\%$ which is very stable, and therefore the accuracy, recall, and F1 score are the SAME for the skeleton recovery (LACR 1) and the final DAG. We then chose to report LACR 1's performance in details as this phase mainly determines the overall performance. We rewrote the tables (still, $100\%$ accuracy for all experiments) for LACR 2, for the original ground truth and the refined ground truth, in Appendix.

(4) With numerical data, we can indeed try to use statistical-based causal discovery methods to construct a causal graph, and then conduct consequent causal inference (e.g., ATE estimation). However, this work flow may have crucial problems, e.g, (1) as we mentioned, statistical methods considerably rely on data quality and sufficiency; (2) In a large part of cases, we cannot recovery the DAG without a strong model assumption (e.g., the linear model assumption), leading to non-identification of causality, and therefore we will need external information (e.g., domain expert or literature).

Besides using LACR in the above work flow, our method can significantly benefit other research processing, for instance data collection in empirical research domains, e.g., medical science and social science. To infer causal estimation (e.g., ATE), it is fundamental to estimate the joint distribution of the treatment, the outcome, and all variables in an admissible adjustment set. With a prior causal graph (e.g., given by LACR), researchers can accurately decide the data dimensions for data collection, as it might be considerably expensive to increase data dimensions, or lead to useless data collection once the data dimensions cannot identify the causality of the treatment and the outcome. This is very important for such empirical study domains.

Thanks for the response.

• The authors are right; they provided complete causal graphs produced by their method. (Solved)
• If I take it right, this paper doesn't reproduce baselines; instead, they pick the best of their reported results. This may have issues with reproducibility. Checking the reproducibility of previous works is definitely a duty of each researcher. Especially: (1) All the baselines have listed their prompts and algorithms in their paper. (2) Many of them are not peer-reviewed.

It is interesting that skeleton recovery could be a more challenging task than orientation. We know that skeleton and V-structures are identifiable with conditional independence tests. This may suggest that finding independent conditions from literature cannot be easy. It is a good attempt, at least.

I agree that the method has the potential for realistic applications. For example, it can serve as a method for meta-analysis; It can also serve as an alternative when data is not available or very expensive.

For the above reasons, I would like to update my score to 5.

We thank the reviewer for their valuable comments, and we response to them as follows.

(1) We ran PC algorithm on both of the Asia and Sachs datasets, and obtained a F1 score no more than 0.5 for both datasets. However, we do not include the statistical-based causal discovery methods' performances in our experiment because such comparisons might be not fair. For example, though the causal graph of Aisa dataset was constructed based on real-world data, the accessible data is artificially synthesized based on the graph, NOT the original data. Therefore, the data's distribution aligns with the causal constraints embedded in the original causal graph. However, by our investigation, there exists knowledge gap between the original causal graph and the SOTA domain knowledge, meaning that the current accessible data is biased from the SOTA domain knowledge. Hence, it is unfair to compare with the results developed from such biased data. Other such old dataset may have the same issue, and thus we decide to only compare with LLM-based causal discovery methods.

(2) We mainly chose evaluation datasets from the popular bnlearn causal package. We would like to emphasize that our aim is beyond recover causal graphs that close to the existing "ground truth" which might be out of date. As described in our experiment section (Section 4.3), we observe obvious scientific evidence showing that knowledge gap exists between the original ground truth and the SOTA domain research. LACR shows better capability in bridging such gap, investigating the causal hypothesis development, and updating the ground truth. This is one of the most important contributions of our work.

In this revised version, we include additional experiments for two new datasets (Appendix E.6), namely the Arctic Ice Coverage and Alzheimer. On both datasets, we evaluate against the original statistical based methods, since such new datasets more align with the SOTA knowledge, and it shows that LACR outperforms the baseline methods on both datasets.

(3) One of the main limitations of the current pipeline is the paper retrieval. Please see our new contents in Appendix E.6, where we added the ratio of unusable documents, i.e., the documents cannot provide relevant information. We found that this ratio is high, especially for new causal evaluation datasets. Our next future work is to enhance this by arming LACR with a more efficient information retrieval component. However, we can still see the efficacy of LACR's workflow as it can identify a large part of causal relations correctly even though suffering from lack of scientific documents. We would add an extended version of future works and limitation in the final version.

