Test-Time Learning of Causal Structure from Interventional Data

Dear Reviewer 8DQE,

We sincerely appreciate your valuable time and the effort you have dedicated to reviewing our paper. We are also pleased that you recognize several strengths of our work, including its clarity and extensive experiments. However, we regret that you have raised a criticism that we believe to be inappropriate. We have carefully considered each of your comments and addressed them systematically to respond to your concerns. Specifically:

W1: Limited novelty, Step 1 is JCI, Step 2 is ML4S

• We respectfully disagree with your assessment. We must emphasize that this is not a mere incremental contribution, but rather the result of long-term, rigorous work.

  • Both reviewers, 4MTP and dQ5H, pointed out that our paper presents a novel paradigm. In particular, reviewer dQ5H highlighted that our approach combines two existing techniques (JCI and SCL), providing a well-described and interesting combination that is both intuitive and clever. We would like to emphasize that the presence of similar existing concepts does not negate the novelty of our work. Rather, it is the ability to effectively address the problem at hand, as well as confronting the challenges throughout the process, that constitutes the true source of innovation. Furthermore, given the complexity of the problem we are tackling, even applying existing concepts requires significant and non-trivial effort.
  • Based on the feedback from all reviewers, we realize that we have presented many things, which may have led to the core novelty of our work not being immediately clear to the readers.
  • Given the complexity and importance of the problem, we have rewritten the introduction to systematically clarify what we are doing and how to identify the unique contributions of our work. This restructured introduction now more clearly outlines our key contribution from the perspectives of problem, idea, and technology to aid reader understanding. Please also refer to our "General Response to All Reviewers Regarding the Main Contributions of Our Paper".
  • To briefly summarize, our core contribution lies in utilizing Supervised Causal Learning (SCL) tools to address Interventional Causal Discovery (ICD) problem, for which we propose the novel Test-Time Training (TTT) + Joint Causal Inference (JCI) paradigm and explore customized IS-MCMC and PC-Like SCL algorithms for training data acquisition and model learning.

• Here, we would like to specifically address why our paper is not simply a combination of JCI and ML4S. The key differences include:

  • Difference from JCI: While we acknowledge and appreciate the contributions of JCI, our systematic investigation shows that it is a promising direction for intervention causal discovery, as it simplifies the causal discovery problem and flexibly handles various intervention settings. However, JCI does not address key questions such as: What are the appropriate learning objectives? How should the learning process be designed? These are precisely the questions we systematically answer in our paper.
  • Difference from ML4S: First, from the problem perspective, we note that ML4S focuses exclusively on skeleton recovery, so our problem space and difficulty far exceed that of ML4S. Second, from the conceptual perspective, ML4S’s Vicinal Graph as training data is merely a heuristic method. It does not systematically investigate when to acquire training data, what kind of training data to collect, and how to gather this data under intervention settings. In contrast, we conduct a thorough investigation into acquiring training data for intervention causal discovery. Finally, from the technical perspective, ML4S uses a simple heuristic algorithm for inference and does not design a rigorous algorithm for data acquisition. Our IS-MCMC algorithm can be seen as a generalization of ML4S, as reflected in the results of our training data study in the experimental section.

We hope that this detailed explanation helps you truly understand the core idea and significant contributions of our paper, and appreciate the considerable effort we have invested in this long-term work.

W2: If conditional independence information is already available, why not use it directly, as this might otherwise undermine theoretical identifiability?

• In response, we clarify that our PC-Liked SCL algorithm retains theoretical identifiability. Moreover, it ensures the correctness of asymptotic properties while encouraging more systematic feature characterization and learning better classification mechanisms, thus making our method more robust than PC. As a result, it achieves superior empirical performance.
• Additionally, in the revised version, Appendix D presents a systematic study of the advantages of our approach over the PC algorithm, from intuitive analysis to theoretical proof. Please also refer to our "General Response to All Reviewers Regarding the Identifiability of Our PC-like SCL Algorithm".

