A Bayesian Contiguous Partitioning Method for Learning Clustered Latent Variables
A Bayesian Contiguous Partitioning Method for Learning Clustered Latent Variables
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发表时间：
2021
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通讯作者：
Z. Luo;H. Sang;B. Mallick
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作者：
Z. Luo;H. Sang;B. Mallick
本文从图的生成树出发，通过对图的生成树进行先验赋值，然后给出生成树中被移除边的个数和位置，建立了一个贝叶斯划分先验模型。该方法保证了聚类的连续性，并允许检测具有任意形状和大小的聚类，而大多数现有的分区模型，如二叉树和Voronoi镶嵌不具备这样的属性。我们将此分区模型嵌入到分层建模框架中，以检测潜在变量中的聚类模式。我们专注于通过空间数据的聚类回归系数模型来说明该方法，并提出对其他层次模型的扩展。我们证明贝叶斯后验浓度的结果下的渐近框架与随机图。我们设计了一种高效的折叠可逆跳跃马尔可夫链蒙特卡罗（RJ-MCMC）算法来估计聚类系数值及其不确定性度量。最后，我们说明了模拟研究和真实的数据分析，检测在大西洋的水团的温度-盐度关系的模型的性能。
This article develops a Bayesian partitioning prior model from spanning trees of a graph, by first assigning priors on spanning trees, and then the number and the positions of removed edges given a spanning tree. The proposed method guarantees contiguity in clustering and allows to detect clusters with arbitrary shapes and sizes, whereas most existing partition models such as binary trees and Voronoi tessellations do not possess such properties. We embed this partition model within a hierarchical modeling framework to detect a clustered pattern in latent variables. We focus on illustrating the method through a clustered regression coefficient model for spatial data and propose extensions to other hierarchical models. We prove Bayesian posterior concentration results under an asymptotic framework with random graphs. We design an efficient collapsed Reversible Jump Markov chain Monte Carlo (RJ-MCMC) algorithm to estimate the clustered coefficient values and their uncertainty measures. Finally, we illustrate the performance of the model with simulation studies and a real data analysis of detecting the temperature-salinity relationship from water masses in the Atlantic Ocean.