Evaluating Robustness and Uncertainty of Graph Models Under Structural Distributional Shifts

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be especially complex since the samples are interdependent. To evaluate the performance of graph models, it is important to test them on diverse and meaningful distributional shifts. However, most graph benchmarks considering distributional shifts for node-level problems focus mainly on node features, while structural properties are also essential for graph problems. In this work, we propose a general approach for inducing diverse distributional shifts based on graph structure. We use this approach to create data splits according to several structural node properties: popularity, locality, and density. In our experiments, we thoroughly evaluate the proposed distributional shifts and show that they can be quite challenging for existing graph models. We also reveal that simple models often outperform more sophisticated methods on the considered structural shifts. Finally, our experiments provide evidence that there is a trade-off between the quality of learned representations for the base classification task under structural distributional shift and the ability to separate the nodes from different distributions using these representations.

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Peer review

Reviewer 2ynW4/10 · confidence 4/52023-06-29

Summary

This paper proposes a benchmark for evaluating model robustness against structural distributional shifts. The authors propose three different metrics to split the datasets for the evaluation. In the experiments, the authors evaluate different models under the proposed distributional shifts and show that they can be quite challenging for existing graph models.

Strengths

1. This paper targets an understudied problem of evaluating model robustness and uncertainty estimation under structural distribution shift. 2. It presents a novel idea of using different evaluation metrics to create data splits for structural distribution shifts. 3. The authors evaluate different methods based on the proposed metrics and show some empirical findings.

Weaknesses

1. The authors consider less important nodes are OOD nodes. However, real-world graphs follow the power-law distribution and only have a small number of nodes that have a high degree/node importance. So the proposed metric is kind of counterintuitive to me. 2. The experimental setup, particularly the equal splitting of in-distribution (ID) and out-of-distribution (OOD) data, raises concerns about the generalizability of the findings. Real-world scenarios typically involve a smaller proportion of OOD data, and investigating varying ratios of ID to OOD data would enhance the practical relevance of the evaluation. 3. Since the authors argue the existing methods only focus on feature distribution shift, while this paper only focuses on the structural distribution shift. It would be better to consider them together rather than separately evaluate them, as they often occur simultaneously and have interdependencies. 4. While the proposed metrics for creating data splits are new, the authors could provide more detailed justification and analysis for their choices. It would be beneficial to explore the sensitivity of the evaluation results to different metric configurations. 5. I have a concern that should this paper be submitted to the datasets and benchmark datasets since this paper doesn't focus on technical contribution. To strengthen the paper, it would be beneficial to address these additional points and provide more comprehensive justifications, analyses, and experiments.

Questions

In addition to the above weaknesses, another question is (line 290-292), the authors"... including DANN, CORAL, EERM, and Mixup, we use the experimental framework from the GOOD benchmark, whereas the remaining methods are implemented in our custom experimental framework ...", what does it mean? Why not just use the same experimental framework?

Rating

4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

N/A

Reviewer E4Gb7/10 · confidence 5/52023-07-03

Summary

The authors propose three domain selections, namely, popularity, locality, and density to equip node prediction datasets with structural distribution shifts. Extensive experiments are conducted to compare present OOD generalization methods and OOD detection methods.

Strengths

S1: The proposed distribution shifts are novel. S2: The paper is well written and easy-to-follow. S3: The evaluations are clear and sufficient.

Weaknesses

W1: The title is misleading. Since this benchmark only focuses on node prediction tasks, the title should reflect it. As we know, structural distribution shifts are different in graph-level and node-level tasks. W2: The chosen shifts are somehow limited because they are not extracted from real-world scenarios. W3: Line 39: "Also, the splitting strategies in GOOD are mainly based on the node features and do not take into account the graph structure" is somehow misleading. I suggest the authors to clarify that "GOOD mainly focuses on node feature shifts in **node-level tasks**".

