Sparse Causal Discovery with Generative Intervention for Unsupervised Graph Domain Adaptation

We sincerely thank the reviewer for the thorough review. Below, we address each of your concerns in detail.

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Q1. Should test more domain split perspectives

Thank you for this valuable suggestion. Our cross-dataset experiments (Tables 1, 3, 4, 6) incorporate natural shift, feature shift, and label shift between datasets (e.g., PTC). To directly address feature shift concerns, we conducted additional experiments on Letter-Med using clustering-based feature distributions to create domain shifts. Results demonstrate SLOGAN's robustness across varied shift scenarios. We will review the paper to include the setup and comprehensive discussion of this experiments.

Q2. Should verify in synthetic experiments

We appreciate your suggestion. To complement evaluations, we implemented synthetic experiments following [3]. We constructed Erdös-Rényi graphs containing both causal factors (structural motifs consistent across domains) and spurious factors (domain-specific correlations). Our experimental design established two domains (D0 and D1). Analysis confirms that SLOGAN successfully conducts knowledge transfer based on causal factors. We will incorporate comprehensive details of this experiment in our revised manuscript.

Q3. Should explain stability and robustness

Thanks for your comment. Our claims are supported by adaptation results (visualizations in Figure 5 and 6), ablation studies (Table 5), and theoretical guarantees (Section 3.5 on bounded target error).

Additionally, to directly address your question about robustness, we conducted additional experiments on Letter-Med by adding Gaussian noise (σ) to node features. Results show the robustness across noise levels. We will update the manuscript with these results.

Q4. Question on performance improvement

Thanks for your comment. SLOGAN shows consistent improvements across all six datasets, with gains reaching 2.3% and 2.2% on challenging benchmarks. In graph learning, particularly in UDA settings where labeled target data is unavailable, such consistent improvements are considered significant. For context, recent work TO-UGDA [2], although achieving relatively limited improvements on some datasets (e.g., 0.5% over CoCo), is still recognized for its methodological contributions. Notably, our synthetic experiments (Q2) show even more substantial gains, with SLOGAN outperforming baselines by 4.6%. Our work's value lies in both the performance gains and the novel perspective for graph domain adaptation theory.

Q5. Should explain L_dis's effectiveness

Thanks for your comment. The effectiveness varies due to dataset characteristics, with greater benefits observed in datasets having cleaner feature distributions and more challenges under higher noise or complex feature correlations. This phenomenon aligns with our theoretical analysis, as disentanglement is inherently more effective when causal signals are more clearly. Our newly added synthetic experiments (Q2) also support this. Across synthetic and real-world datasets (in paper), $L_{dis}$ contributes meaningfully to overall performance (average 1.7%). We will enrich this discussion in the revised manuscript.

Q6. Should test various architectures

Thank you for this suggestion. We chose GCN as primary backbone for fair comparison with baselines. We have now conducted additional experiments as shown below. This confirms the architecture-agnostic nature of SLOGAN. We will revise accordingly.

Q7. Should enrich the comparison

Thank you for the constructive suggestion. We will add [1,2] into comparison and enrich the background section. The results on PTC are shown below, which shows SLOGAN's superiority.

Q8. Undefined Term

The $L_{re}$ in Equation (17) refers to the reconstruction loss. This definition will be explicitly included in the revised manuscript.

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We sincerely appreciate your constructive feedback, which has helped us improve the clarity and comprehensiveness of our work.

[1] Deal: An unsupervised domain adaptive framework for graph-level classification. ACM MM 2022.

[2] TO-UGDA: target-oriented unsupervised graph domain adaptation. Scientific Reports 2024.

[3] Nikolentzos, G., & Vazirgiannis, M. (2020). Random Walk Graph Neural Networks. NeurIPS 2020.

We sincerely thank the reviewer for the thorough assessment of our work and the constructive feedback. Below, we address each of the concerns raised.

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1. Symbols in Eq. 16 not well-defined

We apologize for the lack of clarity in Eq. 16. This equation describes our generative intervention mechanism where we swap spurious features between samples from different domains. Specifically, $z^c_i$ represents the causal features from sample $i$, $z^s_k$ represents the spurious features from sample $k$ (from a different domain), $G$ is our generative model, and $z^+_{i,k}$ is the newly generated composite representation. We will improve the definition of these symbols in the revised manuscript.

