# Gaussian mixture modeling of nodes in Bayesian network according to maximal parental cliques

arXiv: https://arxiv.org/abs/2204.09532 · HTML: https://mlsanity.com/paper/2204.09532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 20 Apr 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [A Transformational Characterization of Equivalent Bayesian Network Structures](https://mlsanity.com/paper/1302.4938/) (2013)
- [A Bayesian Network Classifier that Combines a Finite Mixture Model and a Naive Bayes Model](https://mlsanity.com/paper/1301.6723/) (2013)

## Abstract (arXiv)

This paper uses Gaussian mixture model instead of linear Gaussian model to fit the distribution of every node in Bayesian network. We will explain why and how we use Gaussian mixture models in Bayesian network. Meanwhile we propose a new method, called double iteration algorithm, to optimize the mixture model, the double iteration algorithm combines the expectation maximization algorithm and gradient descent algorithm, and it performs perfectly on the Bayesian network with mixture models. In experiments we test the Gaussian mixture model and the optimization algorithm on different graphs which is generated by different structure learning algorithm on real data sets, and give the details of every experiment.