A Generative Model for Controllable Feature Heterophily in Graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911181489307648 |
|---|---|
| author | Wang, Haoyu Ma, Renyuan Mateos, Gonzalo Ruiz, Luana |
| author_facet | Wang, Haoyu Ma, Renyuan Mateos, Gonzalo Ruiz, Luana |
| contents | We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of the feature heterophily measure to a deterministic functional of the graphon degree profile, based on a graphon-limit law for polynomial averages of Laplacian eigenvalues. These results elucidate how the interplay between the graphon and the filter governs the limiting level of feature heterophily, providing a tunable mechanism for data modeling and generation. We validate the theory through experiments demonstrating precise control of homophily across graph families and spectral filters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generative Model for Controllable Feature Heterophily in Graphs Wang, Haoyu Ma, Renyuan Mateos, Gonzalo Ruiz, Luana Machine Learning Signal Processing We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based random graph generator with Gaussian node features filtered through a smooth spectral function of the rescaled Laplacian. We establish new theoretical guarantees: (i) a concentration result for the empirical heterophily score; and (ii) almost-sure convergence of the feature heterophily measure to a deterministic functional of the graphon degree profile, based on a graphon-limit law for polynomial averages of Laplacian eigenvalues. These results elucidate how the interplay between the graphon and the filter governs the limiting level of feature heterophily, providing a tunable mechanism for data modeling and generation. We validate the theory through experiments demonstrating precise control of homophily across graph families and spectral filters. |
| title | A Generative Model for Controllable Feature Heterophily in Graphs |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2509.23230 |