(4) Since LACR relies on LLM's understanding ability on documents, using a less capable LLM may generate weaker outcomes in respect to evaluating against the baselines. However, our goal is beyond simply constructing a causal graph compared with baselines. One of the most innovative contributions of our approach is its ability to reveal how mainstream causal understandings evolve over time across different periods of literature. By segmenting the corpus into distinct periods (e.g., before 1990, 2000, 2010, or 2020), our method can construct causal graphs that summarize the dominant scientific thinking during each specific period. This provides a dynamic historical view of causal knowledge, allowing us to trace how hypotheses and consensus about key causal relationships have shifted over time, which standard causal discovery algorithms don’t address. For example, in a particular domain, a relationship that was considered causal in earlier periods may be treated as an independent relation in newer analyses or vice versa. The experimental result shown in Table 1 validates this statement, as all the results from our solution improve in the updated dataset (i.e., F1 (new)) compared with the origin dataset (i.e., F1).

We thank the reviewer for their valuable comments, and we response to them as follows.

(1) We thank the reviewer to provide information of more real-world validation datasets. We mainly consider our choice among the networks in the well known bn-learn causal package repository, and select based on two criteria: (1) realistic network because LLM works based on real-world data; (2) large ones among the small scale networks due to the trade-off between running cost/time and evaluation efficacy. For the network memorization issue, (1) we respond Reviewer gpD3's simple prompt strategy by a straightforward modification on the Asia dataset and find that LLM cannot stably identify the apparent causal relations though it seems to have a rich background knowledge (see more details in Appendix E.5 in the revised paper version); (2) LLM's memory may enhance the performance of LACR, however, our focus is definitely beyond recovering causal graphs close to such old ``ground truth'', but specify the causal hypothesis development in literature, and update the graph to fit the SOTA knowledge as we do in our experiments.

Though some of the baseline methods can achieve high performances against the original ground truth, we observe obvious scientific evidence showing that knowledge gap exists between the original ground truth and the SOTA domain research (Section 4.3). LACR shows better capability in bridging such gap, investigating the causal hypothesis development, and updating the ground truth. This is one of the most important contributions of our work.

By your suggestion, we select two new networks: the arctic ice coverage and the alzheimer networks to conduct additional experiments. In the additional experiments, we compare LACR with the statistical methods used in the original papers. Our results show that LACR outperforms the best baseline method in both networks with the best F1 scores of 0.5818 and 0.6364 for the Arctic ice coverage and Alzheimer networks, respectively. We added the detailed results in the appendix, in the latest version of the paper. The main limitation of LACR is the effectiveness of scientific document search APIs, where in the current version, a large part of retrieved papers do not contain useful information. We believe that LACR's performance can be significantly improved with a better paper search tool, and this is one of our main future works.

(2) We design these methods for causality. They may have other use-cases, but we didn't consider them at this stage.

(3) We retrieve a number of papers (e.g., at most 20) for each variable pair, and for each paper, we send a sequence of at most 4 queries to LLM as shown in Algorithm 1. We first ask LLM to clarify the meaning of each variable by only giving it the domain name of the task (e.g., medical science), and then we ask LLM to decide whether the variables are associated based only on the paper. If associated, we ask whether this association can be d-separated, and lastly, we ask LLM to recheck and output the d-separation set if the variable pair can be d-separated. Each document is a full scientific paper in pure text downloaded by the PubMed API without chunking, and we limit each document's size by the limitation of the LLM's input limitation. Therefore, the complexity is $4n^2$ times the number of papers for each variable pair. As we do not have access to most of the existing LLM-based causal discovery methods, we add the interesting idea of ablation study of our method against other LLM-based methods in our research agenda.

(4) We surveyed a list of recent LLM-based causal discovery papers (see the list of surveyed papers in our Appendix) that use the same datasets in evaluations, and for each dataset, we select two baseline methods with the highest reported performances. Due to the lack of details (e.g., code or recovered causal graph structure) of the baseline methods, we cannot compute the metrics for the baseline methods against the new causal graphs, and thus we leave the contents N/A.

(5) For latent variables, we do not assume the absence of latent variables as stated in our model (Line 99-100), and in LACR, if any literature identifies exogenous variables that can d-separate a variable pair, we identify the evidence as a support for "no causal edge exists between the variable pair".

We thank the reviewer for their valuable comments, and we response to them as follows.

