A scalable Bayesian classification approach with fast posterior computation

Bayesian nonparametric classification provides a flexible framework for statistical learning, inherently quantifying uncertainty and adapting model complexity to data. However, its practical adoption is often limited by high computational demands, especially in large-scale settings. This paper introduces a scalable approach that integrates the Gaussian process reconstruction parameterization framework with the design-of-experiments-based interpolation technique for Bayesian computation, enabling fast inference and uncertainty quantification while retaining the expressive power of Bayesian nonparametric models. Based on the uncertainty quantification results from the proposed approach, we further propose an credible interval-based classification procedure in the presence of class imbalance and overlapping distributions. It uses upper credible bounds of the class probabilities as the decision rule to classify the data, and enhances robustness, interpretability, and statistical reliability. Numerical experiments and real-world applications demonstrate the superiority of the proposed methods compared with existing methods.