标题： 在贝叶斯函数聚类中误指误差分布的影响：后果与补救措施 显示英文标题

标题： On Misspecified Error Distributions in Bayesian Functional Clustering: Consequences and Remedies

摘要： 非参数贝叶斯方法提供了一个灵活的聚类框架，无需预先指定组数，但它们众所周知会在功能数据中高估聚类数量。 我们表明，这种现象的根本原因在于误差结构的错误设定：在贝叶斯功能模型中，通常假设观测点之间的误差是独立的。 通过高维聚类理论，我们证明忽略潜在相关性会导致过多的聚类，无论先验分布的灵活性如何。 在该理论的指导下，我们提出通过高斯过程纳入潜在的相关结构，并提出了其可扩展的近似方法以及合理的超参数选择。 数值实验表明，一旦误差依赖性被正确建模，基于狄利克雷过程的简单聚类也能表现良好。 显示英文摘要

摘要： Nonparametric Bayesian approaches provide a flexible framework for clustering without pre-specifying the number of groups, yet they are well known to overestimate the number of clusters, especially for functional data. We show that a fundamental cause of this phenomenon lies in misspecification of the error structure: errors are conventionally assumed to be independent across observed points in Bayesian functional models. Through high-dimensional clustering theory, we demonstrate that ignoring the underlying correlation leads to excess clusters regardless of the flexibility of prior distributions. Guided by this theory, we propose incorporating the underlying correlation structures via Gaussian processes and also present its scalable approximation with principled hyperparameter selection. Numerical experiments illustrate that even simple clustering based on Dirichlet processes performs well once error dependence is properly modeled.