# BANGS: Game-Theoretic Node Selection for Graph Self-Training

arXiv: https://arxiv.org/abs/2410.09348 · HTML: https://mlsanity.com/paper/2410.09348/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [What Makes Graph Neural Networks Miscalibrated?](https://mlsanity.com/paper/2210.06391/) (2022)
- [Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift](https://mlsanity.com/paper/2201.11349/) (2022)
- [Self-training Converts Weak Learners to Strong Learners in Mixture Models](https://mlsanity.com/paper/2106.13805/) (2021)
- [Informative Pseudo-Labeling for Graph Neural Networks with Few Labels](https://mlsanity.com/paper/2201.07951/) (2022)
- [Influence-Based Mini-Batching for Graph Neural Networks](https://mlsanity.com/paper/2212.09083/) (2022)
- [Deep Insights into Noisy Pseudo Labeling on Graph Data](https://mlsanity.com/paper/2310.01634/) (2023)
- [On Calibration of Graph Neural Networks for Node Classification](https://mlsanity.com/paper/2206.01570/) (2022)

## Built on by (most cited first, 2 of 2)

- [TestNUC: Enhancing Test-Time Computing Approaches and Scaling through Neighboring Unlabeled Data Consistency](https://mlsanity.com/paper/2502.19163/) (2025)
- [Spectral Initialization and Scheduled Graph Smoothness for Uncertain Knowledge Graph Completion](https://mlsanity.com/paper/2609.02519/) (2026)

## Abstract (arXiv)

Graph self-training is a semi-supervised learning method that iteratively selects a set of unlabeled data to retrain the underlying graph neural network (GNN) model and improve its prediction performance. While selecting highly confident nodes has proven effective for self-training, this pseudo-labeling strategy ignores the combinatorial dependencies between nodes and suffers from a local view of the distribution. To overcome these issues, we propose BANGS, a novel framework that unifies the labeling strategy with conditional mutual information as the objective of node selection. Our approach -- grounded in game theory -- selects nodes in a combinatorial fashion and provides theoretical guarantees for robustness under noisy objective. More specifically, unlike traditional methods that rank and select nodes independently, BANGS considers nodes as a collective set in the self-training process. Our method demonstrates superior performance and robustness across various datasets, base models, and hyperparameter settings, outperforming existing techniques. The codebase is available on https://github.com/fangxin-wang/BANGS .