A Few Moments Please: Scalable Graphon Learning via Moment Matching

• URL: http://arxiv.org/abs/2506.04206v1
• Date: Wed, 04 Jun 2025 17:51:01 GMT
• Title: A Few Moments Please: Scalable Graphon Learning via Moment Matching
• Authors: Reza Ramezanpour, Victor M. Tenorio, Antonio G. Marques, Ashutosh Sabharwal, Santiago Segarra,
• Abstract summary: We propose a novel, scalable graphon estimator that directly recovers the graphon via moment matching.<n>We also introduce MomentMixup, a data augmentation technique that performs mixup in the moment space to enhance graphon-based learning.
• Score: 32.65958390286061
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Graphons, as limit objects of dense graph sequences, play a central role in the statistical analysis of network data. However, existing graphon estimation methods often struggle with scalability to large networks and resolution-independent approximation, due to their reliance on estimating latent variables or costly metrics such as the Gromov-Wasserstein distance. In this work, we propose a novel, scalable graphon estimator that directly recovers the graphon via moment matching, leveraging implicit neural representations (INRs). Our approach avoids latent variable modeling by training an INR--mapping coordinates to graphon values--to match empirical subgraph counts (i.e., moments) from observed graphs. This direct estimation mechanism yields a polynomial-time solution and crucially sidesteps the combinatorial complexity of Gromov-Wasserstein optimization. Building on foundational results, we establish a theoretical guarantee: when the observed subgraph motifs sufficiently represent those of the true graphon (a condition met with sufficiently large or numerous graph samples), the estimated graphon achieves a provable upper bound in cut distance from the ground truth. Additionally, we introduce MomentMixup, a data augmentation technique that performs mixup in the moment space to enhance graphon-based learning. Our graphon estimation method achieves strong empirical performance--demonstrating high accuracy on small graphs and superior computational efficiency on large graphs--outperforming state-of-the-art scalable estimators in 75\% of benchmark settings and matching them in the remaining cases. Furthermore, MomentMixup demonstrated improved graph classification accuracy on the majority of our benchmarks.

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