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REVIEW 6 major objections 4 minor 30 references

Cooperative Causal GraphSAGE

T0 review · 6 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A graph sampling scheme that combines causal effects with Shapley values to weight neighbor coalitions, improving robustness of GraphSAGE under feature perturbation.

desk verdict New combination of Shapley values and causal sampling for GraphSAGE, with promising robustness results, but the core sampling weight is not actually defined in the paper. read the letter →

arxiv 2505.14748 v1 pith:BJWCXAQK submitted 2025-05-20 cs.LG cs.GT

Zaifa Xue , Tao Zhang , Tuo Xu , Huaixin Liang , Le Gao This is my paper · ORCID
classification cs.LGcs.GT
keywords causalcooperativegraphsagenodescoca-samplingsamplinggraphneighborhood
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Graph neural networks like GraphSAGE learn by passing information between connected nodes. When a node is updated, it samples a fixed number of neighbors and averages their features. Causal GraphSAGE made the sampling smarter by estimating how strongly each neighbor causes the central node's label, then sampling the most causal neighbors. That works well, but it treats each neighbor alone, ignoring that groups of neighbors may work together to influence the label. This paper proposes treating neighbor selection as a cooperative game. Each possible group of neighbors is a coalition, and the contribution of a neighbor is measured by how much it adds to every coalition it can join, which is exactly what the Shapley value computes. The authors plug causal effect estimates into the Shapley formula, producing a cooperative causal weight for each neighbor, and sample the highest-weight neighbors. They test this on five datasets: Cora, Citeseer, Pubmed, Coauthor-CS, and ogbn-arxiv. With no perturbation, accuracy is comparable to existing methods, sometimes slightly better, sometimes slightly worse. When features are corrupted with noise, CoCa-GraphSAGE often maintains accuracy much better than baselines, especially at high noise levels. For example, on Cora with 50 percent feature perturbation, it stays near 68 percent accuracy while Causal GraphSAGE drops to about 64 percent. The paper also reports lower standard deviations across runs, suggesting more stable embeddings.
Extended reading notes

Core claim

The CoCa-sampling algorithm, which uses Shapley values over cooperative coalitions of neighborhood nodes to weight causal sampling, improves the robustness of GraphSAGE under feature perturbation while maintaining comparable clean accuracy. This is stated in the abstract: 'Experiments on publicly available datasets show that the proposed method has comparable classification performance to the compared methods and outperforms under perturbations, demonstrating the robustness improvement by CoCa-sampling.'

Load-bearing premise

The cooperative causal structure model assumes that the causal path from a neighbor node v_t to the central label y_r is confounded only by the coalition set S_r, so that conditioning on S_r satisfies the backdoor criterion and p̂(y_r | do(v_t)) is identified by p̂(y_r | v_t, S_r). This is asserted in Section III-C where they write 'this path meets the backdoor criterion.' If unobserved confounders exist, the computed cooperative causal weights are biased and the sampling is not genuinely causal.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

6 major / 4 minor

Summary. The paper proposes Cooperative Causal GraphSAGE (CoCa-GraphSAGE), which combines cooperative game theory (Shapley values) with Causal GraphSAGE to define a new neighborhood sampling rule, CoCa-sampling. The authors construct a cooperative causal structure model, compute cooperative causal weights for candidate neighbors via a Shapley-like formula, and use these weights to sample neighbors before mean aggregation. Experiments on five node classification datasets report accuracy comparable to baselines without perturbation and improved accuracy under feature perturbation, which is attributed to the robustness of CoCa-sampling.

Significance. If the method were precisely specified and reproducible, the idea of accounting for cooperative interactions among neighborhood nodes during causal sampling would be a plausible and interesting extension of Causal GraphSAGE. The reported robustness gains, e.g., roughly 5–10 percentage points over C-GraphSAGE at high perturbation ratios, are substantial and would be of practical value. However, the current manuscript does not define the core sampling algorithm in an implementable way: key quantities are undefined, the equations are internally inconsistent, and the empirical comparisons are not fully controlled. The contribution is therefore conditional on a substantial rewrite of Sections III-C and IV, plus release of code or an unambiguous algorithmic specification.

