Title: Unveiling Environmental Sensitivity of Individual Gains in Influence Maximization
Venue: NeurIPS 2025
Accepted: yes
Keywords: influence maximization; causal inference; social networks
Abstract: Influence Maximization (IM) seeks a seed set to maximize information dissemination in a network. Elegant IM algorithms could naturally extend to cases where each node is equipped with a specific weight, reflecting individual gains to measure its importance. In prevailing literature, these gains are typically assumed to remain constant throughout diffusion and are solvable through explicit formulas based on node characteristics and network topology. However, this assumption is not always feasible due to two key challenges: 1) \textit{Unobservability}: The individual gains of each node are primarily evaluated by the difference between the outputs in the activated and non-activated states. In practice, we can only observe one of these states, with the other remaining unobservable post-propagation. 2) \textit{Environmental sensitivity}: Beyond nodes’ inherent properties, individual gains are also sensitive to the activation status of surrounding nodes, which change dynamically during propagation even when the network topology is fixed. To address these uncertainties, we introduce a Causal Influence Maximization (CauIM) framework, leveraging causal inference techniques to model dynamic individual gains. We propose two algorithms, G-CauIM and A-CauIM, where the latter incorporates a novel acceleration technique. Theoretically, we establish the generalized lower bound of influence spread and provide robustness analysis. Empirically, experiments on synthetic and real-world datasets validate the effectiveness and reliability of our approach.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript investigates influence maximization (IM) algorithms in the setting where individuals receive inconstant gains throughout the diffusion process. To address the challenges arising from unobservability and environmental sensitivity, the authors propose two algorithms, CauIM and A-CauIM. They validate their methods using both synthetic and real-world networks, demonstrating the algorithms’ effectiveness.\n\nSTRENGTHS AND WEAKNESSES:\nThe study presents a reasonable approach to tackle the IM problem, and the proposed methods address several practical challenges. This work could offer meaningful contributions to the IM literature for two main reasons:\n•\tThe authors attempt to confront multiple real-world challenges in IM, providing valuable inspiration for potential future research;\n•\tThe illustrations in Figure 1 highlight two difficulties encountered in networks, encouraging readers to reflect on practical demands from industry.\nHowever, the manuscript would benefit from stronger empirical support to convincingly demonstrate the effectiveness of the proposed methods. Some aspects of the study design also require further consideration. For instance, the hypergraph construction relies on data from a specific time window, which may be better understood as a temporal hypergraph, especially in datasets like GoodReads and Email-Eu.\nThe manuscript is generally well-written, with a clearly defined problem and well-stated assumptions. Nonetheless, there are still a few typographical and formatting issues—for example, Section/Appendix is missing in Line 163.\n\nQUESTIONS:\n1.\tWhat precisely does the ‘environment information’ T_{-i} in Eq. 1 represent? Does it refer to the states of neighboring nodes or to the external context?\n2.\tHow do the authors guarantee that the proposed algorithms converge to an optimal solution? Can the resulting node sets truly be regarded as those with maximal influence?\n3.\tThe datasets used are relatively small in size, and the simulations are limited in the number of trials. This raises concerns about the generalizability and robustness of the proposed methods.\n4.\tThe baseline comparison is conducted using a basic greedy algorithm, which is somewhat outdated relative to current IM literature. Given the maturity of IM research, it is not clear how the proposed methods improve upon or outperform existing state-of-the-art techniques.\n\nLIMITATIONS:\nThe manuscript does not explicitly discuss limitations or societal impacts. The authors should consider the broader implications of their work, particularly regarding its potential influence on recommender systems in online marketplaces and social media platforms. Furthermore, the limitations of the proposed approach should be clearly acknowledged, along with suggestions for future improvements.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a Causal Influence Maximization (CauIM) framework to address the challenges of unobservability and environmental sensitivity in modeling individual gains during influence propagation. Unlike traditional IM methods that assume static node gains, CauIM leverages causal inference to estimate Individual Treatment Effects (ITE). Two algorithms, G-CauIM and its accelerated variant A-CauIM, are introduced. Theoretical analysis establishes a generalized lower bound and robustness guarantees, while empirical results on synthetic and real-world datasets show the effectiveness of the proposed approach.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths \n1. The CauIM framework captures dynamic and context-dependent individual gains.\n2. The proposed framework is theoretically grounded, with formal guarantees on influence spread and robustness under uncertain and dynamic conditions.\n3. The proposed algorithms achieve good empirical performance on synthetic and real-world networks.\n\nWeaknesses\n1. The methodology for estimating ITE is not clearly presented, and the experimental or theoretical validation of its effectiveness is insufficient.\n2. The explanation of Figure 1 lacks clarity. Specifically, the figure does not provide a concise overview of the initial network structure with different groups, making it challenging for readers to fully grasp the illustration.\n\nQUESTIONS:\n1. What exactly do the dynamic characteristics of ITE refer to in this context? The concept needs further clarification.\n2. The consistency assumption states that potential outcomes are deterministic, which is confusing given the earlier statement that outcomes are also influenced by the attitudes of social contacts. This apparent contradiction needs to be addressed.\n3. The setup for ITE estimation is unclear. Details about the neural network architecture and configuration used, the required sample size, computational overhead, and prediction accuracy should be provided to better understand the approach’s feasibility and effectiveness.\n\nLIMITATIONS:\nIt is recommended to discuss the sample requirements and computational cost required for ITE estimation.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies the Influence Maximization (IM) problem. Motivated by the limitations of unobservability and environmental sensitivity in previous work, it proposes a Causal Influence Maximization (CauIM) framework that leverages causal inference techniques to model dynamic individual gains. Two algorithms, G-CauIM and A-CauIM, are introduced to solve the problem. The paper provides both theoretical analysis and empirical results to evaluate the performance of the proposed methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nS1. Influence Maximization (IM) is an important and well-established research topic. The weighted IM setting studied in this paper is relatively novel and has potential real-world applications. Overall, the paper is well motivated.\n\nS2. Instead of following traditional approaches to the IM problem, the paper proposes leveraging causal inference techniques. This alternative perspective may provide new insights to the community.\n\nS3. The paper presents both theoretical and empirical analyses to evaluate the proposed methods. Most of the key concepts are well explained.\n\nS4. The paper is generally well written and easy to follow.\n\n\n\nWeaknesses and Questions:\n\nW1. This and the next point are more questions than criticisms. IM has a long research history, and the paper briefly mentions related methods in Section 5. However, in the experimental section, the comparison is limited to the basic greedy algorithm. Could the authors clarify why existing methods for standard IM cannot be extended to the weighted IM setting?\n\nAdditionally, some dynamic IM methods seem to be missing from the related work. One example is:\n\nBinghui Peng, Dynamic Influence Maximization, NeurIPS 2021.\n\nAs a suggestion, the related work section would benefit from being more comprehensive and placed earlier in the paper. The current version is brief and appears rather late.\n\nW2. The paper analyzes the approximation error of the proposed methods, but it would also be valuable to provide a meaningful upper bound on their time complexity. In addition, the size of the datasets used in the experiments should be clearly stated.\n\nW3. The idea of applying causal inference to IM is interesting, but the necessity of using such complex methods is still questionable to me, especially considering that the basic IM problem is already quite challenging. Moreover, in the more complex weighted IM setting, there appear to be very few baselines to compare against (as far as the paper shows), making it harder to evaluate the effectiveness of the proposed methods.\n\nW4. Although the writing is generally good, there is still room for improvement. For instance, the theoretical results presented in Section 3.3 would benefit from a high-level explanation to help non-expert readers understand the key ideas.\n\nQUESTIONS:\nI’ve described my questions in the “Weaknesses” section above. Please refer to that for details.\n\nLIMITATIONS:\nThere is not much concern about the potential negative societal impact of this paper.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}

