Adaptation Using Spatially Distributed Gaussian Processes

• 成果类型: Article; Early Access
• 署名作者: Szabo, Botond; Hadji, Amine; van der Vaart, Aad
• 署名单位: Bocconi University; Bocconi University; Leiden University; Leiden University - Excl LUMC; Delft University of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2501717
• 发表日期: 2025
• 关键词: posterior distributions; BAYES; rates; mixtures

摘要

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that this approximate posterior retains the rate of recovery of the full data posterior distribution, where the rate of recovery adapts to the smoothness of the true regression function. As particular examples we consider Gaussian process priors based on integrated Brownian motion and the Mat & eacute;rn kernel augmented with a prior on the length scale. Besides theoretical guarantees we present a numerical study of the methods both on synthetic and real world data. We also propose a new aggregation technique, which numerically outperforms previous approaches. Finally, we demonstrate empirically that spatially distributed methods can adapt to local regularities, potentially outperforming the original Gaussian process. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.