Learning Latent Graph Structures and their Uncertainty
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912399634726912 |
|---|---|
| author | Manenti, Alessandro Zambon, Daniele Alippi, Cesare |
| author_facet | Manenti, Alessandro Zambon, Daniele Alippi, Cesare |
| contents | Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data. Given their latent nature, no graph observations are available to provide a direct training signal to the learnable relations. Therefore, graph topologies are typically learned on the prediction task alongside the other graph neural network parameters. In this paper, we demonstrate that minimizing point-prediction losses does not guarantee proper learning of the latent relational information and its associated uncertainty. Conversely, we prove that suitable loss functions on the stochastic model outputs simultaneously grant solving two tasks: (i) learning the unknown distribution of the latent graph and (ii) achieving optimal predictions of the target variable. Finally, we propose a sampling-based method that solves this joint learning task. Empirical results validate our theoretical claims and demonstrate the effectiveness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Latent Graph Structures and their Uncertainty Manenti, Alessandro Zambon, Daniele Alippi, Cesare Machine Learning Artificial Intelligence Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data. Given their latent nature, no graph observations are available to provide a direct training signal to the learnable relations. Therefore, graph topologies are typically learned on the prediction task alongside the other graph neural network parameters. In this paper, we demonstrate that minimizing point-prediction losses does not guarantee proper learning of the latent relational information and its associated uncertainty. Conversely, we prove that suitable loss functions on the stochastic model outputs simultaneously grant solving two tasks: (i) learning the unknown distribution of the latent graph and (ii) achieving optimal predictions of the target variable. Finally, we propose a sampling-based method that solves this joint learning task. Empirical results validate our theoretical claims and demonstrate the effectiveness of the proposed approach. |
| title | Learning Latent Graph Structures and their Uncertainty |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2405.19933 |