2. Insufficient discussion on Unbiased Discriminative Learning

We agree that this section deserves more explanation. In our approach, unbiased discriminative learning addresses two critical challenges:

1. Class imbalance: Our category-adaptive confidence thresholds (Eq. 11-12) dynamically adjust selection criteria based on class-specific confidence distributions, preventing majority class dominance.

2. Error propagation: By implementing cross-domain stability through both source supervision and target pseudo-labeling, we create a balanced optimization objective that mitigates the risk of error accumulation.

We will expand this discussion in the revised manuscript, further clarifying how these mechanisms ensure unbiased learning across domains.

3. Articulation of contributions and module cohesion

We appreciate this feedback and will revise the manuscript to more clearly articulate our contributions. Specifically, we will emphasize how our three components form a unified framework:

1. Sparse causal discovery identifies stable causal patterns while isolating spurious correlations
2. Generative intervention breaks residual spurious couplings through cross-domain feature recombination
3. Category-adaptive calibration ensures stable pseudo-label learning

These components work together synergistically: causal discovery provides the foundation, generative intervention strengthens it by eliminating remaining spurious correlations, and adaptive calibration ensures robust knowledge transfer.

4. Experimental setup details

We agree that more detailed information would enhance reproducibility. In the revised manuscript, we will add a dedicated section specifying hardware (e.g., NVIDIA A100 GPU with 40GB memory) and training parameters (e.g., batch size, optimizer, learning rate, and training epochs).

5. Discussion of theoretical aspects

Our theoretical framework provides a principled foundation for SLOGAN through a probabilistic error bound directly connected to our three-component architecture. The bound shows that target domain error depends on three stability conditions: causal sufficiency (ensuring predictive information is preserved), spurious suppression (minimizing label-spurious correlations), and generative intervention fidelity (maintaining semantic consistency during feature recombination). The bound's dependence on $\sqrt{\epsilon}_1$ and $\sqrt{\epsilon}_2$ demonstrates why our unified approach outperforms single-strategy methods—optimal domain adaptation requires both preserving causal mechanisms and breaking spurious correlations simultaneously. This theoretical insight explains our empirical results where each component contributes to reducing a specific term in the overall error bound.

6. Color visibility in Figure 4

We thank the reviewer for this practical suggestion. We will adjust the color scheme to improve visibility, specifically making the "Ours" indicator more distinct from other methods using a higher contrast color.

7. Minor issues

We will address all minor issues in the revised manuscript, including correcting punctuation in Eq. 6, ensuring consistent labeling (SLOGAN vs. Ours) in Table 5, reformatting Algorithm 1 to appear on a single page, and adding a detailed description of the MTDF baseline in the appendix.

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We appreciate the reviewer's careful reading and thoughtful suggestions, which will significantly improve the quality of our final manuscript.

Thank you for your thoughtful review and constructive feedback. We appreciate the opportunity to clarify these points and improve our paper.

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Q1. The code of the method has been released, but the model.py and main.py seems only contain graph neural networks, while the location of the code for the proposed method is unclear.

We thank the reviewer for pointing out the lack of clarity in our code organization. The proposed method SLOGAN is indeed implemented in the provided code, but we acknowledge that the current structure and variable naming could be improved for better readability.

The core components of our method can be found in the main.py file:

• Causal Feature Extraction: Implemented in lines 28-34 with causal_loss function, which corresponds to our sparse causal modeling approach using contrastive objectives.

• Spurious Feature Suppression: Implemented in lines 36-42 with non_causal_loss function, which implements our variational information bottleneck for separating domain-specific correlations.

• Generative Intervention Mechanism: Implemented in lines 44-54 with the GraphGenerator class, which enables cross-domain feature recombination.

• Information Bottleneck Disentanglement: Lines 204-224 in the training loop implement our causal-spurious feature disentanglement using mutual information constraints.

• Generative Intervention Processing: Lines 224, where augemented views are generated by recombining causal and shuffled spurious features, with covariance constraints implemented as an MSE loss.

To improve clarity, we will:

1. Reorganize our code to better align with the paper's methodology sections
2. Rename variables to directly match terminology in the paper
3. Add comprehensive comments explaining the implementation of each component
4. Create separate modules for each key component (causal discovery, intervention mechanism, and confidence calibration)

We will update our repository with these improvements to facilitate understanding and reproducibility.

