Sequential sampling of junction trees for decomposable graphs

TL;DR

This paper introduces two novel stochastic algorithms, the junction-tree expander and collapser, for sequentially sampling and manipulating junction trees of decomposable graphs, with applications demonstrated in sequential Monte Carlo methods.

Contribution

The paper presents new algorithms for sequentially expanding and collapsing junction trees, supporting full flexibility in the space of decomposable graphs.

Findings

Algorithms support full graph space with incremental vertex addition.

Demonstrated application in sequential Monte Carlo sampling.

Implemented methods in the Python library trilearn.

Abstract

The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present two novel stochastic algorithms, which we call 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, 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. 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 our suggested algorithms is demonstrated in a sequential-Monte-Carlo setting 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.