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

TL;DR

Unlike traditional methods that rank and select nodes independently, BANGS considers nodes as a collective set in the self-training process, demonstrating superior performance and robustness across various datasets, base models, and hyperparameter settings, outperforming existing techniques.

Abstract

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 .

Figures (4)

• Figure 1: The workflow of Bangs. We utilize the teacher model's predictions to propagate features from both labeled nodes and candidate set ${\mathbb{S}}$, estimating the logits of unlabeled nodes and the Banzhaf value of set ${\mathbb{S}}$ (Equation \ref{['eq: banz']}). For simplicity, only the first step of feature propagation is shown. Using Banzhaf values we rank the individual contributions of unlabeled nodes and add the top $k$ into the pseudo-label set. The student model is subsequently retrained using this updated set.
• Figure 2: Plots of hyperparameter and robustness analysis on Cora dataset. Our method retains the validity and superiority over baselines under different settings and hyperparameters.
• Figure 3: Pipeline of Bangs
• Figure 4: The test accuracy of PubMed data with different node selection criteria in self-training iteration with 40 rounds. In each round, 100 nodes are selected to pseudo-label. Our method with confidence calibration outperforms others.

Theorems & Definitions (12)

• Lemma 2.1
• Definition 3.1: Feature influence distribution
• Theorem 3.1: Feature influence computation via random walk
• Definition 3.2: Output feature estimation with propagation
• Definition 3.3: k-Bounded Banzhaf value
• Theorem 3.2
• proof
• Lemma B.1
• proof
• Lemma B.2