Node importance estimation, a classical problem in network analysis, underpins various web applications. Previous methods either exploit intrinsic topological characteristics, e.g., graph centrality, or leverage additional information, e.g., data heterogeneity, for node feature enhancement. However, these methods follow the supervised learning setting, overlooking the fact that ground-truth node-importance data are usually partially labeled in practice. In this work, we propose the first semi-supervised node importance estimation framework, i.e., EASING, to improve learning quality for unlabeled data in heterogeneous graphs. Different from previous approaches, EASING explicitly captures uncertainty to reflect the confidence of model predictions. To jointly estimate the importance values and uncertainties, EASING incorporates DJE, a deep encoder-decoder neural architecture. DJE introduces distribution modeling for graph nodes, where the distribution representations derive both importance and uncertainty estimates. Additionally, DJE facilitates effective pseudo-label generation for the unlabeled data to enrich the training samples. Based on labeled and pseudo-labeled data, EASING develops effective semi-supervised heteroscedastic learning with varying node uncertainty regularization. Extensive experiments on three real-world datasets highlight the superior performance of EASING compared to competing methods. Codes are available viathis https URL.
View on arXiv@article{chen2025_2503.20697,
title={ Semi-supervised Node Importance Estimation with Informative Distribution Modeling for Uncertainty Regularization },
author={ Yankai Chen and Taotao Wang and Yixiang Fang and Yunyu Xiao },
journal={arXiv preprint arXiv:2503.20697},
year={ 2025 }
}