Enhancing Graph Invariant Learning from a Negative Inference Perspective

• This paper claims that current methods fail to address complex environments when tested with double the scale of spurious substructures. More detailed experiments, including explanations of the datasets and settings, are needed to demonstrate how NeGo outperforms the baselines in addressing this issue. However, the paper only presents two results for NeGo.
• In the experiments, this paper only presents the causal subgraphs extracted by NeGo. To allow for better comparison, it should also include the causal subgraphs extracted by the baseline methods.
• There are some methods like [1] that also considers the environment inference. What is the difference between this paper and those papers considering environments.
• Why GOOD-PCBA in GOOD[2] is not tested?

[1] Learning Invariant Graph Representations for Out-of-Distribution Generalization. NeurIPS2023

[2] Good: A graph out-of-distribution benchmark. NeurIPS2022

1. in section 3.2 you give the theorem about the negative inference in equation 3, but I do not understand what you mean by the negative inference, it is related to the causal subgraph $G_c$ or the spurious subgraph $G_s$?

What does equation 3 means and the following theorem mean?

Furthermore, it seems that in CIGA and GALA, they have given the expression of this equation by constraining the mutual information of the $G_s$, what is the difference between yours and their claims?

2. since the paper has a lot of equations, the meaning of the equations is not explained very well.

• In equation 3, what dose the $\overline{Y}$ means? I am sorry that I can not find the definition before the equation or have I missed some details?
• In equation 6, there is a typo in the $\mathcal{L}_{nega}$.

1. In lines 47-53, the term "complex environments" requires clarification. In the provided example, the decline in test performance is primarily attributed to size shift, a well-recognized challenge. I disagree with the authors' attribution that this decline is due to the emphasis of current methods on extracting causal subgraphs.

2. The statement in lines 135-136, "Our approach, which represents a pioneering practice in utilizing negative inference, is distinct from all existing practices in this field," is inaccurate. EQuAD [1] also employs a similar paradigm that first learns spurious features before learning invariant features. This work, however, does not discuss or compare with EQuAD.

3. In Section 3, the core idea of mixing various environments can be interpreted as environment interpolation. However, the linear environment mixing via latent variable $e$ may prove ineffective in managing extrapolated (unseen) environments. The claim in lines 233-235, "However, we observe that such a goal cannot be achieved by existing methods," is inaccurate; previous works, such as AIA [2] and GraphSplice [3], address environment extrapolation and may offer a more effective alternative to environment interpolation.

4. The objective in Equation 4 appears unusual. Specifically, minimizing the KL divergence using $P(\bar{Y})$: it is unclear how utilizing the label distribution of extra-class samples facilitates accurate environment inference, as they appear unrelated to me.

5. In the experimental section, the authors should analyze whether the negative prompter can truly learn embeddings in $A_N$ that accurately capture spurious patterns.

6. The authors claim that the proposed method can resolve both PIIF and FIIF, regardless of the correlation strengths of $I(G_s;Y)$. However, the experiments are limited to the FIIF case, e.g.,GOODMotif, and all datasets assume $H(G_c;Y) < H(G_s;Y)$. Additional experiments on synthetic datasets are necessary to support this theoretical statement.

7. The EQuAD method also employs a similar learning paradigm by leveraging spurious features for disentanglement to facilitate invariant feature learning. The authors should discuss and compare their approach with EQuAD. Furthermore, AIA and GraphSplice also aim to "broaden the inference space of environments" (line 71). A discussion or comparison with these methods is warranted.

References

1. Yao et al., Empowering Graph Invariance Learning with Deep Spurious Infomax, ICML2024
2. Sui et al., Unleashing the power of graph data augmentation on covariate distribution shift, NeurIPS 2023
3. Li et al., Graph Structure Extrapolation for Out-of-Distribution Generalization, ICML2024

1. Although the motivation is clear to me, the novelty is one of my concerns since the environment-enhance strategies for graph OOD problem seems to be relatively not new. I think the authors could address my concern by presenting more difference with related works clearly.
2. There are a lot of works that study graph OOD in the survey (Out-Of-Distribution Generalization on Graphs: A Survey). The authors should include them in the discussions in the related works, and choose some representative methods for comparisons in the experiments.
3. The theorems are present informally. I suggest the authors use formal math language rather than current imprecise expression, especially for the key concepts (including but not limited to “broader cognitive space”, “G_C can be extracted”, etc.) in the theorems.