(1) We appreciate the reviewer’s comment that the theoretical results build on established graph and approximation theory principles. The approximation bound aims to demonstrate that our solution achieves a provable level of performance even under worst-case conditions, which is critical for ensuring robustness and reliability in practice. While we acknowledge that the approximation bound does not aim to be theoretically novel, we believe that this practical perspective highlights the utility of our solution in handling real-world causal discovery challenges.

(2) As we have fully defined and described the notations in the algorithm. We found that it might be more helpful to add an intuitive description to the algorithm. We revised the contents correspondingly and hope it is more clear now.

(3) Indeed, if our purpose is to estimate the causality (e.g., ATE) of a pair of predefined variables (e.g., treatment and outcome), the influence of causal graph estimation's error on the causality estimation highly depends on the causal graph structure. For example, inaccurate edges that are distant from the treatment and outcome in the causal graph may not influence the estimation of causality. However, in this work, our purpose is to construct the causal graph, the purpose of which is not limited to causality estimation, for instance, to guide data collection. Therefore, we treat each misprediction identically.

(4) We surveyed a list of recent LLM-based causal discovery papers (see the list of surveyed papers in our Appendix) that use the same datasets in evaluations, and for each dataset, we select two baseline methods with the highest reported performances. Averagely, other LLM-based methods (including our baseline methods) input much more task specific information in the prompt, however, we do not input such information to keep LACR's generalization ability. Instead, LACR focuses on prompting the statistical intuition to query LLMs, to extract statistical relationships in general tasks. We believe our way of prompting for associational knowledge extraction and the majority voting aggregation can efficiently enhance the performance, but the constraint maximization may benefit or undermine the performance due to information loss as shown in our experiment results.

(5) LACR is indeed sensitive to retrieved scientific documents. However, in our current version, we do not spend extra effort on the paper pool construction, but only use the simple Google Scholar search and PubMed open access paper download APIs for simultaneous document retrieval, as we describe in the paper. Therefore, LACR do not reply LLM's prior knowledge on the retrieved papers, or dimension labels, and it is capable of tackling generic tasks. We additionally show the paper retrieval quality in Appendix E.6 in the revised paper version, and it shows LACR's efficacy even under relatively low retrieval accuracies, especially for the new additional datasets. However, LACR can still outperform most of the existing results. It is worth noting that due to LACR's sensitivity to retrieved papers, we can gain insights into the causal hypothesis development in the task domain, e.g., shown in our modification to the original ground truth graphs. This is one of the most innovative contribution of LACR.

Thank you for your response. We would like to provide further clarification to your concerns as follows.

(1) We added a paragraph to intuitively describe Algorithm 1 from Line 214 to Line 239 in the revised paper version: "Based on the above key prompts, we use Algorithm 1 to extract a CAR estimation piece from each retrieved document if it contains such analyzing result. Intuitively, for each document or LLM’s background knowledge, i.e., KB on Line 3, we query LLM to extract if the KB indicates association or non-association between the variable pair. If the KB indicates association, LLM further investigates whether the association can be blocked or not (Lines 4-6), and we instruct LLM to return the corresponding d-separation set if the association can be blocked (Lines 7-17)."

(2) We appreciate your suggestion of studying the influence of LACR's noise on the ATE estimation. We agree that edges have different importance, and their estimation errors impose different influence on causality estimation (e.g., ATE), based on a predefined scientific scenario. However, the purpose of our work is causal discovery, i.e., constructing causal graphs. Similar to other causal discovery works, e.g., the PC algorithm (Spirtes and Glymour (1991)), the GES algorithm (Chickering (2003)), and the LiNGAM algorithm (Shimizu et al. (2006)), we treat each edge identically. Studying the influence of causal graph estimation error on causality estimation is a very interesting topic, and it is one of our undergoing research projects.

(3) Extracting knowledge from literature for causal graph construction is one of our main contributions, and another is our workflow, i.e., extracting conditional associational relationships (CARs), and conducting constraint based causal discovery reasoning.

In this workflow, LLM memorization is not a issue, and instead, it may enhance the performance of LACR. Reviewer gpD3's concern about LLM's memorization is that they think the performance of LACR is not because of its workflow, but because of LLM's memory of the network. Therefore, it might be possible to simply prompt the LLM to locate the causal graph obtained from the training data. Our additional experiment of manipulating the Asia network (Appendix E.5) shows that such prompting is not reliable. As a comparison, LACR performs stably against the manipulation and recognizes the correct causal relationships between the modified variables.

