Test-Time Learning of Causal Structure from Interventional Data

Authors: Wei Chen, Rui Ding, Huang Bojun, Yuxuan Liang, Yang Zhang, Qiang Fu, Shi Han, Dongmei Zhang
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Test-Time Traing, Self-Augmentation, Causal Structure Learning, Intervention Target Detection

Abstract:
Inferring causal structures from interventional data remains a challenging task, especially when the intervention targets are unknown. *Supervised Causal Learning (SCL)* demonstrates strong empirical performance in predicting causal structures by training on datasets with known causal relations and applying the learned models to unseen test data. However, existing *SCL* methods often face inherent generalization challenges and struggle with the diverse intervention settings encountered in the *interventional causal discovery* problem. 

In this work, we propose _**TICL**_ (**T**est-time **I**nterventional **C**ausal **L**earning), a novel approach that follows the *Test-Time Training (TTT)* + *Joint Causal Inference (JCI)* paradigm to address these challenges of generalization and versatility, respectively. Specifically, _**TICL**_ employs a self-augmentation technique that generates training data at test time, tailored to the characteristics of the test data, enabling the model to adapt to the inherent biases in the test distribution. Additionally, by integrating the *JCI* framework with *SCL*, _**TICL**_ replaces the rule-based logic of the standard PC algorithm with a learning-based approach, effectively leveraging self-augmented training data. 

Extensive experiments on bnlearn benchmarks demonstrate _**TICL**_'s superiority in multiple aspects of causal discovery and intervention target detection.

Decision: reject
Reviewer scores: 8, 3, 6, 5

Reviews and discussion:
<thread>
creation date:
1730629822852

thread_type:
official_review

<thread_object>
creator: reviewer_8dqe

<content>
summary:
This paper introduces a supervised causal discovery framework that is composed of three steps. First, they convert the given interventional data collection into an augmented observational data samples. Then, they generate simulation training data from the augmented samples. Finally, they tune a supervised PC algorithm for identifiying the causal graph.

strengths:
**1**. The paper is clearly written and easy to read.

**2**. The authors conduct extensive experiments to validate their method.

weaknesses:
**1.** The novelty of this paper is limited. The first step, pooling interventional data into observational data samples, was introduced by Joint Causal Inference (Moiij et al., 2020). The second step, generating simulated trainning data via a proxy algorithm and Maximum Likelihood Estimation (MLE) for estimating the conditional probability, has been proposed by ML4S (Sec. 5; Ma et al., 2022). This paper is just a trivial combination of existing methods.

**2**. The supervised PC algorithm (Step 3) is problematic. Now that you already test conditional independence from data (Sec. 4.1, Freaturization step), why do you use a supervised classifier to determine the v-structure, instead of adopting the orientation rules that enjoy the theoretical identifiability? The approach costs more computations (to train the classifier) and meanwhile loses the identificiation guarantee.

questions:
See the weakness above.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730663170549

thread_type:
official_review

<thread_object>
creator: reviewer_4mtp

<content>
summary:
The authors tackle the problem of inferring causal structures from interventional data with unknown targets, where standard Supervised Causal Learning (SCL) often fails due to distribution shifts. They introduce TICL (Test-time Interventional Causal Learning), which leverages self-augmentation at test time to adapt the model to test data biases. TICL integrates the Joint Causal Inference (JCI) framework, transforming rule-based logic into a learning-based approach that better utilizes augmented data. Extensive experiments show TICL's effectiveness in causal discovery and target detection.

strengths:
The main contribution of the authors is their proposal of a novel JCI+SCL paradigm for causal discovery under unknown interventions from discrete data. Their TICL approach significantly advances the state of the art in discovering causal relations and interventional targets, achieving an average F1-score improvement across diverse real-world datasets. The authors introduce self-augmentation within SCL, enhancing training instances from the test data, and implement the IS-MCMC algorithm, which effectively samples graphs from the posterior distribution and generates compatible data for training. Their systematic study highlights JCI as a promising direction for interventional causal discovery, with TICL offering flexibility and requiring fewer assumptions in various intervention settings.

