Paper: STExplainer: Global Explainability of GNNs via Frequent SubTree Mining (ICLR-2024)

Reviewer comment (Theory):
My first concern regarding the proposed method is its complexity. After selecting the Top-K subtrees, the method merges overlapping subtrees to form subgraph patterns, necessitating access to all graph instances. Furthermore, the technique involves extracting intersection subgraphs from these patterns within a cluster through subgraph matching and employs additional subgraph matching to eliminate redundant subgraphs. Repeatedly accessing all graph instances can amplify the method's complexity. It is imperative for the authors to delve into the method's computational complexity and provide experimental comparisons with other baseline approaches.

Author response:
There is a misunderstanding here. After selecting the Top-M subtrees, our method exclusively works with these M subtrees, eliminating the need to access all graph instances repeatedly. The information about whether two subtrees are in the same data instance is obtained during the initial access to the data instances. Therefore, there is no redundant access to all graph instances, showcasing the efficiency of our design. This highlights that the method's complexity is not amplified, reinforcing the effectiveness of our approach in utilizing subtrees instead of subgraphs or data instances.

Reviewer comment (Experiments):
An initial subtree candidate is derived from an L-hop subgraph, and the size of the subtree candidate will significantly influence the results. This implies that the method's efficacy hinges on the configuration of the target GNNs. I highly recommend authors explain how L affects the method and use an experiment to show it.

Author response:
We would like to clarify a potential misunderstanding. $L$ is NOT a hyperparameter of our approach but represents the number of GNN layers, as mentioned in our paper. That is, when dealing with a pretrained $L$-layer GNN, we need to consider $L$-hop subtrees, where $L$ is fixed and is the same as the number of layers in the GNN in question. Altering $L$ can impact the performance of the original GNN in question. Therefore, changing $L$ wouldn't lead to a fair experiment for evaluating our explainer's performance.

Reviewer comment (Evaluation):
The suggested approach employs a Multi-Layer Perceptron (MLP) to obtain a node embedding matrix from the subtree feature matrix. This embedding matrix subsequently represents the score vector for all subtrees. However, integrating an additional neural network as a scoring mechanism complicates interpretability. Also, as the score of an individual subtree contributes to determining the score for the overall subgraph explanation and the overlapping of subgraph patterns, the construction of the initial subtree will significantly impact the results.

Author response:
The main goal of our paper is to provide understandable global-level GNN explanations for humans, not to tackle the broader challenge of neural network interpretability. We use the MLP to learn the importance of candidate subtrees constructed based on their frequency, and this importance helps explain the GNNs. It's important to note that MLP is not mandatory; we could learn the importance of subtrees as learnable weights. We used an MLP because it allows us to potentially consider more detailed information, such as subtree embeddings, while learning the scores. Additionally, many recent works in local-level GNN explainability, a parallel research domain, use MLPs for generating explanations on data instances [1,2,3]. Therefore, we believe that using an MLP to learn scores is not a major issue.

[1] Mohit Bajaj, Lingyang Chu, Zi Yu Xue, Jian Pei, Lanjun Wang, Peter Cho-Ho Lam, and Yong Zhang. Robust counterfactual explanations on graph neural networks. Advances in Neural Information Processing Systems, 34:5644–5655, 2021.

[2] Dongsheng Luo, Wei Cheng, Dongkuan Xu, Wenchao Yu, Bo Zong, Haifeng Chen, and Xiang Zhang. Parameterized explainer for graph neural network. Advances in neural information processing systems, 33:19620–19631, 2020.

[3] Yaochen Xie, Sumeet Katariya, Xianfeng Tang, Edward Huang, Nikhil Rao, Karthik Subbian, and Shuiwang Ji. Task-agnostic graph explanations. Advances in Neural Information Processing
Systems, 35:12027–12039, 2022.

Reviewer comment (Evaluation):
Subtrees are ranked according to their frequency. However, as depicted in Figure 4, the performance on the NCI datasets appears to be closely linked to some infrequent subtrees. Does this suggest that frequency might not be an optimal criterion for subtree selection?

Author response:
The reviewer's interpretation for Figure 4 might be misleading. First, the figure only displays results for the top frequent subtrees. We do not have information on any “infrequent” subtrees. Only the results for top frequent subtrees are shown. Second, as we discussed in Section 5, Figure 4 illustrates that, despite some variance across runs, the results on all the datasets coverage as T increases. The variance stems from rerunning the model for different runs. Importantly, this figure and the corresponding experiments aim to choose the hyperparameter T on various datasets. It demonstrates that BA-2motifs and BAMultiShapes datasets require fewer subtrees compared to Mutagenicity and NCI1, aligning with our expectations as real-world datasets are more complex and contain more substructure types.

