Learning Latent Graph Structures and their Uncertainty

Alessandro Manenti, Daniele Zambon, Cesare Alippi

Keywords: Graph Structure Learning, GNNs, Latent Distribution Calibration, Discrete Random Variables, Maximum Mean Discrepancy

Abstract:

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.

Submission Number: 74