A Theory of Random Graph Shift in Truncated-Spectrum vRKHS

2026-02-27

AI Summary

This work addresses the domain shift problem in graph classification caused by variations in random graph model (RGM) components, a challenge inadequately handled by existing methods due to their lack of fine-grained characterization of structural distribution shifts. For the first time, we formally incorporate the RGM as the generative mechanism of graph data into domain shift theory. From this generative perspective, we develop an analytical framework grounded in vector-valued reproducing kernel Hilbert spaces (vRKHS) and derive a decomposable generalization bound that jointly captures the influence of domain discrepancy, spectral geometry, and amplitude terms on domain shift. Through truncated spectral analysis and rigorous derivation of the generalization bound, we validate the individual contributions of these factors on both real-world and synthetic datasets, offering both theoretical foundations and practical guidance for graph domain adaptation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• 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 neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

This paper develops a theory of graph classification under domain shift through a random-graph generative lens, where we consider intra-class graphs sharing the same random graph model (RGM) and the domain shift induced by changes in RGM components. While classic domain adaptation (DA) theories have well-underpinned existing techniques to handle graph distribution shift, the information of graph samples, which are itself structured objects, is less explored. The non-Euclidean nature of graphs and specialized architectures for graph learning further complicate a fine-grained analysis of graph distribution shifts. In this paper, we propose a theory that assumes RGM as the data generative process, exploiting its connection to hypothesis complexity in function space perspective for such fine-grained analysis. Building on a vector-valued reproducing kernel Hilbert space (vRKHS) formulation, we derive a generalization bound whose shift penalty admits a factorization into (i) a domain discrepancy term, (ii) a spectral-geometry term summarized by the accessible truncated spectrum, and (iii) an amplitude term that aggregates convergence and construction-stability effects. We empirically verify the insights on these terms in both real data and simulations.

Problem

• graph classification
• domain shift
• random graph model
• distribution shift
• non-Euclidean data

Innovation

• random graph model
• domain shift
• vector-valued RKHS
• truncated spectrum
• graph classification