We greatly value your feedback, and we will incorporate these discussions into the final revision of the paper. We hope that the above responses address your concerns. If possible, we kindly request that you reconsider your score. Should you have any further constructive suggestions, we would be happy to discuss them and make necessary improvements to the paper.

Sincerely,

Authors of submission 3081

Q4: Why is the sample size of 10,000 chosen for forward sampling? Is there a risk of overfitting? Why does performance improve with larger sample sizes?

• We follow the default settings from previous studies to select the sample size for ancestral sampling (please refer to Table 6 in Appendix C.2, which summarizes the configurations of all different methods).
• Additionally, in Table 9 of Appendix C.4, we systematically summarize the configurations of our extensive experiments, including the effects of varying observation and intervention sample sizes.
• In direct response, the goal of our paradigm is to generate as much data as possible for model fitting, thereby avoiding out-of-distribution generalization issues. Hence, larger sample sizes typically lead to better performance, as evidenced by the comparisons in Tables 1 and 16.

We deeply value your feedback and will incorporate these detailed discussions into the final revision of the paper. We hope the above responses address your concerns. If possible, we kindly request that you reconsider the score. Should you have any further suggestions, we would be happy to discuss them and make any necessary improvements to the paper.

Best wishes

Authors of submission 3081

Dear Reviewer 4MTP,

We sincerely appreciate the time and effort you have dedicated to providing insightful feedback on our paper. We are also pleased to see that you recognize several key aspects of our work in the summary and strengths section, including extensive experiments, novel paradigm, significant advancement of the state-of-the-art, systematic study, and flexibility. We have carefully considered each of your detailed comments and addressed them case by case to alleviate your concerns. Specifically:

Q1: Why does the stationary distribution of the constructed Markov chain(s) in IS-MCMC matches the posterior distribution of graphs given the data? Is there a discussion of the convexity of the Markov chain? Please provide some justification.

• As a quick response, we would like to clarify that our IS-MCMC algorithm follows the standard Structure-MCMC procedure in the intervention-augmented graph space. By employing a Metropolis-Hastings sampler, the Markov chain is guaranteed to have a stationary distribution equal to the posterior distribution $P(G | D)$, which has been well studied in the literature[1, 2, 3].
• For a more detailed discussion, please refer to our "General Response to All Reviewers Regarding the Main Contributions of Our Paper".

[1] Madigan, et al. "Bayesian graphical models for discrete data.", International Statistical Review/Revue Internationale de Statistique,1995.

[2] Su, et al. "Improving structure mcmc for bayesian networks through markov blanket resampling.", The Journal of Machine Learning Research, 2016.

[3] Kuipers, et al. "Partition MCMC for inference on acyclic digraphs.", Journal of the American Statistical Association, 2017.

Q2: What is a good criterion (or number of samples) to ensure proper convergence for the constructed Markov chain(s)?

• We assume you are inquiring about methods for diagnosing Markov chain convergence.
• Convergence diagnosis is a complex issue, and multiple tests such as Heidelberger and Geweke can be used to validate convergence from different angles, though they come with additional computational and time costs.
• A common approach is to increase the number of steps to pass through the burn-in phase, but it is important to note that the convergence speed of MCMC-generated chains is highly sensitive to the initial state. Therefore, we cleverly select a good initial state through a proxy algorithm to ensure faster convergence.
• For a more detailed discussion, please also refer to our "General Response to All Reviewers Regarding the Convergence of Our IS-MCMC Algorithm".

Q3: Why is the use of a binary classifier for CI tests preferable? Are there empirical evidences supporting this?

• Here, we provide a simple example by randomly selecting 30 re-generated $D_t$ datasets and running statistical averages and means using the standard PC algorithm, which we term "Proxy-PC". The results, compared with "JCI-PC" and our method on the $\mathcal{I}$-CPDAG task, are as follows:

• In Appendix D of the revised version, we provide a systematic study from intuitive analysis to theoretical proof of the superiority of our method over the PC algorithm. We also recommend reviewing our "General Response to All Reviewers Regarding the Identifiability of Our PC-like SCL Algorithm".
• In brief, our PC-Like SCL algorithm, while maintaining theoretical asymptotic correctness, encourages a more systematic characterization and better classification mechanisms, making it more robust than the PC algorithm, and thus yielding superior empirical performance.