Questions

Q1: Can you find a way to compare your proposed shifts with the real shifts? Q2: I would suggest submitting benchmark works to the Datasets and Benchmarks track, which offers more transparent evaluations to your benchmark.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

4 excellent

Contribution

3 good

Limitations

Broader impacts are expected to be discussed. The licenses of the datasets and the code (GOOD) are expected to be mentioned.

Reviewer gSyv6/10 · confidence 4/52023-07-05

Summary

This paper provides a benchmark solution for producing diverse and meaningful distributional shifts from existing graph datasets. The experiments conducted demonstrate that the proposed distributional shifts can be difficult for existing graph models, and surprisingly, simpler models often outperform more sophisticated ones. The experiments also reveal a trade-off between the quality of learned representations for the base classification task and the ability to distinguish nodes from different distributions using these representations.

Strengths

The proposed data-splitting approach is quite interesting. The overall presentation is quite easy to follow. Based on the provided data-splitting strategy, most graph/node classification methods may not achieve a good classification performance and uncertainty quantification quality. It is also nice to see the authors conduct many empirical studies to validate the idea and compare the difference between various baselines.

Weaknesses

1. The technical novelty is somewhat limited. It seems like the technical contribution is based on existing techniques (PageRank, PPR, ...). I would like to see more discussions of the rationale/motivation for choosing the specific metric. For example, the PageRank is selected because of the need to quantify the node popularity, but other node centrality-based metrics can also be used to quantify the node popularity. 2. The dataset size is also quite small. It's not promising the experience learned from these small networks can be extended to million-scale networks. 3. Some important baselines (e.g., GOOD: A Graph Out-of-Distribution Benchmark) are not included in the main context. I feel like this paper should be more suitable for the dataset and benchmark track.

Questions

Please refer to the Weakness section.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

I am not seeing limitations of this work.

Reviewer AZW57/10 · confidence 5/52023-07-06

Summary

This paper proposes a general approach for inducing diverse distributional shifts based on graph structure and evaluates the robustness and uncertainty of graph models under these shifts. The authors define several types of distributional shifts based on graph characteristics, such as popularity and locality, and show that these shifts can be quite challenging for existing graph models. They also find that simple models often outperform more sophisticated methods on these challenging shifts. Additionally, the authors explore the trade-offs between the quality of learned representations for the base classification task and the ability to separate nodes under structural distributional shift. Overall, the paper's contributions include a novel approach for creating diverse and challenging distributional shifts for graph datasets, a thorough evaluation of the proposed shifts, and insights into the trade-offs between representation quality and shift detection.

Strengths

Originality: The paper's approach for inducing diverse distributional shifts based on graph structure is novel and fills a gap in the existing literature, which has mainly focused on node features. The authors' proposed shifts are also motivated by real-world scenarios and are synthetically generated, making them a valuable resource for evaluating the robustness and uncertainty of graph models. Quality: The paper's methodology is rigorous and well-designed, with clear explanations of the proposed shifts and the evaluation metrics used. The authors also provide extensive experimental results that demonstrate the effectiveness of their approach and highlight the challenges that arise when evaluating graph models under distributional shifts. Clarity: The paper is well-written and easy to follow, with clear explanations of the proposed shifts and the evaluation methodology. The authors also provide helpful visualizations and examples to illustrate their points. Significance: The paper's contributions are significant and have implications for the development of more robust and reliable decision-making systems based on machine learning. The authors' approach for inducing diverse distributional shifts based on graph structure can be applied to any dataset, making it a valuable resource for researchers and practitioners working on graph learning problems. The insights into the trade-offs between representation quality and shift detection are also important for understanding the limitations of existing graph models and developing more effective ones. Overall, the paper's contributions have the potential to advance the field of graph learning and improve the reliability of machine learning systems.

Weaknesses

Limited scope: The paper focuses solely on node-level problems of graph learning and does not consider other types of graph problems, such as link prediction or graph classification. This limited scope may restrict the generalizability of the proposed approach and its applicability to other types of graph problems. Synthetic shifts: While the authors' proposed shifts are motivated by real-world scenarios, they are synthetically generated, which may limit their ability to capture the full complexity of real distributional shifts. The paper acknowledges this limitation, but it is still worth noting that the proposed shifts may not fully reflect the challenges that arise in real-world scenarios. Limited comparison to existing methods: While the paper provides extensive experimental results that demonstrate the effectiveness of the proposed approach, it does not compare the proposed approach to other existing methods for evaluating graph models under distributional shifts. This limits the ability to assess the relative strengths and weaknesses of the proposed approach compared to other approaches.

