Learning to quantify graph nodes

2025-03-19

AI Summary

This paper addresses network quantification—the task of accurately estimating class proportions within unlabeled node subsets of a graph, without access to node labels, while confronting challenges including prior shift, structural heterogeneity, and scalability to large-scale graphs. Traditional post-classification counting paradigms fail in this setting, and existing methods lack sufficient flexibility and robustness. To overcome these limitations, we propose XNQ, the first unified framework for unsupervised network quantification. XNQ employs random recursive GNNs to generate efficient, label-free node embeddings and integrates a quantification-aware EM calibration mechanism to adaptively model diverse connection patterns, distributional shifts, and heterogeneous graph structures. Extensive evaluation on multi-class network quantification benchmarks demonstrates that XNQ consistently outperforms state-of-the-art methods, achieving significantly lower average quantification error. Moreover, it accelerates training by 10–100×, while maintaining high accuracy, strong robustness to distribution shifts, and linear scalability to large graphs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Network Quantification is the problem of estimating the class proportions in unlabeled subsets of graph nodes. When prior probability shift is at play, this task cannot be effectively addressed by first classifying the nodes and then counting the class predictions. In addition, unlike non-relational quantification on i.i.d. datapoints, Network Quantification demands enhanced flexibility to capture a broad range of connectivity patterns, resilience to the challenge of heterophily, and efficiency to scale to larger networks. To meet these stringent requirements we introduce XNQ, a novel method that synergizes the flexibility and efficiency of the unsupervised node embeddings computed by randomized recursive Graph Neural Networks, with an Expectation-Maximization algorithm that provides a robust quantification-aware adjustment to the output probabilities of a calibrated node classifier. We validate the design choices underpinning our method through comprehensive ablation experiments. In an extensive evaluation, we find that our approach consistently and significantly improves on the best Network Quantification methods to date, thereby setting the new state of the art for this challenging task. Simultaneously, it provides a training speed-up of up to 10x-100x over other graph learning based methods.

Problem

• Estimating class proportions in unlabeled graph nodes.
• Addressing prior probability shift in network quantification.
• Enhancing flexibility and efficiency for large-scale networks.

Innovation

• Combines unsupervised node embeddings with EM algorithm
• Uses randomized recursive Graph Neural Networks
• Achieves significant training speed-up and accuracy