Semiparametric Bayesian network classifiers

Continuous Bayesian network classifiers are attractive because they provide probabilistic interpretability, but they face a trade-off between the computational efficiency of parametric modeling and the flexibility and computational cost of nonparametric density estimation. This paper studies whether semiparametric modeling can provide a better solution for continuous classification than purely Gaussian or kernel-based approaches. Therefore, we define a family of semiparametric Bayesian network classifiers in which each continuous node is modeled either parametrically or nonparametrically, and we instantiate this framework across seven established classifier structures. We propose efficient learning algorithms that automatically determine the best structure and distribution type (parametric or nonparametric) from data. Experiments on 25 UCI benchmark datasets using multiple predictive metrics, runtime analysis, and statistical significance testing show that the proposed models generally achieve better classification performance than their parametric counterparts, while incurring lower prediction-time costs than fully nonparametric alternatives. These results are relevant for researchers and practitioners who require interpretable probabilistic classifiers in settings where Gaussian assumptions may be too restrictive and uniformly nonparametric modeling may be computationally burdensome. More broadly, the findings suggest that adaptive node-wise distribution selection is a promising framework for probabilistic classification and motivate future work on mixed-type variables and alternative learning strategies.