Stacking Factorizing Partitioned Expressions in Hybrid Bayesian Network Models

Hybrid Bayesian networks (HBN) contain complex conditional probabilistic distributions (CPD) specified as partitioned expressions over discrete and continuous variables. The size of these CPDs grows exponentially with the number of parent nodes, and when using discrete inference methods, it results in significant execution time and space inefficiency. To reduce the CPD size, a binary factorization (BF) algorithm can be used to decompose the statistical or arithmetic functions in the CPD by factorizing the number of connected parent nodes into sets of size two. However, the BF algorithm was not designed to handle partitioned expressions. Therefore, we propose a new stacking factorization (SF) algorithm to decompose partitioned expressions. The SF algorithm creates intermediate nodes to incrementally reconstruct the conditional densities in the original partitioned expression, ensuring that no more than two continuous parent nodes are connected to each child node in the resulting HBN. It generally applies to both discrete and continuous child nodes with complex partitioned expressions. When we combine SF with a dynamic discretization (DD) inference algorithm, we achieve a significant improvement in inference efficiency. Experimental results demonstrate that the combination of SF and DD can effectively manage HBNs with complex CPDs that may challenge other algorithms, which also outperform competing inference algorithms in accuracy.