Learning Latent Graph Structures and their Uncertainty
<|reference_start|>Learning Latent Graph Structures and their Uncertainty: Within a prediction task, Graph Neural Networks (GNNs) use relational information as an inductive bias to enhance the model's accuracy. As task-relevant relations might be unknown, graph structure learning approaches have been proposed to learn them while solving the downstream prediction task. In this paper, we demonstrate that minimization of a point-prediction loss function, e.g., the mean absolute error, does not guarantee proper learning of the latent relational information and its associated uncertainty. Conversely, we prove that a suitable loss function on the stochastic model outputs simultaneously grants (i) the unknown adjacency matrix latent distribution and (ii) optimal performance on the prediction task. 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.<|reference_end|>
@article{manenti2024learning,
    title={Learning Latent Graph Structures and their Uncertainty},
    author={Alessandro Manenti, Daniele Zambon, Cesare Alippi},
    journal={arXiv preprint arXiv:2405.19933},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.19933},
    primaryClass={cs.LG cs.AI stat.ML}
}