The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present a novel stochastic algorithm, which we call the junction-tree expander, for sequential sampling of junction trees for decomposable graphs. We show that recursive application of the junction-tree expander, expanding incrementally the underlying graph with one vertex at a time, has full support on the space of junction trees with any given number of underlying vertices. A direct application of our suggested algorithm is demonstrated in a sequential Monte Carlo setting designed for sampling from distributions on spaces of decomposable graphs, where the junction-tree expander can be effectively employed as proposal kernel; see the companion paper Olsson et al. 2019 [16]. A numerical study illustrates the utility of our approach by two examples: in the first one, how the junction-tree expander can be incorporated successfully into a particle Gibbs sampler for Bayesian structure learning in decomposable graphical models; in the second one, we provide an unbiased estimator of the number of decomposable graphs for a given number of vertices. All the methods proposed in the paper are implemented in the Python library trilearn.

中文翻译：

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可分解图的连接树的顺序采样

连接树表示为组织可分解图提供了有吸引力的结构特性。在这项研究中，我们提出了一种新的随机算法，我们称之为连接树扩展器，用于对可分解图的连接树进行顺序采样。我们展示了结点树扩展器的递归应用，一次一个顶点递增地扩展底层图，完全支持具有任何给定数量底层顶点的结点树空间。我们建议的算法的直接应用在设计用于从可分解图空间上的分布中采样的顺序蒙特卡罗设置中得到证明，其中连接树扩展器可以有效地用作建议内核；参见Olsson 等人的配套论文。2019 [16]。数值研究通过两个例子说明了我们方法的实用性：在第一个例子中，连接树扩展器如何成功地合并到粒子吉布斯采样器中，用于可分解图形模型中的贝叶斯结构学习；在第二个中，我们为给定数量的顶点提供了可分解图数量的无偏估计量。论文中提出的所有方法都在 Python 库 trilearn 中实现。