Quantifying predictive uncertainty of neural networks has recently attracted increasing attention. In this work, we focus on measuring uncertainty of graph neural networks (GNNs) for the task of node classification. Most existing GNNs model message passing among nodes. The messages are often deterministic. Questions naturally arise: Does there exist uncertainty in the messages? How could we propagate such uncertainty over a graph together with messages? To address these issues, we propose a Bayesian uncertainty propagation (BUP) method, which embeds GNNs in a Bayesian modeling framework, and models predictive uncertainty of node classification with Bayesian confidence of predictive probability and uncertainty of messages. Our method proposes a novel uncertainty propagation mechanism inspired by Gaussian models. Moreover, we present an uncertainty oriented loss for node classification that allows the GNNs to clearly integrate predictive uncertainty in learning procedure. Consequently, the training examples with large predictive uncertainty will be penalized. We demonstrate the BUP with respect to prediction reliability and out-of-distribution (OOD) predictions. The learned uncertainty is also analyzed in depth. The relations between uncertainty and graph topology, as well as predictive uncertainty in the OOD cases are investigated with extensive experiments. The empirical results with popular benchmark datasets demonstrate the superior performance of the proposed method.

Abstract The problem of adaptive learning from evolving and possibly non-stationary data streams has attracted a lot of interest in machine learning in the recent past, and also stimulated research in related fields, such as computational intelligence and fuzzy systems. In particular, several rule-based methods for the incremental induction of regression models have been proposed. In this paper, we develop a method that combines the strengths of two existing approaches rooted in different learning paradigms. More concretely, our method adopts basic principles of the state-of-the-art learning algorithm AMRules and enriches them by the representational advantages of fuzzy rules. In a comprehensive experimental study, TSK-Streams is shown to be highly competitive in terms of performance.