A Theory of Random Graph Shift in Truncated-Spectrum vRKHS

TL;DR

This paper develops a theoretical framework for understanding graph classification under domain shift by modeling graphs with a random graph model and analyzing the spectral properties in a vector-valued RKHS, providing insights into generalization bounds.

Contribution

It introduces a novel theory connecting random graph models, spectral analysis, and domain adaptation for graph data, with a new generalization bound involving spectral and geometric terms.

Findings

Spectral-geometry term summarized by truncated spectrum influences generalization.

Domain discrepancy and amplitude terms significantly affect model performance.

Empirical verification confirms the theoretical insights on real and simulated data.

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.