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The junction-tree representation provides an attractive structural propertyfor organizing a decomposable graph. In this study, we present two novelstochastic algorithms, which we call the junction-tree expander andjunction-tree collapser for sequential sampling of junction trees fordecomposable graphs. We show that recursive application of the junction-treeexpander, expanding incrementally the underlying graph with one vertex at atime, has full support on the space of junction trees with any given number ofunderlying vertices. On the other hand, the junction-tree collapser provides acomplementary operation for removing vertices in the underlying decomposablegraph of a junction tree, while maintaining the junction tree property. Adirect application of our suggested algorithms is demonstrated in asequential-Monte-Carlo setting designed for sampling from distributions onspaces of decomposable graphs. Numerical studies illustrate the utility of theproposed algorithms for combinatorial computations on decomposable graphs andjunction trees. All the methods proposed in the paper are implemented in thePython library trilearn.

Sequential sampling of junction trees for decomposable graphs