weaknesses:
Although the paper is a well-contributed effort on empirical and experimental sides, showing significant advancements over the state of the art, I still believe the paper can improve with some theoretical justification on key steps involved in the proposed approach. For instance, the claim that the algorithm IS-MCMC samples $G$ from the posterior estimation $P(G|D)$ and that the data $D_i$ is compatible with $G_i$ is made. However, the authors do not justify how the stationary distribution of the constructed Markov chain matches the posterior distribution of graphs given the data. Similarly, there is a lack of discussion on the sampling convexity for convergence of the Markov chain. If the authors can clarify these issues, I would be willing to revise my score for the paper and see it as a more valuable contribution to the field.

questions:
I have few question for the authors:

* Can the authors provide some justification on how the stationary distribution of the constructed Markov chain(s) in IS-MCMC matches the posterior distribution of graphs given the data?
    
* What is a good criterion (or number of samples) to ensure proper convergence for the constructed Markov chain(s)?
    
* The authors claim that a binary classifier enables us to replace heuristic searches and potentially erroneous conditional independence (CI) tests with a robust classification mechanism. Do the authors have any empirical evidence for this claim in their set of experiments?
    
* In experiment section 5.1, the authors mention that they sample, or forward-sample, 10,000 samples for both observational cases and each intervention. I wanted to ask how one would choose this number. Is there a risk of overfitting if the chosen sample size is too large? If not, can you explain why it is generally better to use a larger number of samples?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730872806599

thread_type:
official_review

<thread_object>
creator: reviewer_ya31

<content>
summary:
This paper proposes an algorithm that performs causal discovery from observational and interventional data while adapting to test-time training. It is built upon the joint causal inference and supervised causal learning frameworks. The authors provide their performance results on a variety of causal graphs.

strengths:
The authors address a very interesting and important problem. The experiments are extensive, and the necessary background to understand the paper is provided.

weaknesses:
## Minor Weaknesses:
* The introduction discusses many contributions, which might be a little distracting.
* Figure 2's caption should mention what the numbers in the curly brackets refer to.
* $X_2 \to X_1 \leftarrow \\{1\\}$. It is unclear why $\\{1\\}$ is considered a node here.
* Assumptions such as Markovian, faithfulness, sufficiency, etc. should be defined and explained.
* I-CPDAG is not discussed in detail, although it is used many times.
* JCI considers data samples under interventions as observations under imposed conditions — this statement appears repetitive.
* $D_i$ is likely to be in the neighborhood of the original augmented dataset. It is unclear what "neighborhood" means.
* It is unclear what "high-quality training data" means. This should be made precise.
* It is not properly defined what $G^{(t-1)}$ refers to in the mutation step.
* The numbers 1-6 in the key steps could be shown in Figure 3 for better mapping.

## Major Weaknesses:
* It is hard to focus on the main contribution: Is it I-CPDAG discovery, finding the intervention target, test-time adaptation, PC+SCL, prior knowledge, etc.?
* The presentation of the paper needs to improve a little more. It feels like too many things are going on. The description needs to be clearer.
* Although test-time adaptation was the main motivation of the proposed approach, it is discussed very little.
* Are the authors proposing to train a classifier for each possible triplet to detect if it forms a v-structure? That would be very computationally inefficient. How is that better than using the PC algorithm? The training procedure needs more detailed discussion.
* The Asia graph from bnlearn is not a real-data graph. Please check its reference.

