  We introduce semiparametric Bayesian networks that combine parametric and
nonparametric conditional probability distributions. Their aim is to
incorporate the advantages of both components: the bounded complexity of
parametric models and the flexibility of nonparametric ones. We demonstrate
that semiparametric Bayesian networks generalize two well-known types of
Bayesian networks: Gaussian Bayesian networks and kernel density estimation
Bayesian networks. For this purpose, we consider two different conditional
probability distributions required in a semiparametric Bayesian network. In
addition, we present modifications of two well-known algorithms (greedy
hill-climbing and PC) to learn the structure of a semiparametric Bayesian
network from data. To realize this, we employ a score function based on
cross-validation. In addition, using a validation dataset, we apply an
early-stopping criterion to avoid overfitting. To evaluate the applicability of
the proposed algorithm, we conduct an exhaustive experiment on synthetic data
sampled by mixing linear and nonlinear functions, multivariate normal data
sampled from Gaussian Bayesian networks, real data from the UCI repository, and
bearings degradation data. As a result of this experiment, we conclude that the
proposed algorithm accurately learns the combination of parametric and
nonparametric components, while achieving a performance comparable with those
provided by state-of-the-art methods.
