# HC-GST: Heterophily-aware Distribution Consistency based Graph Self-training

arXiv: https://arxiv.org/abs/2407.17787 · HTML: https://mlsanity.com/paper/2407.17787/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Rethinking Pre-training and Self-training](https://mlsanity.com/paper/2006.06882/) (2020)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Be Confident! Towards Trustworthy Graph Neural Networks via Confidence Calibration](https://mlsanity.com/paper/2109.14285/) (2021)
- [Graph Prototypical Networks for Few-shot Learning on Attributed Networks](https://mlsanity.com/paper/2006.12739/) (2020)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Debiased Self-Training for Semi-Supervised Learning](https://mlsanity.com/paper/2202.07136/) (2022)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift](https://mlsanity.com/paper/2201.11349/) (2022)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [Robust Unsupervised Domain Adaptation for Neural Networks via Moment Alignment](https://mlsanity.com/paper/1711.06114/) (2017)
- [FAITH: Few-Shot Graph Classification with Hierarchical Task Graphs](https://mlsanity.com/paper/2205.02435/) (2022)

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

- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Heterophily-Aware Adaptive Knowledge Distillation for Hypergraph Neural Networks](https://mlsanity.com/paper/2606.08978/) (2026)

## Abstract (arXiv)

Graph self-training (GST), which selects and assigns pseudo-labels to unlabeled nodes, is popular for tackling label sparsity in graphs. However, recent study on homophily graphs show that GST methods could introduce and amplify distribution shift between training and test nodes as they tend to assign pseudo-labels to nodes they are good at. As GNNs typically perform better on homophilic nodes, there could be potential shifts towards homophilic pseudo-nodes, which is underexplored. Our preliminary experiments on heterophilic graphs verify that these methods can cause shifts in homophily ratio distributions, leading to textittraining bias that improves performance on homophilic nodes while degrading it on heterophilic ones. Therefore, we study a novel problem of reducing homophily ratio distribution shifts during self-training on heterophilic graphs. A key challenge is the accurate calculation of homophily ratios and their distributions without extensive labeled data. To tackle them, we propose a novel Heterophily-aware Distribution Consistency-based Graph Self-Training (HC-GST) framework, which estimates homophily ratios using soft labels and optimizes a selection vector to align pseudo-nodes with the global homophily ratio distribution. Extensive experiments on both homophilic and heterophilic graphs show that HC-GST effectively reduces training bias and enhances self-training performance.