mlsanityData to 7 Oct 2026

Characterizing the Influence of Graph Elements

arXiv 2210.07441 ↗First posted 14 Oct 2022cs.LGcited by 16

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Abstract (arXiv)

Influence function, a method from robust statistics, measures the changes of model parameters or some functions about model parameters concerning the removal or modification of training instances. It is an efficient and useful post-hoc method for studying the interpretability of machine learning models without the need for expensive model re-training. Recently, graph convolution networks (GCNs), which operate on graph data, have attracted a great deal of attention. However, there is no preceding research on the influence functions of GCNs to shed light on the effects of removing training nodes/edges from an input graph. Since the nodes/edges in a graph are interdependent in GCNs, it is challenging to derive influence functions for GCNs. To fill this gap, we started with the simple graph convolution (SGC) model that operates on an attributed graph and formulated an influence function to approximate the changes in model parameters when a node or an edge is removed from an attributed graph. Moreover, we theoretically analyzed the error bound of the estimated influence of removing an edge. We experimentally validated the accuracy and effectiveness of our influence estimation function. In addition, we showed that the influence function of an SGC model could be used to estimate the impact of removing training nodes/edges on the test performance of the SGC without re-training the model. Finally, we demonstrated how to use influence functions to guide the adversarial attacks on GCNs effectively.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 35 of its 50 references that are in the map. First posted on arXiv 14 Oct 2022.

Builds on

35 of 50 references.

References · 35

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2021Convex optimizationcited by 2,479
  6. 2017Understanding Black-box Predictions via Influence Functionscited by 1,714
  7. 2019Simplifying Graph Convolutional Networkscited by 1,470
  8. 2020LightGCN: Simplifying and Powering Graph Convolution Network for Recommendationcited by 1,134
  9. 2018Deep Graph Infomaxcited by 1,101
  10. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  11. 2018Link Prediction Based on Graph Neural Networkscited by 829
  12. 2015Gated Graph Sequence Neural Networkscited by 792
23 more
  1. 2019GNNExplainer: Generating Explanations for Graph Neural Networkscited by 735
  2. 2019Graph Neural Networks for Social Recommendationcited by 711
  3. 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 583
  4. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 395
  5. 2021On Explainability of Graph Neural Networks via Subgraph Explorationscited by 280
  6. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  7. 2020Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networkscited by 253
  8. 2020GraphLIME: Local Interpretable Model Explanations for Graph Neural Networkscited by 209
  9. 2019Topology Attack and Defense for Graph Neural Networks: An Optimization Perspectivecited by 196
  10. 2019On the Accuracy of Influence Functions for Measuring Group Effectscited by 146
  11. 2020Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functionscited by 144
  12. 2018Adversarial Attacks on Node Embeddings via Graph Poisoningcited by 109
  13. 2020Influence Function based Data Poisoning Attacks to Top-N Recommender Systemscited by 61
  14. 2018A Swiss Army Infinitesimal Jackknifecited by 51
  15. 2021Graph Robustness Benchmark: Benchmarking the Adversarial Robustness of Graph Machine Learningcited by 44
  16. 2017Learning Graph-Level Representation for Drug Discoverycited by 43
  17. 2022Achieving Fairness at No Utility Cost via Data Reweighing with Influencecited by 38
  18. 2019Less Is Better: Unweighted Data Subsampling via Influence Functioncited by 30
  19. 2018AceKG: A Large-scale Knowledge Graph for Academic Data Miningcited by 28
  20. 2021Graph-Enhanced Multi-Task Learning of Multi-Level Transition Dynamics for Session-based Recommendationcited by 18
  21. 2019Graph Neural Based End-to-end Data Association Framework for Online Multiple-Object Trackingcited by 15
  22. 2020Efficient, Direct, and Restricted Black-Box Graph Evasion Attacks to Any-Layer Graph Neural Networks via Influence Functioncited by 14
  23. 2018Help Me Find a Job: A Graph-based Approach for Job Recommendation at Scalecited by 3

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Citing papers per year: 2023: 4; 2024: 8; 2025: 4.

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  1. 2023GIF: A General Graph Unlearning Strategy via Influence Functioncited by 59
  2. 2024Dynamic Graph Unlearning: A General and Efficient Post-Processing Method via Gradient Transformationcited by 15
  3. 2024Erase then Rectify: A Training-Free Parameter Editing Approach for Cost-Effective Graph Unlearningcited by 12
  4. 2024Precedence-Constrained Winter Value for Effective Graph Data Valuationcited by 6
  5. 2024Can Graph Neural Networks Expose Training Data Properties? An Efficient Risk Assessment Approachcited by 3
  6. 2024Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learningcited by 2
  7. 2024A Cognac Shot To Forget Bad Memories: Corrective Unlearning for Graph Neural Networkscited by 2
  8. 2025Adaptive Graph Unlearningcited by 2
  9. 2025Influence Functions for Edge Edits in Non-Convex Graph Neural Networkscited by 2
  10. 2025DeGLIF for Label Noise Robust Node Classification using GNNscited by 1
  11. 2023On the Cause of Unfairness: A Training Sample Perspectivecited by 0
  12. 2023Promoting Fairness in GNNs: A Characterization of Stabilitycited by 0
4 more
  1. 2023On the Equivalence of Graph Convolution and Mixupcited by 0
  2. 2024Salutary Labeling with Zero Human Annotationcited by 0
  3. 2024Explaining Graph Neural Networks for Node Similarity on Graphscited by 0
  4. 2025GraphToxin: Reconstructing Full Unlearned Graphs from Graph Unlearningcited by 0