# Semi-supervised Node Importance Estimation with Informative Distribution Modeling for Uncertainty Regularization

arXiv: https://arxiv.org/abs/2503.20697 · HTML: https://mlsanity.com/paper/2503.20697/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 26 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Label Propagation for Deep Semi-supervised Learning](https://mlsanity.com/paper/1904.04717/) (2019)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Benchmarking Multimodal Retrieval Augmented Generation with Dynamic VQA Dataset and Self-adaptive Planning Agent](https://mlsanity.com/paper/2411.02937/) (2024)
- [EcomGPT: Instruction-tuning Large Language Models with Chain-of-Task Tasks for E-commerce](https://mlsanity.com/paper/2308.06966/) (2023)
- [Estimating Node Importance in Knowledge Graphs Using Graph Neural Networks](https://mlsanity.com/paper/1905.08865/) (2019)
- [Recent Advances of Multimodal Continual Learning: A Comprehensive Survey](https://mlsanity.com/paper/2410.05352/) (2024)
- [Meta Propagation Networks for Graph Few-shot Semi-supervised Learning](https://mlsanity.com/paper/2112.09810/) (2021)
- [Semi-Supervised Deep Regression with Uncertainty Consistency and Variational Model Ensembling via Bayesian Neural Networks](https://mlsanity.com/paper/2302.07579/) (2023)
- [Deep Structural Knowledge Exploitation and Synergy for Estimating Node Importance Value on Heterogeneous Information Networks](https://mlsanity.com/paper/2402.12411/) (2024)
- [Semi-Supervised Heterogeneous Graph Learning with Multi-level Data Augmentation](https://mlsanity.com/paper/2212.00024/) (2022)
- [Node Importance Estimation Leveraging LLMs for Semantic Augmentation in Knowledge Graphs](https://mlsanity.com/paper/2412.00478/) (2024)

## Built on by (most cited first, 4 of 4)

- [DP-DGAD: A Generalist Dynamic Graph Anomaly Detector with Dynamic Prototypes](https://mlsanity.com/paper/2508.00664/) (2025)
- [PINE: Pipeline for Important Node Exploration in Attributed Networks](https://mlsanity.com/paper/2512.07244/) (2025)
- [Explaining Synergistic Effects in Social Recommendations](https://mlsanity.com/paper/2601.18151/) (2026)
- [Online Test-Time Adaptation for Generalizable Dynamic Graph Anomaly Detection](https://mlsanity.com/paper/2608.19858/) (2026)

## Abstract (arXiv)

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 via https://github.com/yankai-chen/EASING.