major comments (6)
  1. [Section III-C, Eqs. (5)–(8)] The quantity T appears in the factorial coefficient ((M-1)!(T-M)! / T!) in Eq. (5) and in Q_T^M in Eq. (8), but T is never defined anywhere in the manuscript. If T is intended to be the neighborhood size |N(v_r)| or the total number of players in the cooperative game, this must be stated explicitly and used consistently; otherwise Eq. (5) is not an implementable algorithm.
  2. [Section III-C, Eq. (6)] The unexplained multiplicative factor M in the second term of Eq. (6) (and later absorbed into Q_T^M in Eq. (8)) does not follow from the standard Shapley value formula, whose weights are |S|!(n-|S|-1)!/n! for a coalition of size |S|. The authors should justify why only coalitions of size M-1 are considered and why the weight includes an extra factor of M; as written, the formula is not derived from Eq. (2) or Eq. (4).
  3. [Section III-C, Eq. (7) and Algorithm 1] The object summed in Eq. (7), p̂(y_r | v_t, S_r) - p̂(y_r | S_r), does not match the marginal contribution φ(S_r) defined in Eq. (4), which is the difference between causal weights with and without v_t in the coalition. Consequently, the cooperative causal weight E(v_t) computed in Algorithm 1, line 6, is ill-defined, and the reported sampling rule cannot be reproduced from the equations given.
  4. [Section III-C, Eq. (3) and text after Eq. (3)] The paper states that p̂ denotes a kernel density estimate, but no kernel, bandwidth, or estimation procedure is provided. Since all cooperative causal weights in Eqs. (5)–(7) depend on p̂(y_r | v_t, S_r), the method cannot be implemented or evaluated by others without this information; please specify the estimator and any hyperparameters (e.g., bandwidth selection) used in the experiments.
  5. [Section III-C, backdoor criterion] The assertion that the path v_t ← S_r → y_r 'meets the backdoor criterion' presupposes that the coalition set S_r contains all confounders of v_t and y_r. This is a strong structural assumption that is not justified by the graph in Fig. 3. If unobserved confounders exist, the quantity estimated by Eq. (3) is a conditional association, not a causal effect, and the claim that the sampling is 'genuinely causal' would not hold. The authors should state this assumption explicitly and discuss its plausibility for the datasets used.
  6. [Section IV-A and Tables III–VII] The empirical comparison is not fully controlled: C-GraphSAGE is run with sampling numbers (25, 10) for its two layers, whereas CoCa-GraphSAGE uses (10, 10), so the robustness differences could partly reflect the number of samples rather than the sampling rule. Moreover, no code or data splits are provided, and no statistical significance tests are reported. Given that the central claim is empirical robustness improvement, the paper should include these details or release code to allow verification.
minor comments (4)
  1. [Section IV-A, Table I] The statistics of the Coauthor-CS and ogbn-arxiv datasets are missing from Table I; the table only lists Cora, Citeseer, and Pubmed, even though five datasets are used.
  2. [Section IV-A, Tables VI and VII] The results for RL-GraphSAGE, GCNSS, and RN-GLVNMR are omitted for Coauthor-CS and ogbn-arxiv, so the comparison on those datasets is incomplete relative to the other three datasets.
  3. [Section III-C] There are typos and garbled equations throughout the section (e.g., 'Shapely' instead of 'Shapley', and the OCR of Eqs. (3)–(7) appears corrupted); the authors should carefully proofread the manuscript and ensure all equations are typeset correctly.
  4. [Section IV-A, perturbation description] The description of Bernoulli-matrix XOR perturbation for the citation datasets is too brief; please specify how the perturbation matrix is generated, how it interacts with the features, and what fraction of the feature entries are modified.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the robustness claim is an empirical result, and the cited Causal GraphSAGE formula is independently benchmarked here.

full rationale

The claimed derivation chain is: construct a cooperative causal graph (Section III-B); compute coalition causal weights with Eq. (3); form Shapley-style marginal contributions via Eqs. (4)-(8); sample neighborhoods in Algorithm 1; aggregate with Eq. (9); train with Eq. (11). The final claim is an experimental one: CoCa-GraphSAGE 'outperforms under perturbations,' and it is supported by reported test accuracies in Tables II-VII against GCN, GAT, GraphSAGE, C-GraphSAGE, and others. No equation in this chain defines the predicted accuracy to be equal to the fitted p-hat or to a cooperative causal weight; the weights are intermediate quantities used for sampling, and accuracy is an independent evaluation metric. The only self-citation is reference [13] (Causal GraphSAGE), co-authored by T. Zhang, which supplies Eq. (1) as the base causal weight; however, C-GraphSAGE is also re-run as a baseline in the present experiments, so the citation is not the sole evidence for the method's behavior. The paper's real weaknesses are non-circular: T is never defined in Eqs. (5)-(8), the factor M and the set S_r^- are unexplained, the kernel density estimator for p-hat is unspecified, and the assertion that the path 'meets the backdoor criterion' is an unproven modeling assumption. These are correctness and reproducibility risks, not a reduction of the output to the input by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 1 invented entities

The central claim rests on a data-driven sampling weight that depends on hand-picked hyperparameters (M, KDE bandwidth) and on causal identification assumptions that are asserted but not verified. The fixed-size Shapley approximation is an ad hoc modeling choice rather than a derived result.

