Let θ and φ denote the optimal parameters after model training. The detailed statistics of three datasets used in this paper are listed in Table 1. In this paper, when evaluating the performance in the standard experimental scenario and in the label-scarce scenario, we compare with six state-of-the-art baselines used for graph-based semisupervised learning. Three of them are deterministic GNN-based models, which are GCN [1], Graph Attention Networks(GAT)[2]andGraphSAGE[3]respectively.

Graph Neural Networks (GNNs) have achieved remarkable performance in the task of the semi-supervised node classification. However,most existing models learn a deterministic classification function, which lack sufficient flexibility to explore better choices in the presence of kinds of imperfect observed data such as the scarce labeled nodes and noisy graph structure.

Positive-Unlabeled (PU) learning aims to achieve high-accuracy binary classification with limited labeled positive examples and numerous unlabeled ones. Existing cost-sensitive-based methods often rely on strong assumptions that examples with an observed positive label were selected entirely at random. In fact, the uneven distribution of labels is prevalent in real-world PU problems, indicating that most actual positive and unlabeled data are subject to selection bias. In this paper, we propose a PU learning enhancement (PUe) algorithm based on causal inference theory, which employs normalized propensity scores and normalized inverse probability weighting (NIPW) techniques to reconstruct the loss function, thus obtaining a consistent, unbiased estimate of the classifier and enhancing the model's performance. Moreover, we investigate and propose a method for estimating propensity scores in deep learning using regularization techniques when the labeling mechanism is unknown. Our experiments on three benchmark datasets demonstrate the proposed PUe algorithm significantly improves the accuracy of classifiers on non-uniform label distribution datasets compared to advanced cost-sensitive PU methods.