Dear Reviewer 4MTP,

We sincerely appreciate the time you spent reviewing our responses and your willingness to raise your score in recognition of our work.

We are pleased to hear that our rebuttal has effectively addressed most of your concerns, given the complexity of the material we need readers to understand.

We would like to summarize the revisions made for you during this period (please refer to the current revised version with changes highlighted in purple):

• We have rewritten the IS-MCMC process described in Algorithm 1 and revised the related Figure 3 to include corresponding labels, making it easier for readers to follow the process. Furthermore, we have added new Appendix C, which specifically discusses the convergence of IS-MCMC and the motivations and considerations behind convergence optimization. Additionally, we plan to explore further improvements and experiments in this algorithm in the future.

• In response to your concerns regarding the advantages of the modified PC algorithm and, most notably, its identifiability, we have added a new Appendix D. This section provides a detailed analysis of the observations, motivations, and theoretical proofs to address the concerns related to the PC-like algorithm.

We also warmly invite you to review our general response, which offers a quick and clear overview of the positioning and contributions of our work. We believe our progress is worth sharing with the community. Should you have any further suggestions, we would be happy to hear them and continue improving our work in next days.

Once again, Thank you!

Sincerely,

Authors of submission 3081

Q1: Gradually converging to incorrect graphs?

• Our approach follows the standardized Structural-MCMC process, converging to the posterior distribution $P(G | D)$. Thus, from a theoretical perspective, we do not converge to incorrect graphs.
  • Note 1: With standard MCMC-based training data, we demonstrate consistent performance, as shown in Figure 5.
  • Note 2: While MCMC guarantees convergence, some local fluctuations may occur, which relate to optimizing the MCMC algorithm—a topic for future work.
• For a detailed discussion on MCMC convergence, please refer to our "General Response to All Reviewers Regarding the Convergence of Our IS-MCMC Algorithm".

Q2: The 14 graphs in bnlearn are mainly observational (except for Sachs). How do the authors generate observational and intervention data from these graphs?

• The bnlearn repository includes causal graphs inspired by real-world applications, and these can be considered semi-realistic simulator data based on true causal graphs.
• Each causal graph in bnlearn provides conditional probability distributions (CPDs), allowing us to easily simulate intervention experiments. Specifically, we implement both hard and soft interventions.
  • A hard intervention directly sets the value of a variable, ignoring its normal distribution. Our code implementation for hard intervention is: hard_intervention[var] = self.bn.states[var][np.random.randint(0, self.bn.get_cardinality(var))].
  • A soft intervention adjusts the CPD of a variable to influence its distribution. We implement this via a Dirichlet distribution for the target variable: values = [[x] for x in np.round(np.random.dirichlet(np.ones(cardinality) * probability), 2)].

Once again, we greatly appreciate your valuable feedback and have incorporated these discussions into the final revision of the paper. We hope the above responses address your concerns. If possible, we kindly request that you reconsider the score. Should you have any further suggestions, we are more than willing to discuss them and make necessary improvements.

Best wishes

Authors of submission 3081

Minor-W1: The contributions discussed in the introduction are too many and somewhat distracting.

• We believe our response to Major-W1 addresses this concern effectively. We have reworked the introduction to focus more clearly on our key contributions.

Minor-W2: What do the numbers in the curly braces of Figure 2 represent? They should be explained.

• The numbers in the curly braces of Figure 2 represent intervention variables (or environmental nodes). We apologize for any confusion, as we may have assumed a higher level of background knowledge of Joint Causal Inference from the reader. Reviewer dQ5H also pointed out this weakness.
• We appreciate your suggestion and have moved this explanation to the last section of the Preliminaries, naming it "Identifiability with Intervention Data", to improve clarity and reader experience.

