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.Comment: 31 pages, 7 figure