However, only the combination of accurate document retrieval and LLM's good understanding capability can realize LACR's potential. LACR extracts knowledge from a number of scientific documents as well as from LLM's background knowledge, and aggregates the extracted knowledge to reach a consensus. Based on this feature, the major scientific opinion determines the result. Both of the literature knowledge and LLM's background knowledge are noisy representations of the ground truth, and they together contribute to the rationale of the collective decision making.

We thank the reviewer for their valuable comments, and we response to them as follows.

(1) We write faithfulness assumption mainly for the introduction of constraint based causal discovery methods. Obviously, literature based methods can easily violate faithfulness assumption, otherwise there is no inconsistency issue mentioned in our paper. We propose the MaxCon method, i.e., the inconsistency elimination method, aiming at mitigate such violation to some extent.

For latent variables, as we introduced in Section 2.1, we do allow the existence of latent variables as stated in our model. If any literature identifies exogenous variables that can d-separate a variable pair, LACR identifies it as supported evidence for "no causal edge exists between the variable pair".

(2) Our method is fundamentally different from a large part of literature-based causal discovery methods. We would like to stress that LACR does not recover causal graphs directly from individual pieces of literature. Instead, it extracts Conditional Associational Relationships (CARs) for each pair of factors, which is much easier to induce than causal relations, using evidence aggregated from a large corpus of scientific literature. The inferred causal relationships between factors are determined based on broad scientific consensus rather than individual studies. By aggregating knowledge from a diverse set of sources, LACR mitigates the influence of biases or limitations intrinsic to individual papers. We agree that causal graph building from text data can be viewed as another modality for causal discovery. Addressing inconsistency is a key part for fusing this modality, which is exactly our contribution. With different sets of papers published in different time, our method can reveal how causal understandings evolve.

(3) Thanks for raising this interesting point. However, the fact that a dataset is in the training data of the LLM does not mean the LLM knows the causality among the variables. Here are the details regarding your examples: (1) The recovered causal graph of SACHS dataset you provided does not match the ground truth, with accuracy of 0.5, recall of 0.25, and F1 score of 0.33. This indicates ChatGPT's weak understanding on such highly professional causal relationships; (2) To show that directly prompting ChatGPT cannot provide reliable causal graphs even it uses the data in training, we slightly modify the prompt to observe the vulnerability of causal relations derived from GPT-4o. The prompt recovers a causal graph similar to the ASIA dataset by replacing two variables: Visit Asia $\rightarrow$ Visit US, X-ray $\rightarrow$ CT scan, where Visit US should not be causally related to Tuberculosis. ChatGPT outputs wrong graphs by the simple prompt, specifically connecting Visit US to Tuberculosis. However, LACR can manage such changes and output reasonable causal graphs, where the only ``wrong'' recovered edge (against the original ground truth graph) aligns with the SOTA scientific evidence shown in Section 4.3. The result indicates that simple prompting of ChatGPT does not lead to reliable answers on causality. We show these additional experimental details in Appendix E.5 in the revised paper.

Additionally, we added complementary experiments on two relatively new datasets, namely the Arctic Ice Coverage and Alzheimer, in Appendix E.6 of the revised paper version. The results show LACR outperforms the original statistical based methods in both datasets though the document retrieval quality is low.

(4) Thank you for your insightful question. Resolving inconsistencies in CARs by removing the minimum number of conflicts could be path-dependent if the specific order in which conflicts are resolved affects the overall process. This concern is especially valid in iterative or greedy algorithms, where decisions made early in the process could constrain the options available in subsequent steps.

Despite the potential for path dependence, practically, we observe that the removal process in LACR converges towards consistent results when LACR retrieves a satisfying number of informative documents. Most of the extracted CARs in the dataset reflect a broad scientific consensus, meaning that the number of conflicting CARs is typically small. Hence, the specific choice of which conflicting CARs are removed has only slight impact on the overall structure of the final causal graph. Additionally, the approximation algorithm we use ensures that the retained CARs collectively maximize consistency while satisfying global acyclic and causal constraints. This further mitigates any effects of path dependence, as the removal process is designed to prioritize global consistency rather than being overly influenced by local decisions.