Sequential sampling of junction trees for decomposable graphs

• Published in: Statistics and computing Vol. 32; no. 5
• Main Authors: Olsson, Jimmy, Pavlenko, Tatjana, Rios, Felix L.
• Format: Journal Article
• Language: English
• Published: New York Springer US 2022; Springer Nature B.V
• Subjects: Algorithms; Apexes; Artificial Intelligence; Combinatorial analysis; Computer Science; Decomposable graphs; Decomposition; Graph theory; Graphical models; Graphical representations; Graphs; Junction trees; Monte Carlo simulation; Probability and Statistics in Computer Science; Random graphs; Sequential Monte Carlo; Sequential sampling; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Trees; Trees (mathematics); Junction trees; Sequential Monte Carlo; Graphical models; Decomposable graphs; Random graphs
• ISSN: 0960-3174; 1573-1375; 1573-1375
• DOI: 10.1007/s11222-022-10113-2

The junction-tree representation provides an attractive structural property for organising a decomposable graph . In this study, we present two novel stochastic algorithms, referred to as the junction-tree expander and junction-tree collapser , for sequential sampling of junction trees for decomposable graphs. We show that recursive application of the junction-tree expander, which expands incrementally the underlying graph with one vertex at a time, has full support on the space of junction trees for any given number of underlying vertices. On the other hand, the junction-tree collapser provides a complementary operation for removing vertices in the underlying decomposable graph of a junction tree, while maintaining the junction tree property. A direct application of the proposed algorithms is demonstrated in the setting of sequential Monte Carlo methods, designed for sampling from distributions on spaces of decomposable graphs. Numerical studies illustrate the utility of the proposed algorithms for combinatorial computations on decomposable graphs and junction trees. All the methods proposed in the paper are implemented in the Python library trilearn .