GPN applies a personalized page rank (PPR) module to diffuse the evidence among neighboring nodes.

Inmost meta-learning methods, tasks areimplicitly related bysharing parameters oroptimizer. We develop a novel meta-learner of this type for prototype based classification, in which a prototype is generated for each class, such that the nearest neighbor search among the prototypes produces an accurate classification.

Meta-learning extracts the common knowledge from learning different tasks and uses it for unseen tasks. It can significantly improve tasks that suffer from insufficient training data, e.g., few-shot learning. In most meta-learning methods, tasks are implicitly related by sharing parameters or optimizer. In this paper, we show that a meta-learner that explicitly relates tasks on a graph describing the relations of their output dimensions (e.g., classes) can significantly improve few-shot learning. The graph's structure is usually free or cheap to obtain but has rarely been explored in previous works. We develop a novel meta-learner of this type for prototype based classification, in which a prototype is generated for each class, such that the nearest neighbor search among the prototypes produces an accurate classification. The meta-learner, called "Gated Propagation Network (GPN)", learns to propagate messages between prototypes of different classes on the graph, so that learning the prototype of each class benefits from the data of other related classes.

GPN applies a personalized page rank (PPR) module to diffuse the evidence among neighboring nodes.

It can significantly improve tasks that suffer from insufficient training data, e.g., few-shot learning.

Meta-learning extracts the common knowledge from learning different tasks and uses it for unseen tasks. It can significantly improve tasks that suffer from insufficient training data, e.g., few-shot learning. In most meta-learning methods, tasks are implicitly related by sharing parameters or optimizer. In this paper, we show that a meta-learner that explicitly relates tasks on a graph describing the relations of their output dimensions (e.g., classes) can significantly improve few-shot learning. The graph's structure is usually free or cheap to obtain but has rarely been explored in previous works.

In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.

We address the problem of uncertainty quantification for graph-structured data, or, more specifically, the problem to quantify the predictive uncertainty in (semi-supervised) node classification. Key questions in this regard concern the distinction between two different types of uncertainty, aleatoric and epistemic, and how to support uncertainty quantification by leveraging the structural information provided by the graph topology. Challenging assumptions and postulates of state-of-the-art methods, we propose a novel approach that represents (epistemic) uncertainty in terms of mixtures of Dirichlet distributions and refers to the established principle of linear opinion pooling for propagating information between neighbored nodes in the graph. The effectiveness of this approach is demonstrated in a series of experiments on a variety of graph-structured datasets.