Linear Opinion Pooling for Uncertainty Quantification on Graphs

TL;DR

This paper introduces a novel method for quantifying predictive uncertainty in graph-based semi-supervised node classification by using mixtures of Dirichlet distributions and linear opinion pooling to leverage graph structure.

Contribution

It proposes a new approach that models epistemic uncertainty with Dirichlet mixtures and propagates information via linear opinion pooling, challenging existing assumptions.

Findings

Effective in various graph datasets

Improves uncertainty quantification accuracy

Supports differentiation of uncertainty types

Abstract

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.