Mixed Bayesian networks: a mixture of Gaussian distributions.
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.
Chevrolat
J P
JP
INSERM 194 et Département de Biostatistique et Informatique Médicale, CHU Pitié Salpêtrière, Paris, France.
Rutigliano
F
F
Golmard
J L
JL
D000465:Algorithms; D001499:Bayes Theorem; D003196:Computer Graphics; D003198:Computer Simulation; D006801:Humans; D008432:Mathematical Computing; D015233:Models, Statistical; D016011:Normal Distribution; D010599:Pharmacokinetics