# Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learning

arXiv: https://arxiv.org/abs/2405.19919 · HTML: https://mlsanity.com/paper/2405.19919/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 64 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 37)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Classification with Asymmetric Label Noise: Consistency and Maximal Denoising](https://mlsanity.com/paper/1303.1208/) (2013)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond](https://mlsanity.com/paper/2209.06177/) (2022)
- [Mixture Proportion Estimation and PU Learning: A Modern Approach](https://mlsanity.com/paper/2111.00980/) (2021)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications](https://mlsanity.com/paper/2106.07767/) (2021)
- [Characterizing the Influence of Graph Elements](https://mlsanity.com/paper/2210.07441/) (2022)
- [Rethinking Class-Prior Estimation for Positive-Unlabeled Learning](https://mlsanity.com/paper/2002.03673/) (2020)
- [Nonparametric semi-supervised learning of class proportions](https://mlsanity.com/paper/1601.01944/) (2016)

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

- [Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networks](https://mlsanity.com/paper/2411.02279/) (2024)
- [Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithms](https://mlsanity.com/paper/2509.24228/) (2025)

## Abstract (arXiv)

While Positive-Unlabeled (PU) learning is vital in many real-world scenarios, its application to graph data still remains under-explored. We unveil that a critical challenge for PU learning on graph lies on the edge heterophily, which directly violates the irreducibility assumption for Class-Prior Estimation (class prior is essential for building PU learning algorithms) and degenerates the latent label inference on unlabeled nodes during classifier training. In response to this challenge, we introduce a new method, named Graph PU Learning with Label Propagation Loss (GPL). Specifically, GPL considers learning from PU nodes along with an intermediate heterophily reduction, which helps mitigate the negative impact of the heterophilic structure. We formulate this procedure as a bilevel optimization that reduces heterophily in the inner loop and efficiently learns a classifier in the outer loop. Extensive experiments across a variety of datasets have shown that GPL significantly outperforms baseline methods, confirming its effectiveness and superiority.