Reviewer comment (Theory):
In the process of selecting the Top-K subtrees, there is no provision to detect isomorphic subtrees. As a result, isomorphic subtrees might be assigned differing importance scores.

Author response:
Isomorphic subtrees will not have differing importance scores because we employ GNNs to identify subtrees, rather than manually selecting them. GNNs will always ensure that isomorphic subtrees yield identical embeddings. Consequently, the scores computed from these identical subtree embeddings would be the same.

Reviewer comment (Experiments):
The experimental section could be more detailed.

Author response:
**W1**: Due to space limitations, we had moved more details about the experiments to Appendix A.1~A.6.

Reviewer comment (Evaluation):
It is expected that the authors could explain the reasons for why not select accuracy as one of the metrics?

Author response:
**Q1**: We have evaluated the Fidelity in accuracy in Section 5. As we defined in Section 5.2. The Fidelity metric in our paper, represents the percentage of prediction matching with the original graphs when only the explanation patterns are used to make prediction, for the instances covered by the global explanations. This metric is called “accuracy” in some literature. But to be consistent with the common terminology in this domain [1], we called it “Fidelity” in our paper. 

[1] Hao Yuan, Haiyang Yu, Shurui Gui, and Shuiwang Ji. Explainability in graph neural networks:
A taxonomic survey. IEEE transactions on pattern analysis and machine intelligence, 45(5):
5782–5799, 2022.

Reviewer comment (Experiments):
In Table 1, the authors present the results of their model, suggest that they could choose some baselines for comparison to better illustrate the model's effectiveness.

Author response:
**Q2**: The main focus of our approach is to provide higher quality global-level explanations for GNNs. That is, we provide global explanations in a different form from the previous approaches, where our explanations are more intuitive and human-understandable graph concepts, and can potentially be easier to use in the downstream analysis (e.g. constructing building blocks), while the existing approaches provide either the latent representations or the human-defined rules as explanations (see Figure 2 and Figure 9). The empirical results demonstrate that our method provides significantly higher quality global explanations than the existing methods as also mentioned by Reviewer GgEn. Moreover, an advantage of our method is that we can quantitatively evaluate it by removing subgraphs from the original graph data. In contrast, existing methods provide either latent representations or human-defined rules, making such removal infeasible. As a result, these existing methods didn't conduct quantitative comparisons with any baseline in their own paper. Although we couldn't provide a quantitative comparison with them, we quantitatively assessed our approach using widely accepted metrics like Fidelity and Infidelity, as shown in Table 1. The high quantitative performance indicates that STExplainer effectively extracts global explanations aligning closely with the original GNNs’ behavior.

Reviewer comment (Experiments):
Certain choices in the introduced method seem arbitrary and perhaps even sub-optimal without justification. For example, when conducting k-means clustering, the authors choose k so that the centers of the clusters are distant enough, which is parameterized by a hyperparameter tau. The choice of tau clearly influences the choice of k and thus the rest of the method. In all experiments, they set tau = 2, but it is not clear why this particular value was chosen. Since the authors aim to incentivize the center of the clusters to be close to each other, it would be relevant and important to explore the performance of this method with different choices of tau and hence k.

Author response:
**W1&Q2&Q3**: We understand the reviewer's concern regarding hyperparameter settings and would like to provide clarification. Regarding $\tau$ and $k$-cluster, we would like to clarify that we did not fix $k=40$, but only let $k_{max}=40$, where $k_{max}$ is an argument to reproduce the results in this paper using our code, meaning that a maximum of 40 clusters is allowed. In our implementation, the exact number of clusters used for each dataset is dynamically determined. We have updated the manuscript by reporting the exact number of $k$ in the appendix (highlighted in red). For $\tau$, typically we want $\tau$ to be small, such that we are able to find the intersections on the S subgraphs in each cluster. As discussed in Section 4, we would discard a cluster in cases no common subgraphs are found in the cluster. We chose $\tau=2$ for the datasets since we find that we only need to discard a small ratio of clusters when $\tau \leq 2$. The choice of $\lambda$ is set to $\lambda=0.1$ as it is relatively more stable in achieving high performance. With other settings of $\lambda$, our method is still able to achieve high performance, which further demonstrates the robustness of our proposed pipeline. We updated the manuscript by the experiments for choosing $\tau$  and $\lambda$ in Appendix A.6. Regarding $T$, our choice is explained in Section 5.3 with Figure 4. The figure illustrates that BA-2motifs and BAMultiShapes datasets require fewer subtrees compared to Mutagenicity and NCI1. This aligns with expectations since real-world datasets are more complex and contain more types of substructures.

