标题： 分组间聚类的分层泊松噪声柯克斯过程混合模型 显示英文标题

标题： Hierarchical shot-noise Cox process mixtures for clustering across groups

摘要： 在部分可交换的数据组中对观测进行聚类是贝叶斯非参数学中的常规任务。 先前提出的模型通过在组特定的混合度量中共享原子来实现跨组的聚类。 然而，当组之间存在细微差异时，精确的原子共享可能会过于僵硬，这在较大样本量下会引入聚类和密度估计之间的权衡，并导致跨组聚类的碎片化。 我们引入了分层噪声点 Cox 过程（HSNCP）混合模型，其中组特定的原子通过核函数集中在共享中心周围。 这使得组内的密度估计更加准确，并实现了跨组的灵活借用，克服了之前方法的密度-聚类权衡。 我们的构造基于噪声点 Cox 过程，保持了分析上的可处理性：我们推导出闭合形式的先验矩和组间相关性，得到了潜在参数的边缘分布和预测分布，以及给定潜在参数的混合度量的后验分布。 我们开发了一个高效的条件 MCMC 算法用于后验推断。 我们通过模拟和对一个大型星系数据集的应用评估了 HSNCP 模型的性能，证明了与分层 Dirichlet 过程相比，HSNCP 模型能够实现平衡的跨组聚类和改进的密度估计，包括在模型误指的情况下。 显示英文摘要

摘要： Clustering observations across partially exchangeable groups of data is a routine task in Bayesian nonparametrics. Previously proposed models allow for clustering across groups by sharing atoms in the group-specific mixing measures. However, exact atom sharing can be overly rigid when groups differ subtly, introducing a trade-off between clustering and density estimates and fragmenting across-group clusters, particularly at larger sample sizes. We introduce the hierarchical shot-noise Cox process (HSNCP) mixture model, where group-specific atoms concentrate around shared centers through a kernel. This enables accurate density estimation within groups and flexible borrowing across groups, overcoming the density-clustering trade-off of previous approaches. Our construction, built on the shot-noise Cox process, remains analytically tractable: we derive closed-form prior moments and an inter-group correlation, obtain the marginal law and predictive distribution for latent parameters, as well as the posterior of the mixing measures given the latent parameters. We develop an efficient conditional MCMC algorithm for posterior inference. We assess the performance of the HSNCP model through simulations and an application to a large galaxy dataset, demonstrating balanced across-group clusters and improved density estimates compared with the hierarchical Dirichlet process, including under model misspecification.