Questions

Here are some questions and suggestions for the authors: Can the proposed approach be extended to other types of graph problems, such as link prediction or graph classification? If so, how might the approach need to be modified to accommodate these different types of problems? How might the proposed approach be adapted to handle real-world distributional shifts, rather than synthetically generated shifts? Are there any limitations to the proposed approach that might make it less effective in handling real-world shifts? How does the proposed approach compare to other existing methods for evaluating graph models under distributional shifts? Are there any specific strengths or weaknesses of the proposed approach compared to other approaches? The paper notes that there is a trade-off between the quality of learned representations for the target classification task and the ability to detect distributional shifts using these representations. Can the authors provide more details on this trade-off and how it might impact the effectiveness of the proposed approach in different scenarios? The paper proposes several different types of distributional shifts based on graph structure. Can the authors provide more details on how these shifts were chosen and whether there are other types of shifts that might be relevant for evaluating graph models? The paper focuses on evaluating graph models under distributional shifts, but does not provide any guidance on how to modify existing models to improve their robustness to these shifts. Can the authors provide any suggestions or guidelines for modifying existing models to improve their performance under distributional shifts? The paper notes that the proposed approach can be applied to any dataset, but does not provide any guidance on how to choose the appropriate node property to use as a splitting factor. Can the authors provide any suggestions or guidelines for choosing an appropriate node property for a given dataset? Overall, the paper presents an interesting and novel approach for evaluating graph models under distributional shifts. However, there are several areas where the authors could provide more details or guidance to help readers better understand and apply the proposed approach.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The paper briefly acknowledges some of the limitations of the proposed approach, such as the fact that the synthetic shifts may not fully reflect the complexity of real-world distributional shifts. However, the paper does not provide a detailed discussion of the potential negative societal impact of the work. Given the technical nature of the paper, it is possible that the authors did not see a direct connection between their work and potential negative societal impacts. However, it is always important for authors to consider the broader implications of their work, especially in fields like machine learning where there is a growing awareness of the potential risks and harms associated with these technologies. In future work, the authors could consider providing a more detailed discussion of the potential societal impacts of their work, including any ethical or social considerations that may arise from the use of their approach. This could help to ensure that the work is being developed and applied in a responsible and ethical manner.

Reviewer E4Gb2023-08-11

Thank you for your replies. Most of my concerns are addressed. And I also noticed that some of them cannot be addressed in this single work, so please list them and discuss them in the limitations and further works extensively. Although this is not a paper on the dataset and benchmark track, I have to clarify that my current score of 7 is partially based on the trust that the authors can be responsible and responsive for their released code, which is *essential even though the authors claim that it is not a traditional benchmark paper*. Furthermore, I'm willing to defend my review: Although I acknowledge that the suggestions of Reviewer 2ynW are beneficial, many concerns proposed are **not major** to reject this paper, since I don't think these concerns can undermine the contributions and conclusions of this paper. Score: $6\rightarrow 7$: Accept.

Authorsrebuttal2023-08-18

Thanks for your support! We plan to extend the discussion of future work based on your questions. Our code will be supported in our open source repository and also in the most popular frameworks for deep learning on graphs: PyG and DGL.

