Crossed Linear Gaussian Bayesian Networks, parsimonious models

Résumé

Linear Gaussian Bayesian networks can dramatically reduce the parametric dimension of the covariance matrices in the framework of multivariate multiple regression models. This idea is developed using structured, crossed directed acyclic graphs (DAGs) when node sets can be interpreted as the cartesian product of two sets. Some interesting properties of these DAGs are shown as well as the probability distributions of the associated Bayesian networks. A numerical experiment on simulated data was performed to check that the idea could be applied in practice. This modelling is applied to the prediction of body composition from easily measurable covariates and compared with the results of a saturated regression prediction.