Hybrid semiparametric Bayesian networks

This paper presents a new class of Bayesian networks called hybrid semiparametric Bayesian networks, which can model hybrid data (discrete and continuous data) by mixing parametric and nonparametric estimation models. The parametric estimation models can represent a conditional linear Gaussian relationship between variables, while the nonparametric estimation model can represent other types of relationships, such as non-Gaussian and nonlinear relationships. This new class of Bayesian networks generalizes the conditional linear Gaussian Bayesian networks, including them as a special case. In addition, we describe a learning procedure for the structure and the parameters of our proposed type of Bayesian network. This learning procedure finds the best combination of parametric and nonparametric models automatically from data. This requires the definition of a cross-validated score. We also detail how new data can be sampled from a hybrid semiparametric Bayesian network, which in turn can be useful to solve other related tasks, such as inference. Furthermore, we intuitively relate our proposal with adaptive kernel density estimation models. The experimental results show that hybrid semiparametric Bayesian networks are a valuable contribution when dealing with data that do not meet the parametric assumptions that are expected for other models, such as conditional linear Gaussian Bayesian networks. We include experiments with synthetic data and real-world data from the UCI repository which demonstrate the good performance and the ability to extract useful information about the relationship between the variables in the model.