Learning Latent Graph Structures and their Uncertainty

TL;DR

This paper addresses the challenge of learning latent graph structures in graph neural networks by proposing a loss function and sampling method that jointly learn the graph distribution and improve prediction accuracy.

Contribution

It introduces a theoretical framework showing proper loss functions are essential for learning latent graphs and presents a sampling-based method to achieve this joint learning task.

Findings

Proper loss functions enable learning of latent graph distributions.

Sampling-based approach improves prediction and graph learning.

Empirical results validate theoretical claims.

Abstract

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.