I highly appreciate the author's effort on this paper. I hope my comments help them to improve it further.

questions:
## Questions:
* If the $\text{score}(G^{\text{cand}}) < \text{score}(G^{(t-1)})$ and $\frac{\text{score}(G^{\text{cand}})}{\text{score}(G^{(t-1)})} = 0.9$, does that mean $G^{\text{cand}}$ is chosen with probability 0.9 even if its score is lower? Doesn't that mean we will gradually move toward incorrect graphs?
* To my knowledge, the 14 graphs from bnlearn are mainly observational (except Sachs). How are the authors generating observational and interventional datasets from these graphs?
</content>
</thread_object>

</thread>
<thread>
creation date:
1731223214089

thread_type:
official_review

<thread_object>
creator: reviewer_dq5h

<content>
summary:
The authors focus on the setting where we have multiple datasets describing the same system, but each dataset was collected under a different set of interventions, whose targets may be unknown.  This problem setting matches that of the joint causal inference framework proposed by Mooij et al., which provides a framework for combining such a collection of datasets and conceptualizing them with a single graph.  The authors propose a novel method, TICL, that first generates semi-synthetic data from from a graph structure learned from the unified JCI datasets, producing a training dataset.  TICL then uses this data to in a two-phase PC-like supervised causal learning process, using classifiers to determine first edge existence and then V-structure orientation.  The authors compare TICL to a variety of other methods on bnlearn baselines and find that it consistently performs the best.

strengths:
I think this is a good paper.  The authors take two existing techniques (JCI and SCL), describe both of them well, and provide an interesting combination that both feels intuitive and clever.  The writing is, for the most part, clear throughout, with consistent terminology and notation.  The experimental results, while only semi-synthetic (due to the lack of real-world interventions), are thorough and compelling, comparing against a solid range of competitive methods in multiple categories.

weaknesses:
I appreciate the attempt at a "When", "What", "How" framing in the introduction, but the framing of "We create training data after accessing the test data" is strange and over-complicates what you're actually doing.  If I understand correctly, your approach is a two-stage process, using the input data $D$ to generate augmented semi-synthetic data, which is used to train a model that to classify $D$ in your second stage.  I think part of the confusion is the use of the term "test data" here, since in ML, tests data is usually a dataset that is used at the very end of a pipeline to assess model performance, which doesn't really match the standard causal inference setting.  I didn't understand the text of the "When" section in the introduction at all until I had nearly finished the paper, and even then it took multiple times reading it to understand what you were trying to say.  Rewording that section to focus on how the data that is typically use for SCL training differs from what you use, and how that allows you to train an SCL model that is far more tailored to your specific problem.

Not being very familiar with the JCI framework before reading this paper, I found the organization around Sections 3.1 and 3.2 confusing.  Figure 2, and the discussion of it at the end of 3.1, is very helpful, but it makes use of the JCI framework (referencing intervention families and showing how intervention targets are present in the graph).  This figure makes a lot of sense after reading Section 3.2, but since it's presented and discussed in 3.1 (even using terms like "intervention family" before they are defined), it mostly serves to confuse and force the reader to try to understand the JCI framework from context clues.  Moving the final paragraph of 3.1 until after Section 3.2 would help a lot.

While I generally like the experimental results, some of the discussion there feels a bit disingenuous.  The authors state one of their key advantages  over other recent methods is that you tested on "real causal graph datasets with over 100 nodes", and in the "Benchmarks & Baselines" section, you say that you "use discrete datasets of 14 real-world datasets collected from the bnlearn repository".  This implies that all 14 of the datasets are "real-world datasets", many of which are over 100 nodes.  However, unless I'm missing some experiments or missing something about the bnlearn datasets, the only one of the 14 you list that has over 100 nodes is Pathfinder, which has 104, and some of the bnlearn datasets you chose (Asia, Insurance, Alarm, Hailfinder) are synthetic, so calling them "real-world datasets" is strange. 
 You definitely test on a broader array of datasets than "only synthetic with 10-30 nodes", so I think that's a fine distinction to highlight, but it would be helpful, when describing the datasets you used in the "Benchmarks & Baselines" section, to be clearer about the range of nodes and realism of the datasets you chose.

I understand your reasoning, but it's a bit strange to call AVICI and ENCO "unfair baselines".  While they are told the intervention targets and other methods are not, TICL and the other JCI-based methods also have the distinct advantage that the data you are testing on is data from bnlearn that you modified (via interventions) to exactly match the problem setting for the JCI framework, upon which TICL is based, so it's not surprising that methods designed to work on data with multiple interventions with unknown targets perform better than methods intended to work on data with either a single intervention or known intervention targets.  You of course should make it clear to the reader that AVICI and ENCO had access to that information, since the fact that TICL doesn't need it to be competitive is a clear advantage, but I would drop the language about them being unfair baselines because of it.

