Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds, most existing approaches require access to specific input features, and rely on posterior mean and variance estimates or the tuning of hyperparameters. These limitations hinder robustness and fail to capture the model’s global behavior in expectation. To address these limitations, we propose a chaining-based framework for estimating upper and lower bounds on the expected extreme values over unseen data, without requiring access to specific input features. We provide kernel-specific refinements for commonly used kernels such as RBF and Matérn, in which our bounds are tighter than generic constructions. We further improve numerical tightness by avoiding analytical relaxations. In addition to global estimation, we also develop a novel method for local uncertainty quantification at specified inputs. This approach leverages chaining geometry through partition diameters, adapting to local structures without relying on posterior variance scaling. Our experimental results validate the theoretical findings and demonstrate that our method outperforms existing approaches on both synthetic and real-world datasets.

Accurately assessing and forecasting bank credit ratings at an early stage is vitally important for a healthy financial environment and sustainable economic development. However, the evaluation process faces challenges due to individual attacks on the rating model. Some participants may provide manipulated information in an attempt to undermine the rating model and secure higher scores, further complicating the evaluation process. Therefore, we propose a novel approach called the preferential selective-aware graph neural network (PSAGNN) model to simultaneously defend against feature and structural nontarget poisoning attacks on Interbank credit ratings. In particular, the model establishes a phased optimization approach combined with biased perturbation and explores the Interbank preferences and scale-free nature of networks, to adaptively prioritize the poisoning training data and simulate a clean graph. Finally, we apply a weighted penalty on the opposition function to optimize the model so that the model can distinguish between attackers. Extensive experiments on our newly collected Interbank quarter dataset and case studies demonstrate the superior performance of our proposed approach in preventing credit rating attacks compared to state-of-the-art baselines.

Accurately credit rating on Interbank assets is essential for a healthy financial environment and substantial economic development. But individual participants tend to provide manipulated information in order to attack the rating model to produce a higher score, which may conduct serious adverse effects on the economic system, such as the 2008 global financial crisis. To this end, in this paper, we propose a novel selective-aware graph neural network model (SA-GNN) for defense the Interbank credit rating attacks. In particular, we first simulate the rating information manipulating process by structural and feature poisoning attacks. Then we build a selective-aware defense graph neural model to adaptively prioritize the poisoning training data with Bernoulli distribution similarities. Finally, we optimize the model with weighed penalization on the objection function so that the model could differentiate the attackers. Extensive experiments on our collected real-world Interbank dataset, with over 20 thousand banks and their relations, demonstrate the superior performance of our proposed method in preventing credit rating attacks compared with the state-of-the-art baselines.