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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.23880 |
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| _version_ | 1866914357491793920 |
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| author | Wan, Zhang Mu, Tingting Kaski, Samuel |
| author_facet | Wan, Zhang Mu, Tingting Kaski, Samuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23880 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Theory of Random Graph Shift in Truncated-Spectrum vRKHS Wan, Zhang Mu, Tingting Kaski, Samuel Machine Learning 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. |
| title | A Theory of Random Graph Shift in Truncated-Spectrum vRKHS |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.23880 |