利用贝叶斯双聚类与对数线性图模型探索复杂依赖结构
Exploring complex dependence structures using Bayesian bi-clustering and log-linear graphical modelling
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中文总结 AI 辅助
该研究结合贝叶斯双聚类与对数线性图模型，通过理论推导与模拟、真实数据验证，揭示变量依赖结构，阐明混合建模与图对数线性建模的关系，助力高效探索庞大的模型空间。
中文摘要 AI 辅助
本研究同时对研究对象与分类变量采用贝叶斯划分，以揭示复杂的依赖结构，变量的聚类被称为视图。变量选择会突出每个视图内驱动研究对象聚类的变量。我们推导了变量依赖结构与双聚类推断之间关系的理论结果，这些结果涉及边缘独立和条件独立。通过模拟数据和真实数据，我们展示了双聚类结果在辅助对数线性图模型确定方面的适用性，可高效探索通常庞大的模型空间。本研究阐明了两种截然不同但同样流行的贝叶斯方法之间的关系：受益于大量变量的混合建模，以及明确描述变量依赖结构并允许评估与模型确定相关不确定性的图对数线性建模。
英文摘要
Bayesian partitioning is utilised simultaneously on subjects and categorical variables to reveal complex dependence structures. Clusters of variables are referred to as views. Variable selection highlights the variables that drive the clustering of the subjects within each view. We derive theoretical results on the relation between the variables' dependence structure and the inferences derived from bi-clustering. The results relate to marginal independence and conditional independence. Using simulated and real data, we demonstrate the applicability of bi-clustering results in assisting log-linear graphical model determination, leading to the efficient exploration of typically vast model spaces. This work sheds light on the relation between two very different but equally popular Bayesian approaches; mixture modelling, that benefits from a large number of variables, and graphical log-linear modelling, which describes explicitly the variables' dependence structure and allows to evaluate the uncertainty associated with model determination.