Q2. I would recommend the authors to also highlight the second best methods in the tables. Besides, the year of the baselines would also be helpful for checking whether the baselines are up-to-date.

We appreciate this valuable suggestion. In the revised version, we will:

1. Highlight the second-best methods in all result tables (using underlined values or alternative formatting)
2. Add publication years for all baseline methods to provide context on the recency of comparisons

Regarding up-to-date baselines, we have already compared with recent state-of-the-art methods published in 2024, such as MTDF. In the revised version, we will also enrich the comparison with recent methods [1,2]. This will enhance table readability and allow readers to better assess our method's improvements relative to the most recent state-of-the-art approaches.

[1] TO-UGDA: target-oriented unsupervised graph domain adaptation. Scientific Reports, 2024.

[2] Deal: An unsupervised domain adaptive framework for graph-level classification. ACM MM 2022.

Q3. The graph domain generalization problem seems to be closely related to continual graph learning, which also aims to train a model over graphs with different distributions. I would recommend the authors to discuss the difference between these two research directions.

Thank you for highlighting this important connection. We agree that discussing the relationship between graph domain generalization and continual graph learning would strengthen our paper. We will add a dedicated paragraph with proper references in the related work section addressing this relationship:

"While graph domain generalization and continual graph learning both address distribution shifts in graph data, they differ in several key aspects. Continual graph learning focuses on sequential learning across multiple tasks without catastrophic forgetting, enabling models to adapt to new distributions while retaining performance on previously encountered ones. In contrast, graph domain generalization aims to learn domain-invariant representations that transfer directly to unseen target domains without adaptation. Our approach, SLOGAN, specifically addresses the latter by identifying stable causal mechanisms that generalize across domains rather than incrementally adapting to new distributions."

We believe this discussion will provide valuable context and clarify the positioning of our work within the broader landscape of graph learning research.

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Thank you again for your constructive comments, which will help improve our paper.

We sincerely thank you for your valuable feedback and thoughtful comments. We address each point below:

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Q1. While the paper thoroughly discusses prior work on UDA, GNNs, and causal representation learning, it overlooks several recent works that integrate causal inference with domain adaptation in structured data.

Thank you for your constructive suggestion. We will enhance our literature review to include recent works integrating causal inference with domain adaptation in structured data. [1] presents important contributions to invariant causal representation learning with exponential family distributions. In our revised manuscript, we will provide a discussion and add proper references of how our approach relates to and advances beyond these existing methods. The revised paragraph is as follows:

While [1] makes significant contributions to invariant causal representation learning for general out-of-distribution generalization, our work extends these principles specifically for graph-structured data by introducing sparse causal discovery mechanisms that capture the unique interplay between node features and graph topology, enhancing transfer capabilities across heterogeneous graph domains.

[1] Invariant causal representation learning for out-of-distribution generalization. ICLR 2021.

Q2. Although the paper reports significant improvements, it does not consistently report standard deviations.

Thanks for your constructive suggestion. We will add the standard deviation metrics for results. We have already conducted these measurements across 5 independent runs with different random seeds. The results for PTC, Letter-Med and NCI1 datasets are shown below.

Q3. The paper's writing occasionally suffers from dense technical jargon, which may hinder readability for a broader machine learning audience.

We appreciate your feedback. We will improve the manuscript's accessibility by focusing on two key areas:

1. Clarifying complex technical concepts with intuitive explanations
2. Adding illustrative examples for abstract mechanisms

For instance, in Section 3.4, we will revise the description of our generative intervention approach from: "We design a generative model to reconstruct original graph representations with a cross-domain spurious feature exchange strategy. By perturbing local coupling of spurious features, this approach forces the model to rely solely on causal features for reconstruction, effectively suppressing spurious residuals."

To the more accessible:

Our method uses a targeted approach to ensure the model doesn't rely on misleading patterns. Consider the TWITTER dataset in our experiments: when classifying discussion topics in social networks, our method can distinguish between fundamental network structures (like community clusters and information flow patterns) and platform-specific features (like temporary trending hashtags or regional engagement patterns). It achieves this by deliberately exchanging these platform-specific features between different network samples while preserving the essential community structures, forcing the model to focus only on truly predictive patterns that work consistently across different social media environments.

These revisions will maintain the paper's technical rigor while making it more accessible to readers from various machine learning backgrounds.

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Thank you again for your constructive comments, which will help us improve the quality of our paper.