Minor-W3: It is unclear why {1} is considered a node here.

• We believe our response to Minor-W2 clarifies this confusion. More directly, this is default setting in the context of JCI.

Minor-W4: Definitions of Markov, faithfulness, and sufficiency should be provided for clarity.

• These concepts have been clearly defined in the Preliminaries section and Appendix A:
  • A joint probability distribution $P_{\mathbf{X}}$is Markov compatible with $\mathcal{G}$, i.e., $P_{\mathbf{X}} = \prod_{i=1}^{d} P(X_i | pa(X_i))$, where $pa(X_i)$ are the parents of $X_i$.
  • Faithfulness assumption: $X \perp_P Y | Z \Rightarrow X \perp_{\mathcal{G}} Y | Z$.
  • Causality sufficiency: Exogenous variables are ignored.

Minor-W5: The I-CPDAG is not discussed in sufficient detail.

• We have clearly described the $\mathcal{I}$-CPDAG as an instance of the I-MEC in the problem summary.
• Our main text: "We aim to predict all causal relations entailed by the given data $\mathcal{D}$ (subject to the above assumptions), which correspond to the invariant causal structures in the I-MEC set of the causal graph $\mathcal{G}$ behind $\mathcal{D}$, as explained in Section 2. Such invariant causal structures can be computationally encapsulated as a partial DAG, called the Interventional-Complete Partial Directed Acyclic Graph ($\mathcal{I}$-CPDAG), in which each directed edge indicates an invariant causal relation in the I-MEC set."

Minor-W6: The phrase 'JCI considers data samples under interventions as observations under imposed conditions' seems redundant.

• Thank you for your feedback. We have rewritten the phrasing for clarity.

Minor-W7: The meaning of "high-quality training data" is not sufficiently clear. This should be clarified.

• This refers to the training data mentioned in the "What" stage of Test-Time Training.
• Thank you for your reminder; we have revised the wording accordingly to ensure clarity.

Minor-W8: $\mathcal{G}_i$ is likely in the "neighborhood" of the original augmented dataset. It is unclear what "neighborhood" means.

• We apologize for the confusion. We meant that $\mathcal{G}_{i}$ is likely to maintain a certain "similarity" with the original augmented graph $\mathcal{G} _ {\mathcal{I}}$, which entails the similarity properties of the data $\mathcal{D}_i$.
• We have rewritten this for better clarity.

Minor-W9: The meaning of $\mathcal{G} ^ {(t-1)}$ in the mutation step is not properly defined.

• We apologize for the confusion in the algorithm workflow description.
• Based on your feedback, we have rewritten Algorithm 1 to clearly map the notation to the revised steps, ensuring it is easier to understand.

Minor-W10: The numbers 1-6 in the key steps could be shown in Figure 3 for better mapping.

• Following your suggestion, we have added the numbers 1-6 to Figure 3 in the revised version for clearer mapping to the steps.

Dear Reviewer ya31,

We sincerely appreciate the time and effort you invested in providing insightful feedback on our paper. We are also glad to see that you recognize several key aspects of our work, such as the "very interesting and important problem", "extensive experiments", and "thorough background". We have carefully considered each of your detailed suggestions and addressed them one by one to alleviate any concerns. Specifically:

Major-W1: The main contributions are unclear: Is it I-CPDAG discovery, intervention target identification, testing time adaptation, PC+SCL, or prior knowledge, etc.?

• We apologize for any confusion caused and appreciate your recognition of the importance of this problem.
• Based on feedback from all reviewers, we acknowledge that we have covered too many aspects, which may have made it difficult for readers to identify our core contribution.
• To clarify our work and make our contributions more discernible, we have rewritten the introduction section to systematically outline our work from the perspectives of problem, idea, and technique. This should help the reader better understand our paper. Please refer to our "General Response to All Reviewers Regarding the Main Contributions of Our Paper".
• In short, our core contribution lies in utilizing Supervised Causal Learning (SCL) tools to address Interventional Causal Discovery (ICD) problem, for which we propose the novel Test-Time Training (TTT) + Joint Causal Inference (JCI) paradigm and explore customized IS-MCMC and PC-Like SCL algorithms for training data acquisition and model learning.