Reviewer comment (Theory):
After extracting overlapping subtrees which lead to subgraphs, the method applies k-means clustering on the embeddings. From this cluster, they sample S subgraphs and average them to obtain a representative subgraph for the cluster. Using this method to obtain a prototype seems arbitrary; it is unclear why they do not simply use the centroid itself or other prototype learning techniques to obtain the representative sample.

Author response:
**W2&Q1**: As we discussed in the paragraph of “Intersections of the subgraph patterns in the same cluster” in Section 4.2, after we “sample S subgraphs” and before we “average to obtain a representative subgraph for the cluster”, we perform subgraph matching on the S subgraphs, ultimately yielding the intersection of these S subgraphs. The intersection is not necessarily one of the S subgraphs, but likely a new one, hence it can be better represented by the mean of the corresponding S subgraphs in comparison with a prototype in them.

Reviewer comment (Experiments):
The experimental section is not exhaustive, as it only includes two real datasets and two synthetic datasets. While the authors justify why they do not compare to other global explainers, providing more cases where other methods fail and theirs succeeds would strengthen their approach. Moreover, they only use one choice for major hyperparameters such as tau and lambda; they should show experiments examining how the choice of these parameters affects their method.

Author response:
**W3**: We provide global explanations in a different form from the previous approaches, where our explanations are more intuitive and human-understandable graph concepts, while the existing approaches provide either the latent representations of clusters or the human-defined rules as explanations (see Figure 2 and Figure 9). It's not that existing approaches sometimes fail to give intuitive global graph concepts; rather, they cannot provide them at all. We hope our work can help the community to give more attention to the global graph explanations because of their intuitiveness and potential for further analysis (e.g. constructing building blocks). Additionally, the existing works conducted experiments on 3~4 datasets, such as GLGExplainer on 3 datasets and GCNeuron on 4 datasets. Therefore, we believe demonstrating the effectiveness of our approach with 4 datasets is sufficient in comparison.

Reviewer comment (Theory):
There is a lack of justification for particular choices used in their method, such as why averaging S subgraphs from a cluster is considered the optimal choice for a representative subgraph.

Author response:
**W2&Q1**: As we discussed in the paragraph of “Intersections of the subgraph patterns in the same cluster” in Section 4.2, after we “sample S subgraphs” and before we “average to obtain a representative subgraph for the cluster”, we perform subgraph matching on the S subgraphs, ultimately yielding the intersection of these S subgraphs. The intersection is not necessarily one of the S subgraphs, but likely a new one, hence it can be better represented by the mean of the corresponding S subgraphs in comparison with a prototype in them.

Reviewer comment (Experiments):
There is no explanation for why tau = 2 was chosen for all experiments, nor what other good choices might be for this hyperparameter.

Author response:
**W1&Q2&Q3**: We understand the reviewer's concern regarding hyperparameter settings and would like to provide clarification. Regarding $\tau$ and $k$-cluster, we would like to clarify that we did not fix $k=40$, but only let $k_{max}=40$, where $k_{max}$ is an argument to reproduce the results in this paper using our code, meaning that a maximum of 40 clusters is allowed. In our implementation, the exact number of clusters used for each dataset is dynamically determined. We have updated the manuscript by reporting the exact number of $k$ in the appendix (highlighted in red). For $\tau$, typically we want $\tau$ to be small, such that we are able to find the intersections on the S subgraphs in each cluster. As discussed in Section 4, we would discard a cluster in cases no common subgraphs are found in the cluster. We chose $\tau=2$ for the datasets since we find that we only need to discard a small ratio of clusters when $\tau \leq 2$. The choice of $\lambda$ is set to $\lambda=0.1$ as it is relatively more stable in achieving high performance. With other settings of $\lambda$, our method is still able to achieve high performance, which further demonstrates the robustness of our proposed pipeline. We updated the manuscript by the experiments for choosing $\tau$  and $\lambda$ in Appendix A.6. Regarding $T$, our choice is explained in Section 5.3 with Figure 4. The figure illustrates that BA-2motifs and BAMultiShapes datasets require fewer subtrees compared to Mutagenicity and NCI1. This aligns with expectations since real-world datasets are more complex and contain more types of substructures.

Reviewer comment (Writing):
There are typos and editorial errors that should be corrected, including:
- In the second last sentence of the Introduction, ‘methos’ should be ‘methods.’
- In the Introduction when listing the authors’ contributions, specifically the last sentence of ii), it should read ‘...concepts rather than latent representation...’ instead of ‘...concepts rather latent representation...’
- In Appendix section A5, there are several incorrect uses of forward and backward quotation marks.
- In the Appendix, the title of section A6 is misspelled; it should be ‘Hyperparameter.’

Author response:
**Q4**: Thanks a lot for pointing out the typos, we have updated the manuscript accordingly (highlighted in red).