A real-world example would help a lot towards showing the value of this method.  While the method seems interesting, the setting of "We have both observational and interventional data that measures the same variables, but the targets of each intervention are unknown" comes across as very niche and not very applicable.  I don't think that's necessarily the case, but providing even a simple motivating example in the introduction would help explain to the readers why we should care about your method.

In Table 1, the meaning of blue/bold and red/underlined should be included in the Table 1 caption, rather than in the "Training Datasets & Metrics" section, so the table can be at least somewhat stand-alone.  I would also put Footnote 1 on the table, rather than at the beginning of the list of methods (especially since you don't actually use the * until the table).

A minor point, but in Table 1, it would be good to use some other indicator for "JCI-Improved baseline", "Unfair baseline", and "classic baseline" besides a light background color.  As is, it's impossible distinguish when printed in black and white and even in color, the light yellow for "classic baseline" blends in far too much with the background and looks too similar to the pale green.  Similarly, in the two right plots of Figure 4, it's odd to use different symbols and colors for the points, but only include the colors (and not the symbols) in the legend.  You should make the legend show the shapes as well.

questions:
Can you clarify the loop structure of Algorithm 1?  The parallelization loop index, $i$, is not used in the algorithm pseudo-code, and if that loop is being done in parallel, then presumably there's no looping back to step 1 from step 7, right?  But then step 1 starts with us already having $G^{t-1}$.  Where is $t$ initialized?  I wondered if maybe steps 1-7 were being done iteratively until IS-MCMC converges, but then I'm not sure what's happening with the $D^{(t)}$ that's sampled in step 7, since if we're making a list of each $D^{(T)}$ dataset for each variant of $G^{(t)}$ we see, then we'd probably want some sort of burn-in period, which isn't part of the algorithm.  But if we're just keeping the final $D^{(t)}$, then there's no reason for it to be in a loop... Clearly there's something I'm missing with how this algorithm is set-up.

You mention that you consider soft-interventions for your experiments.  Can you give an example of the type of soft intervention you simulated?  Did you try experiments with hard interventions, and, if so, were the results essentially the same?

Did you try comparing against generating $D^{(t)}$ from Algorithm 1 and then just using standard PC on it, rather than your custom PC-like approach?
</content>
</thread_object>

</thread>
<thread>
creation date:
1732573136812

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response to All Reviewers Regarding the Convergence of Our IS-MCMC Algorithm

comment:
Dear All Reviewers (and AC),

We are delighted to see that most reviewers are interested in this problem. Below, we provide a point-by-point response to address the concerns raised by the reviewers:

---

> **Guarantee of Posterior Distribution Convergence:**
>
- Our IS-MCMC algorithm follows a standardized Structure-MCMC process in the intervention-augmented graph space. Please refer to **Algorithm 1** in the revised manuscript, which corresponds to **Steps 1-6** in the main text as a general introduction to the Structure-MCMC process.
- By employing the Metropolis-Hastings sampler within the standardized Structure MCMC framework, the Markov chain is guaranteed to have a stationary distribution equal to the posterior distribution $P(G \mid D)$ [2], which has been well studied in the literature[1, 2, 3].
- It is important to note that, under the premise of this theoretical guarantee, the novelty of our work lies in proposing the use of the posterior distribution as the target for acquiring training samples and optimizing feasible solutions in intervention scenarios.


[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.

