  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.
