A hybrid method for learning multi-dimensional Bayesian network classifiers based on an optimization model

Bayesian networks, which have a solid mathematical basis as classifiers, take the prior information of samples into consideration. They have gained considerable popularity for solving classification problems. However, many real-world applications can be viewed as classification problems in which instances have to be assigned to a set of different classes at the same time. To address this problem, multi-dimensional Bayesian network classifiers (MBCs), which organize class and feature variables as three subgraphs, have recently been proposed. Because each subgraph has different structural restrictions, three different learning algorithms are needed. In this paper, we present for the first time an MBC learning algorithm based on an optimization model (MBC-OM) that is inspired by the constraint-based Bayesian network structure learning method. MBC-OM uses the chi-squared statistic and mutual information to estimate the dependence coefficients among variables, and these are used to construct an objective function as an overall measure of the dependence for a classifier structure. Therefore, the problem of searching for an optimal classifier becomes one of finding the maximum value of the objective function in feasible fields. We prove the existence and uniqueness of the numerical solution. Moreover, we validate our method on five benchmark data sets. Experimental results are competitive, and outperform state-of-the-art algorithms for multi-dimensional classification.