Major-W2: The paper’s presentation could be improved; too many things are happening.

• We believe the changes made in response to Major-W1 effectively address this concern. Specifically, we have revised the introduction to emphasize and highlight the key contributions of our method.

Major-W3: Although testing time adaptation is a key motivation, it is discussed minimally.

• We believe the revisions made in response to Major-W1 also address this concern. We have clarified in the introduction why testing time training is necessary.

Major-W4: Are the authors proposing to train a classifier for each possible triplet to detect whether it forms a v-structure? This would be highly inefficient. How does it compare to the PC algorithm? The training process requires more detailed discussion.

• We do not train a classifier for each possible triplet to detect v-structures. Instead, we train a classifier on triplet features extracted from all training data to detect whether any new triplet forms a v-structure.
• Our method is not inefficient. As shown in the revised version Figure 8 (b), our method demonstrates a runtime similar to that of non-learning methods while achieving better performance.
• In addition, we provide a detailed theoretical analysis of the superiority of our approach over the PC algorithm in Appendix D of the revised version, and we encourage you to refer to our "General Response to All Reviewers Regarding the Identifiability of Our PC-like SCL Algorithm".
• In short, our PC-like SCL algorithm, while preserving theoretical correctness, encourages a more systematic feature representation and learns better classification mechanisms, making our method more robust than PC and thus leading to superior empirical performance.

Major-W5: The Asian network in bnlearn is not a real-world data graph.

• We apologize for any confusion caused by our wording.
• The bnlearn repository contains various causal graphs inspired by real-world applications and has been referred to as a "real benchmark" in previous literature [1, 2, 3]. While these also can be seen as semi-real synthetic datasets generated from real causal graphs.
• Following your suggestion, we have thoroughly reviewed and revised the wording throughout the paper regarding "real-world datasets".

[1] Ke et al., Neural Causal Structure Discovery from Interventions, TMLR, 2023.

[2] Ke et al., Learning to Induce Causal Structure, ICLR, 2023.

[3] Lippe et al., Efficient Neural Causal Discovery without Acyclicity Constraints, ICLR, 2022.

Dear Reviewer ya31,

Since the End of the Rebuttal is coming very soon - only a few days left, we would like to inquire whether our responses have addressed your major concerns.

We also cordially invite you to review our general response, which quickly and clearly outlines the positioning and contributions of our work. We would like to emphasize that proposing the use of the TTT+JCI paradigm through SCL tools to address ICD problem is by no means trivial. Currently, the state-of-the-art solutions for this problem, such as CSIvA[1] and AVICI[2], do not take test-time training into account, which means they are unable to avoid the generalization problem. Moreover, they can only handle limited intervention settings and thus are unable to adapt to diverse intervention scenarios.

We have incorporated this perspective and updated our related work in the current revised version in purple font.

We believe that our progress is worthy of being shared with the community. If you have any further suggestions, we will be glad to listen to them and continue to improve our work in the coming days.

We look forward to your feedback.

Sincerely,

Authors of submission 3081

[1] Ke et al., "Learning to Induce Causal Structure", ICLR, 2023.

[2] Lorch et al., "Amortized inference for causal structure learning", NeuIPS, 2022.

I cordially thank the authors for their details response and appreciate their effort for this paper. However, I personally think the paper needs in-depth look and some major revision. Thus, I prefer not to increase the score.

Thank you for taking the time to respond.

