  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 when using discrete inference, resulting in significant
inefficiency. Normally, an effective way to reduce the CPD size is to use a
binary factorization (BF) algorithm to decompose the statistical or arithmetic
functions in the CPD by factorizing the number of connected parent nodes to
sets of size two. However, the BF algorithm was not designed to handle
partitioned expressions. Hence, we propose a new algorithm called stacking
factorization (SF) to decompose the partitioned expressions. The SF algorithm
creates intermediate nodes to incrementally reconstruct the densities in the
original partitioned expression, allowing no more than two continuous parent
nodes to be connected to each child node in the resulting HBN. SF can be either
used independently or combined with the BF algorithm. We show that the SF+BF
algorithm significantly reduces the CPD size and contributes to lowering the
tree-width of a model, thus improving efficiency.
