Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.26533 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909921245659136 |
|---|---|
| author | Weihs, Adrien Bertozzi, Andrea L. Thorpe, Matthew |
| author_facet | Weihs, Adrien Bertozzi, Andrea L. Thorpe, Matthew |
| contents | Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure. Prior work established the well- and ill-posedness of HOHL through an asymptotic consistency analysis in geometric settings. We extend this theoretical foundation by proving the consistency of a truncated version of HOHL and deriving explicit convergence rates when HOHL is used as a regularizer in fully supervised learning. We further demonstrate its strong empirical performance in active learning and in datasets lacking an underlying geometric structure, highlighting HOHL's versatility and robustness across diverse learning settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-Order Regularization Learning on Hypergraphs Weihs, Adrien Bertozzi, Andrea L. Thorpe, Matthew Machine Learning Statistics Theory Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure. Prior work established the well- and ill-posedness of HOHL through an asymptotic consistency analysis in geometric settings. We extend this theoretical foundation by proving the consistency of a truncated version of HOHL and deriving explicit convergence rates when HOHL is used as a regularizer in fully supervised learning. We further demonstrate its strong empirical performance in active learning and in datasets lacking an underlying geometric structure, highlighting HOHL's versatility and robustness across diverse learning settings. |
| title | Higher-Order Regularization Learning on Hypergraphs |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2510.26533 |