---

> **Optimization Considerations for IS-MCMC:**
>
- However, two critical factors need to be addressed. 
  - **First**, managing the time complexity of this process is crucial for maintaining efficient inference. 
  - **Second**, ensuring the effectiveness of the IS-MCMC process on the augmented graph.
- We try to solve the above two problems:
  - **From the TTT-driven perspective on efficiency:** Since we leverage the "test-time" phase, the convergence speed of IS-MCMC is particularly important. We observed that a good initial state enables the Markov chain to converge faster, as evidenced by **Figure 5** in the experimental section of our paper. Additionally, we modified the algorithm to use parallel multi-chain sampling, allowing for further efficiency, as shown in **Figure 8** of our experimental results.
  - **From the JCI-driven perspective on adaptability:** The MCMC process operates on augmented graphs rather than standard causal graphs. Thus, additional constraints are required to ensure the validity of the augmented graph. To address this, we introduced intervention constraints to ensure consistency of the augmented graph within the JCI framework.

---

In summary, our IS-MCMC algorithm effectively addresses multiple challenges under the TTT + JCI framework and demonstrates that using posterior estimates as training data is highly beneficial for test-time SCL.

As a practical response, we have included a **new Section C** in the revised appendix, which further organizes these insights in detail to aid reader understanding.

Sincerely,

Authors of submission 3081
</content>
</thread_object>

</thread>
<thread>
creation date:
1732573267102

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response to All Reviewers Regarding the Identifiability of Our PC-like SCL Algorithm

comment:
Dear All Reviewers (and AC),

We are pleased to see that all reviewers are interested in this issue. The main motivation for modifying the PC algorithm to the PC-Like SCL method is to leverage its powerful **error redundancy** and **theoretical identifiability**:

---

- **Empirical Performance:** In finite sample scenarios, the reliance of the PC algorithm on conditional independence (CI) tests can lead to errors. The PC-Like SCL algorithm combines feature-rich representations with a robust classification mechanism, achieving outstanding empirical results when compared to JCI-PC or other non-SCL methods. This is demonstrated in **Tables 1-2, 10-17** and **Figure 13** of our paper.
  
- **Theoretical Guarantees:** Our PC-Like SCL method **retains** the asymptotic properties of the original PC algorithm. Specifically, when the sample size approaches infinity, the method will detect the correct $\mathcal{I}$-CPDAG in the intervention environment, ensuring theoretical identifiability.

---

More specifically, our PC-Like SCL method encompasses the following ideas:

- **Feature Extraction:**
    - PC-Like SCL algorithm extracts a richer set of features that capture the conditional dependencies and structural patterns around training instances.

- **Classifier:**
    - Unlike heuristic rules in methods like PC or MPC, we train a classifier on synthetic data. Our model learns the complex interactions between features, overcoming the limitations of CI tests, which are prone to errors.
    - As the sample size approaches infinity, the learned classifier converges to an equivalent and theoretically correct solution, as would be provided by PC or MPC. However, in practical settings, PC-Like SCL's broader feature set and data-driven optimization enable superior empirical performance.

---

In summary, our **PC-Like SCL algorithm preserves the theoretical guarantees of PC while addressing its empirical limitations**. By combining feature-rich representations with a learned classification mechanism, PC-Like SCL achieves significant performance improvements in finite sample scenarios.

---

As a practical response, we have included a **new Section D** in the revised appendix, which explains the underlying reasons from intuitive analysis to theoretical proof to assist readers in understanding.

Sincerely,

Authors of submission 3081
</content>
</thread_object>

</thread>
<thread>
creation date:
1732573363059

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response to All Reviewers Regarding the Main Contributions of Our Paper——(Part 2)

comment:
---

> **Technical Level**

While the conceptual framework unifies the paradigm, its practical implementation requires addressing specific research challenges. To this end, we design two **customized algorithms**, **IS-MCMC** and **PC-Liked SCL**, to support data acquisition and model training within the TTT+JCI paradigm.

- **Training Data Acquisition under TTT**
    - We systematically address three critical questions:
        + **Q1**. *When should training data be acquired?*
        + **Q2**. *What types of training data are effective for SCL?*
        + **Q3**. *How can such data be obtained in our context?*
    - We give the answer:
        + **A1**. We note that the "test time" can be divided into two subphases: "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.
        + **A2**. We observe that posterior estimates of causal graphs, provide highly effective training data, as evidenced by empirical results in **Section 5.2**. *(We have also added a discussion on convergence in **Appendix C** of the revised version.)*
        + **A3**. We introduce the _**IS-MCMC**_ algorithm, which constructs Markov chains in an augmented graph structure space under interventional constraints. This method efficiently samples from the posterior distribution and incorporates optimization strategies tailored for intervention settings.
        
