Mixed Bayesian Networks: A Mixture of Gaussian Distributions - Chevrolat, J. P.; Rutigliano, F.; Golmard, J. L. (Methods of Information in Medicine, 1994)
Mixed Bayesian networks are probabilistic models associated with a graphical representation, where the graph is directed and the random variables are discrete or continuous. We propose a comprehensive method for estimating the density functions of continuous variables, using a graph structure and a set of samples. The principle of the method is to learn the shape of densities from a sample of continuous variables. The densities are approximated by a mixture of Gaussian distributions. The estimation algorithm is a stochastic version of the Expectation Maximization algorithm (Stochastic EM algorithm). The inference algorithm corresponding to our model is a variant of junction three method, adapted to our specific case. The approach is illustrated by a simulated example from the domain of pharmacokinetics. Tests show that the true distributions seem sufficiently fitted for practical application.
Keywords: Belief Networks; Gaussian Mixtures; SEM Algorithm; Statistical Tests