Graph neural networks (GNNs) have advanced the state of the art in various domains. Despite their remarkable success, the uncertainty estimation of GNN predictions remains under-explored, which limits their practical applications especially in risk-sensitive areas. Current works suffer from either intractable posteriors or inflexible prior specifications, leading to sub-optimal empirical results. In this paper, we present graph neural stochastic diffusion (GNSD), a novel framework for estimating predictive uncertainty on graphs by establishing theoretical connections between GNNs and stochastic partial differential equation. GNSD represents a GNN-based parameterization of the proposed graph stochastic diffusion equation which includes a $Q$-Wiener process to model the stochastic evolution of node representations. GNSD introduces a drift network to guarantee accurate prediction and a stochastic forcing network to model the propagation of epistemic uncertainty among nodes. Extensive experiments are conducted on multiple detection tasks, demonstrating that GNSD yields the superior performance over existing strong approaches.

Graph meta-learning which is used to deal with graph few-shot learning attracts more and more research interests. Existing graph meta-learning methods mainly focus on capturing node-level relations, but they ignore task-level relations which are beneficial for improving the performance of few-shot node classification. Furthermore, contrastive learning which can learn knowledge without labeled data is suitable for few-shot scenario, but existing graph few-shot learning methods have never exploited it. To tackle above problems, in this paper, we combine conventional graph meta-learning framework with graph contrastive learning and propose a novel joint model named -${\underline T}$asklevel -${\underline R}$elations Modelling for -${\underline G}$raph ${\underline M}$eta-learning (TRGM). By constructing auxiliary contrastive pretext tasks, TRGM can fully capture the inter-task relations (task correlation and task discrepancy) and promote the primary few-shot learning. Finally, we conduct extensive experiments on six benchmark datasets to validate the effectiveness and efficiency of TRGM. Experimental results show that our model outperforms several strong baselines and achieves the new state-of-the-art.

In the fraud graph, fraudsters often interact with a large number of benign entities to hide themselves. So, there are not only the homophilic connections formed by the same label nodes (similar nodes), but also the heterophilic connections formed by the different label nodes (dissimilar nodes). However, the existing GNN-based fraud detection methods just enhance the homophily in fraud graph and use the low-pass filter to retain the commonality of node features among the neighbors, which inevitably ignore the difference among neighbor of heterophilic connections. To address this problem, we propose a Graph Neural Network-based Fraud Detector with Homophilic and Heterophilic Interactions (H2-FDetector for short). Firstly, we identify the homophilic and heterophilic connections with the supervision of labeled nodes. Next, we design a new information aggregation strategy to make the homophilic connections propagate similar information and the heterophilic connections propagate difference information. Finally, a prototype prior is introduced to guide the identification of fraudsters. Extensive experiments on two real public benchmark fraud detection tasks demonstrate that our method apparently outperforms state-of-the-art baselines.