Reviewer 2ynW2023-08-16

Thanks for the response, part of my concerns have been addressed. I would like to consider raising my score if the following questions can be answered. Regarding W2, I appreciate that the authors provide a new analysis on the setting with 70% ID, and 30% OOD, but 30% OOD is still a lot, if it is possible to show the prediction/detection performance for 5% or 10% OOD data? And what would be findings? For W3, the authors show that the structure distribution shifts can induce the feature distribution shift as shown in Appendix (Figure 1). It's a bit unclear to me by saying "reducing the original node feature space into the 2D space of t-SNE representations". Why the structural shift will affect the original node features? Or you use models such as GNN to learn the embeddings and then do T-SNE. My last concern is about the contribution/insights of this paper. This paper proposes multiple ways to create structure shifts and evaluate the performance of existing methods on it. We know it is quite challenging for existing methods, but I would expect the authors to propose a solution (could be straightforward) for solving the problem as well, or at least provide the insights or design principles for addressing the structural distribution shifts.

Authorsrebuttal2023-08-18

Thank you for your feedback and involvement in the discussion! > … if it is possible to show the prediction/detection performance for 5% or 10% OOD data? And what would be findings? Following your suggestion, we have conducted an additional series of experiments where the ID to OOD ratio is 90% to 10%. Our findings are the following: The drop in predictive performance under the popularity-based and locality-based shifts reaches almost 7% instead of 3% in the previous setup (where we had 70% to 30% ratio) and 10% instead of 6%, respectively. This was expected and can be explained by the fact that graph models are now tested on the nodes with the most extreme structural properties (i.e., nodes with the lowest PageRank or clustering coefficient), and their inaccurate predictions are no longer compensated by the more accurate ones, which were made on the nodes with far less anomalous properties. At the same time, the performance drop on locality-based shift appears to be no more than 1% on average. This result is quite reasonable, since now graph models have access to the whole variety of graph substructures and node features, which allows them to predict equally well for any graph region regardless of its distance to some particular node. The observed effects are interesting and also important to consider when using our approach for evaluating graph models. Regarding the OOD detection performance, we observe that results on the locality-based shift keep decreasing and reach 72 points, in contrast to 78 points in the previous setup (and this might happen for the same reason as we discussed the rebuttal). At the same time, the detection metrics on the remaining structural shift appear to be nearly the same (80 points instead of the previous 81 on the popularity-based shift) or even better on average (62 points instead of 56 on the density-based shift), which is consistent with the changes in predictive performance discussed above. As for the ranking of baseline models, it remains almost the same, with the most simple methods providing top performance on the majority of prediction tasks. > … It's a bit unclear to me by saying "reducing the original node feature space into the 2D space of t-SNE representations" We apologize for causing misunderstanding in our response. In Figure 1, we have just applied t-SNE to the original node features (i.e., we did not use any supervised GNN embeddings) to visualize the distribution of multi-dimensional node features in 2D. This Figure shows that the considered structural shift not only affects the graph structure, but may also lead to a distributional shift in the node features, although the significance of this effect may vary between graph datasets. Our finding is natural, as node features and graph structure are correlated in real-world graphs. > … but I would expect the authors to propose a solution (could be straightforward) for solving the problem as well, or at least provide the insights or design principles for addressing the structural distribution shifts. Regarding your last question, we partially cover this in Section 5.3 and demonstrate that it is possible to make several simple modifications to the GNN model which help it to deal with distributional shifts. Additionally, we have conducted several experiments with data augmentation techniques that were expected to improve the performance of graph models. In particular, we tried using DropEdge or stacking the original node features with the structural node characteristics that correspond to particular distributional shifts. However, we have not achieved consistent improvements in these experiments. In summary, this is a very important question, but a principled solution to it is non-trivial and requires further investigation. We believe that our proposed method for creating distributional shifts will support studies in this area. We hope that our response answers your questions and we are open to further discussion on the raised points.

Reviewer gSyv2023-08-17

Rebuttal Acknowledgement

Thanks for the rebuttal. Part of my concerns have been addressed, I would still like to raise my score from 5 to 6. However, my concerns about the network size and potential impact still remain. In terms of network size, the large scale typically means million scales of node numbers, but the largest network used in this work is CoauthorPhysics (34493, 495924), which is far from large-scale.

Authorsrebuttal2023-08-18

Thanks for your positive feedback! Following your suggestion, we plan to conduct experiments on ogbn-products, an OGB dataset that contains more than 2M nodes, and include them in the revised version.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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