- **Learning Objective Design under JCI**
    - Although the JCI paradigm simplifies the unification of diverse intervention settings, it does not directly address:
        + **Q1**. *What is the appropriate learning objective?*
        + **Q2**. *How should the learning process be designed?*
    - We give the answer:
        + **A1**. A straightforward idea is to use the generated training data to train models that directly predict causal graphs. However, we highlight the overlooked connection between identifiability in ICD and SCL: models should aim to predict identifiable causal structures, specifically **$\mathcal{I}$-CPDAG**. Recall that a causal edge is identifiable only if it consistently appears across all causal graphs compatible with the given data. Unidentifiable edges lack stable associations with the data, even if they exist in the true causal graph. *(We have also added a theoretical proof of identifiability in **Appendix D** of the revised version.)*
        + **A2**. We chose to focus on identifying identifiable components in **$\mathcal{I}$-CPDAG**, namely the **skeleton** and **v-structure**. Inspired by the PC algorithm, we adapt it into a **PC-Liked SCL algorithm**. This approach structures learning as a two-phase process: skeleton identification in the first stage, followed by orientation prediction in the second stage. This design ensures theoretical asymptotic correctness while fostering systematic feature extraction and improved classification mechanisms. Consequently, our method demonstrates greater robustness compared to PC, achieving superior empirical performance.

---

> **Conclusion**
>
In summary, 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.

---

In light of the reviewers’ feedback, we recognize that many readers may struggle to grasp the core ideas of this paper. As a concrete response, we have **rewritten the introduction section**, systematically organizing our work across the dimensions of **problem**, **idea**, and **technique** to aid comprehension.

Sincerely,

Authors of submission 3081
</content>
</thread_object>

</thread>
<thread>
creation date:
1732573373357

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response to All Reviewers Regarding the Main Contributions of Our Paper——(Part 1)

comment:
Dear All Reviewers (and AC),

We extend our sincere gratitude to all reviewers for recognizing the _**significance of this research problem**_. It is crucial to emphasize that this work is not a mere incremental contribution but the outcome of a long-term and rigorous research effort, given the inherent challenges of the problem. To clarify our objectives and highlight the core contributions, we have structured our responses around three key dimensions. Specifically:

---

> **Problem Level**
>
Our aim is to address the _problem of **Interventional Causal Discovery (ICD)**_ using a _**Supervised Causal Learning (SCL)** tool_. This paper **deepens the understanding** of why SCL is used to address ICD from the _problem perspective_, and it outlines the specific challenges faced in this context.

- **Why address this fundamental problem?**
    - Causal discovery (CD) is a cornerstone of scientific inquiry. We posit that SCL is a novel and promising tool for tackling CD due to its scalability (via free training samples) and robust empirical performance. However, causal discovery using observational data is merely a special case of ICD, often hindered by limited identifiability. Addressing ICD is thus essential, yet the community has only made limited progress in realizing the potential of SCL for ICD. Existing studies, such as AVICI and ENCO, primarily focus on specific scenarios like hard interventions with known targets, leaving much of the problem space unexplored.
- **What fundamental challenges must be addressed?**
    - From the perspectives of both SCL and ICD, we identify two intrinsic challenges:
        + The *out-of-distribution generalization* issues inherent to SCL.
        + The *complexity and diversity* of ICD problems arising from different intervention experiments.

---

> **Idea Level**

To address the non-trivial challenge of leveraging SCL for ICD, we propose a **novel paradigm** combining **Test-Time Training (TTT)** and **Joint Causal Inference (JCI)**.