Regarding "the paper needs in-depth look and major revision", we feel there might be a misunderstanding here -- in fact we have already uploaded a revised manuscript of the paper. The revised paper has articulated a concise summary of our main contributions (which seems to be your main concern in the review). So by "major revision", do you mean further revision on top of this revised manuscript? Have our existing revisions and responses addressed your main concerns? If not, we would highly appreciate it if you could outline your remaining concerns at the moment. This could help us better understand the issues and make meaningful improvements to our work.

In any case, we want to make sure that you didn't miss the revised manuscript, where the introduction, related work, and analysis of IS-MCMC / PC-like SCL (Appendix C and D), has been significantly revised particularly for addressing your specific concerns.

W6: The meanings of blue/bold and red/underlined text, as well as Footnote 1, should be included in the table's caption so that the table can stand alone.

• Thank you for your suggestion. We have included the meanings of blue bold and red underlined text in the caption of Table 1. However, regarding Footnote 1, since it does not relate to the information in the table and the only related baseline adjustment is already changed in W4, we have decided to leave it unchanged.

W7: The colors of different categories of methods are difficult to distinguish, and ensure that the legend and icons in Figure 4 align correctly.

• Thank you for your suggestion. We have implemented your recommendation by enhancing the background color distinctions in Table 1 and ensuring the legend and icons in Figure 4 are aligned.

Q1: Clarify the loop structure in Algorithm 1 and explain how it is parallelized.

• We apologize for the confusion caused by the algorithm flow, which mixed practical aspects. In reality, your understanding is correct: Steps 1–6 in original manuscript iterate continuously, while Step 7 is sampled after the burn-in period, and these two components operate in parallel processors. The index $i$ is not required in the loop, indicating internal parallelism.
• To clarify, we have rewritten Algorithm 1 in the revised manuscript and aligned it with the notation introduced in the main text. We believe the revised algorithm flow is now sufficiently clear and easy to understand.

Q2: Could you provide an example of the soft interventions you simulate? Have you tried hard intervention experiments? If so, are the results similar?

• Hard intervention refers to directly setting the value of a variable. In other words, a hard intervention forces the target variable to assume a specific value, disregarding its normal probability distribution. Specifically, our code implementation is: hard_intervention[var] = self.bn.states[var][np.random.randint(0, self.bn.get_cardinality(var))], which randomly selects a state value for each target variable and assigns it as the value for the hard intervention.

• Soft intervention is a more subtle form of intervention. Instead of directly setting a variable’s value, it influences its distribution by adjusting its Conditional Probability Distribution (CPD). Specifically, our code implementation is: values = [[x] for x in np.round(np.random.dirichlet(np.ones(cardinality) * probability), 2)]. Here, we use the Dirichlet distribution to generate a new probability distribution for the target variable. The Dirichlet distribution is suitable for discrete data and multiclass problems, as it effectively generates a set of non-negative values that sum to 1, representing a valid probability distribution.

• For the hard intervention experiments , detailed results and analysis can be found in Appendix F.1.1, Table 14 of the revised version. Comparing this with Table 1, the results are similar.

Q3: Have you tried comparing the results from Algorithm 1 generating $D_t$ and then using the standard PC instead of your custom PC-like SCL method?

• Yes, this typically yields better performance. We provide a simple example where we randomly select 30 generated $D_t$ samples and run standard PC, reporting the statistical averages as "Proxy-PC," which is compared with JCI-PC and our method on the $\mathcal{I}$-CPDAG task performance, as follows:

• In Appendix D, we provide a systematic study from intuition to theoretical proofs to demonstrate the superiority of our method over the PC algorithm. Please also refer to our "General Response to All Reviewers Regarding the Identifiability of Our PC-like SCL Algorithm".

• In summary, our PC-Like SCL algorithm retains the theoretical asymptotic correctness of PC while promoting richer feature representations and improved classifier learning, making our method more robust and yielding superior empirical performance.

Once again, we sincerely appreciate your valuable feedback, which has significantly strengthened our manuscript! We hope the above responses address your concerns, and we are happy to discuss further suggestions to improve the paper.