comments: SUMMARY:
This paper introduces Causal Influence Maximization (CauIM), a framework that integrates causal inference into the influence maximization (IM) problem on hypergraphs. It addresses two key challenges in weighted IM:

1. Unobservability of individual gains (i.e., counterfactual outcomes).
2. Environmental sensitivity—individual gains depend on the dynamic activation status of neighboring nodes.

To tackle these, the authors propose two algorithms:

1. G-CauIM: A greedy-based method.
2. A-CauIM: An accelerated version using differentiable approximations.

They provide theoretical guarantees and empirical validation on synthetic and real-world datasets.

STRENGTHS AND WEAKNESSES:
**Strengths:**

1. The problem is interesting.
2. The theoretical results are good. However, I did not check the math in great detail.

**Weaknesses:**

1. I am not sure if causality is well-studied in the given context. There is no clear discussion on confounders, mediators, and other related concepts.
2. The paper is dense, especially in the methodology section. Readers unfamiliar with causal inference or hypergraphs may struggle.
3. The representation learning and MLP steps look tedious and unnecessary. I think there might be an easier way. For instance, using a simpler encoder and a smaller model to recover the individual ITE from observational data.
4. Is the hypergraph you are referring to the reverse influence sampling-like hypergraph?
5. The paper assumes that ITE can be reliably estimated from observational data, which may not hold in sparse or noisy networks.
6. Assumptions like bounded ITE and environmental independence are strong and not empirically tested.

QUESTIONS:
Refer to the weaknesses.

LIMITATIONS:
Refer to the weaknesses.
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-03