# Stacking Factorizing Partitioned Expressions in Hybrid Bayesian Network Models

arXiv: https://arxiv.org/abs/2402.15075 · HTML: https://mlsanity.com/paper/2402.15075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 6 of 6)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Join-Graph Propagation Algorithms](https://mlsanity.com/paper/1401.3489/) (2014)
- [Exact Inference in Networks with Discrete Children of Continuous Parents](https://mlsanity.com/paper/1301.2289/) (2013)
- [Nonuniform Dynamic Discretization in Hybrid Networks](https://mlsanity.com/paper/1302.1555/) (2013)
- [A hybrid Bayesian network for medical device risk assessment and management](https://mlsanity.com/paper/2209.03352/) (2022)
- [AMIDST: a Java Toolbox for Scalable Probabilistic Machine Learning](https://mlsanity.com/paper/1704.01427/) (2017)

## Abstract (arXiv)

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.