Best wishes

Authors of submission 3081

Dear Reviewer dQ5H,

We sincerely appreciate the time and effort you have spent providing insightful feedback on our paper. We are also pleased that you recognize several strengths of our work, including its "interesting, intuitive, and clever idea", "clear writing", and "thorough and compelling experiments". We have carefully considered each of your detailed comments and have addressed them one by one to alleviate your concerns. Specifically:

W1: The "when," "what," and "how" sections are well written, but the phrasing of the "when" part is confusing, as it conflates the term "test data". The expression needs to be revised for clearer understanding.

• We greatly appreciate your recognition of our writing style and apologize for any confusion caused.
• Based on your suggestion, we have revised the wording here. Specifically, we define two stages during the "test time": "accessing the test data" and "performing the actual test." Our method operates between these two stages—after accessing the test data but before performing the actual test—by generating free training data, training the model, and using it for final testing.
• However, based on feedback from other reviewers, we realized that many readers might struggle to follow the core ideas of the paper. Therefore, we have rewritten the Introduction to systematically clarify our work from the perspectives of the problem, idea, and technique, which we believe will aid the readers' understanding. Please see our "General Response to All Reviewers Regarding the Main Contributions of Our Paper".

W2: The organization of Sections 3.1 and 3.2 in original draft is confusing, and moving the last paragraph of 3.1 to the end of 3.2 would be very helpful.

• Thank you for your feedback. It is important to note that we defined and used terms such as "intervention family" in the second-to-last paragraph of Section 3.1 in the previous version, where we aimed to describe the identifiability using intervention data.
• However, we agree with your suggestion. We have moved this content to the end of the "Preliminaries" section and renamed it "Identifiability with Intervention Data" to enhance clarity and improve the reading experience.

W3: The wording seems misleading, as the only dataset with more than 100 nodes, Pathfinder, and some of the datasets in bnlearn are synthetic.

• We apologize for the misleading wording. Our intention was to select causal graphs of various sizes and challenges to emphasize the difficulty of causal discovery under our setting, which prior works rarely valued.
• The bnlearn repository contains causal graphs inspired by real-world applications, often referred to as "real-world benchmarks" in previous literature [1, 2, 3]. While these also can be seen as semi-real synthetic datasets generated from real causal graphs.
• Based on your suggestions, we have thoroughly checked all inappropriate wordings regarding the dataset description and revised them in the new version.

[1] Ke et al., "Neural Causal Structure Discovery from Interventions," TMLR, 2023.

[2] Ke et al., "Learning to Induce Causal Structure," ICLR, 2023.

[3] Lippe et al., "Efficient Neural Causal Discovery without Acyclicity Constraints," ICLR, 2022.

W4: Referring to AVICI and ENCO as "unfair baselines" is somewhat strange, and the phrase should be abandoned.

• Thank you for your suggestion. We have adopted your recommendation and no longer refer to AVICI and ENCO as "unfair baselines." Instead, we have renamed them as "Modified adaptation baseline" in the revised manuscript.

W5: Providing a real-world example would be helpful. The paper presents both observational and intervention data for the same variables, but the targets of the interventions are all unknown, which may seem a niche setting.

• It is important to note that our setting is not particularly niche. On the contrary, it is one of the most comprehensive and rich settings we are aware of, as demonstrated in Appendix E.2, Table 6 and Appendix E.4, Table 9.
• Additionally, you may have missed further experimental results in Appendix F, which include varying types of intervention targets (hard vs. soft, single vs. multiple), different sample sizes for observational and intervention data, and the number of intervention experiments.
• If you were referring to experiments with known intervention targets, this can be viewed as a simpler special case of our method. As described in the last paragraph of Section 3.2, when the intervention targets are known, the prior knowledge from the augmented graph can directly identify the environmental nodes pointing to the system nodes of the intervention target.

Dear Reviewer dQ5H,

We have just noticed that your current comments appear to be unrelated to our paper. Could you kindly confirm if you might have accidentally responded regarding another paper you are reviewing?