free parameters (2)
  • M (sampling number per layer) = 10, 10 (first and second layer)
    Chosen 'according to experimental experience' in Section IV-A. Figure 10 shows accuracy and runtime depend on M, so the robustness claim is tied to this hand-picked value.
  • Kernel density estimate bandwidth
    The kernel density estimates p̂ in Eq. (3) require a bandwidth and estimator choice. The paper never specifies these, so the causal weights are not fully determined and reproducibility suffers.
assumptions (3)
  • domain assumption Backdoor criterion holds for the cooperative causal graph in Fig. 3.
    Stated in Section III-C: 'this path meets the backdoor criterion.' If unobserved confounding exists, the causal weights are not identified.
  • ad hoc to paper Fixed-size Shapley value over coalitions of size M-1 is a valid measure of cooperative contribution.
    Eqs. (5)-(8) restrict coalitions to |S|=M-1 and multiply the standard Shapley weight by M, without derivation or justification. The full Shapley value over all coalition sizes is not used.
  • domain assumption Kernel density estimates p̂ are unbiased estimates of the causal conditional probabilities.
    Eq. (3) uses p̂; the estimator and its consistency are not described in the paper, so the causal weights are not grounded in a stated statistical methodology.
invented entities (1)
  • Cooperative causal weight E(v_t)
    purpose: Score for sampling neighborhood nodes in CoCa-sampling; combines the causal weight of a node with Shapley-weighted marginal contributions over coalitions.
    This quantity is new to this paper and is not validated outside the context of the proposed method. No independent test of its causal meaning is provided, and it is not tied to external benchmarks.

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Pith. "Pith review of Cooperative Causal GraphSAGE." pith.science (2026). https://pith.science/paper/BJWCXAQK

@misc{pith2026250514748,
  author       = {Pith},
  title        = {Pith review of: Cooperative Causal GraphSAGE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BJWCXAQK}},
  note         = {Machine review of arXiv:2505.14748}
}
read the original abstract

GraphSAGE is a widely used graph neural network. The introduction of causal inference has improved its robust performance and named as Causal GraphSAGE. However, Causal GraphSAGE focuses on measuring causal weighting among individual nodes, but neglecting the cooperative relationships among sampling nodes as a whole. To address this issue, this paper proposes Cooperative Causal GraphSAGE (CoCa-GraphSAGE), which combines cooperative game theory with Causal GraphSAGE. Initially, a cooperative causal structure model is constructed in the case of cooperation based on the graph structure. Subsequently, Cooperative Causal sampling (CoCa-sampling) algorithm is proposed, employing the Shapley values to calculate the cooperative contribution based on causal weights of the nodes sets. CoCa-sampling guides the selection of nodes with significant cooperative causal effects during the neighborhood sampling process, thus integrating the selected neighborhood features under cooperative relationships, which takes the sampled nodes as a whole and generates more stable target node embeddings. Experiments on publicly available datasets show that the proposed method has comparable classification performance to the compared methods and outperforms under perturbations, demonstrating the robustness improvement by CoCa-sampling.

Figures

Figures reproduced from arXiv: 2505.14748 by the authors.

Figure 1
Figure 1. The abstract causal graph underlying C-GraphSAGE. causal diagram of Fig.1, the relationship ii v U y  → satisfies the backdoor criterion. When n v = i v and n y = i y , the causal weight can be obtained according to the causal sampling principle, as shown in (1). ( ( )) 1 |= ˆ( | ) ii i p y do v Np v U (1) Where p ˆ represents the estimate of p . In the causal sampling phase, for all candidate neighbors, their caus… view at source ↗
Figure 3
Figure 3. The cooperative causal structure graph of CoCa￾GraphSAGE. (a)The causality between neighborhood nodes and labels. (b)The causality between sampling sets and labels. (c)The causality between nodes. Before sampling, all nodes in the neighborhood node set are alternative nodes, which act as components of players to form a gaming coalition to participate in the cooperative gaming process. For the node r v in the graph a… view at source ↗
Figure 2
Figure 2. The framework of CoCa-GraphSAGE on first-order neighbor nodes. The neighborhood node weights in CoCa-sampling are obtained as shown on the top. Different neighborhood nodes are distinguished by different colors, and different rectangle lengths represent the sampling weights of neighborhood nodes in CoCa-sampling. rr = v , there is still a causal path rr → y in the causal model, as shown by the orange line on the rig… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The cooperative causal model considering the influence of perturbations. (a) Cooperative causal model considering perturbations. (b) Simplified cooperative causal model. C. Cooperative Causal Sampling Algorithm Here, the case without perturbation is taken as an example…
Figure 5
Figure 5. Figure 5: Classification performance on Cora dataset with perturbation. (a) Test data perturbed, Train data perturbed, (b) Test data non perturbed, (c) Train data non perturbed [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 10
Figure 10. Figure 10: The accuracy and running time of a single epoch under different number of sampling nodes in Cora dataset. However, as the amount of data increases, the gradient of the curve representing the accuracy in the graph gradually decreases especially after the number of samp…

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