- **Test-Time Training for Generalization**
    - Although causal graph simulators can be designed to encompass diverse types, mechanisms, and scales, causal structure learning is inherently high-risk, often prioritizing performance at the expense of universality. SCL, due to the limitations of machine learning, inevitably faces out-of-distribution generalization issues. Instead of **_"scaling up the pre-training stage"_**, we prioritize _**"scaling up the inference stage"**_.
    - *To this end, we introduce a novel TTT framework tailored for causal discovery. By employing context-customized supervised learning during inference, this approach effectively circumvents the generalization challenges of SCL.*
- **Joint Causal Inference for Diversity**
    - Developing a unified and effective learning framework for ICD is challenging due to the diversity of intervention experiments. This diversity complicates the application of learning-based methods.
    - *We innovatively incorporate the JCI framework from traditional causal discovery, facilitating a unified learning process. This integration enables SCL tools to accommodate various intervention conditions, effectively unifying ICD. Additionally, our approach simultaneously unifies SCL for intervention target identification, which previously required bespoke algorithmic designs.*
</content>
</thread_object>

</thread>
<thread>
creation date:
1733228489919

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Author's Summary of Major Revisions

comment:
Dear All Reviewers,

We sincerely thank all reviewers for their valuable suggestions, which have significantly improved our paper. We provide a summary of the revisions to facilitate discussion between the reviewers and the AC (all revisions are highlighted in purple in the [`new manuscript`](https://openreview.net/pdf?id=ZXs3pkmrRG)).

---
- **Presentation:**
    - Based on feedback from reviewers **ya31**, **8DQE**, and **dQ5H**, our revisions include:
        - ① Reorganizing the _Introduction section_ systematically from the perspectives of the problem, ideas, and techniques, and further refining the writing to better clarify our main contributions.
        - ② Revising the _"When" part_ of the introduction regarding test-time training to provide clearer definitions and avoid unnecessary misunderstandings.
        - ③ Adjusting the order of content in the _Preliminaries section_ to improve clarity and enhance the reading experience.
- **Method:**
    - Based on feedback from reviewers **8DQE**, **ya31**, and **4MTP**, our revisions include:
        - ① Clarifying how our PC-Like SCL algorithm preserves the theoretical identifiability of PC while addressing its empirical limitations. _A new Section D_ has been included in the appendix to address readers' concerns.
    - Following feedback from reviewers **4MTP**, **ya31**, and **dQ5H**, our revisions include:
        - ② We discussed and clarified the convergence guarantee of the posterior distribution in our IS-MCMC algorithm and highlighted key issues that need to be addressed during optimization. _A new Section C_ has been included in the appendix to help readers better understand these insights.
- **Minor Detail:**
    - Based on feedback from reviewers **dQ5H** and **ya31**, our revisions include:
        - ① Rewriting unclear or potentially misleading phrases such as "high-quality training data," "neighborhood," "real-world data," and "unfair baselines."
        - ② Organizing and improving the presentation of confusing content, including the algorithm flow, figure legends, and color differentiation.

---
We hope that all these efforts will greatly address the reviewers' concerns. Once again, thank you!

Sincerely,

Authors of submission 3081
</content>
</thread_object>

</thread>


Metareview:
metareview:
The reviews are mixed. We have strong support, borderline support, borderline reject and strong reject. The method, by design, has many moving parts, which makes it naturally hard to understand where the actual contribution lies. I am guessing this caused some reviewers to not fully understand and appreciate the novelty. However, some reviewers explicitly said the proposed approach is not novel, and only combines some existing approaches such as JCI and test time learning. Even the extremely supportive reviewer commented that some claims are overdone and the wording and presentation are very confusing and need to be improved. Their review does not fully match their score and I have to use the content of their review more so than the number given. 

Based on where the reviews stand after rebuttal, I believe a round of revision will greatly help emphasize the contribution better. 

Based on my own reading, I also recommend that the authors cite and perhaps even leverage the more recent interventional causal discovery algorithms instead of only JCI. Specifically, Jaber et al. 2020 "Causal Discovery from Soft Interventions with Unknown Targets: Characterization and Learning" provides an improvement over JCI and could have been used as the backbone algorithm instead of or in addition to JCI.