Martin Sterchi | Searcharxiv

arXiv2026

Strictly proper scoring rules for node selection tasks on graphs

In node selection tasks, the goal is to identify a single unknown target node in a graph. We consider probabilistic supervised node selection, where the estimator outputs a probability distribution over the nodes of the graph and the ground-truth node is available for evaluation. Classical evaluation metrics for such tasks are either statistically ill-conceived or blind to the graph structure. To fill this gap, we introduce two strictly proper scoring rules that are explicitly graph-aware: the Resistance score, which is parameter-free, and the Diffusion score, which operates at an adjustable coarse-graining resolution. We show that the Diffusion score interpolates between the multi-category Brier score and a cluster-level weighted Brier score. The Resistance score generalises two classical scoring rules: the multi-category Brier score and the Ranked probability score. Applied to rooted trees, it also serves as the strictly proper version of the improper Hierarchical error distance used in hierarchical classification. In the same setting, we furthermore establish strict propriety of the Hierarchical cross-entropy family, a recently introduced separate class of hierarchy-aware scoring rules. Experiments on epidemic source detection and on ImageNet classification confirm that the proposed scores detect meaningful differences in estimation quality that classical metrics miss.

cs.LG↗

arXiv2026

Graph Neural Networks for Source Detection: A Review and Benchmark Study

The source detection problem arises when an epidemic process unfolds over a contact network, and the objective is to identify its point of origin, i.e., the source node. Research on this problem began with the seminal work of Shah and Zaman in 2010, who formally defined it and introduced the notion of rumor centrality. With the emergence of Graph Neural Networks (GNNs), several studies have proposed GNN-based approaches to source detection. However, there is room to strengthen methodological clarity and reproducibility across these works. As a result, it remains unclear whether GNNs truly outperform more traditional source detection methods across comparable settings. In this paper, we first systematically review existing GNN-based methods for source detection, clearly outlining the specific settings each addresses and the architectures they employ. We then reproduce and benchmark four representative GNN architectures against a diverse set of traditional and MLP-based baselines under controlled, comparable conditions. We also investigate key questions surrounding this problem, including how detectability evolves over time, how performance scales with training set size, and how sensitive methods are to uncertainty in observation timing and epidemic parameters. Our experiments show that GNNs substantially outperform all other methods we test across a variety of network topologies. Although we initially set out to challenge the notion of GNNs as a solution to source detection, our results instead demonstrate their remarkable effectiveness for this task. To ensure full reproducibility, we release all code and data on GitHub. Finally, we argue that epidemic source detection constitutes a natural and attractive benchmark task for evaluating GNN architectures.

cs.SI↗