ABC-Miner+: constructing Markov blanket classifiers with ant colony algorithms

ABC-Miner is a Bayesian classification algorithm based on the Ant colony optimization (ACO) meta-heuristic. The algorithm learns Bayesian network Augmented Naïve-Bayes (BAN) classifiers, where the class node is the parent of all the nodes representing the input variables. However, this assumes the existence of a dependency relationship between the class variable and all the input variables, and this relationship is always a type of “causal” (rather than “effect”) relationship, which restricts the flexibility of the algorithm to learn. In this paper, we extended the ABC-Miner algorithm to be able to learn the Markov blanket of the class variable. Such a produced model has a more flexible Bayesian network classifier structure, where it is not necessary to have a (direct) dependency relationship between the class variable and each of the input variables, and the dependency between the class and the input variables varies from “causal” to “effect” relationships. In this context, we propose two algorithms: $${\hbox {ABC-Miner}+_1}$$ABC-Miner+1, in which the dependency relationships between the class and the input variables are defined in a separate phase before the dependency relationships among the input variables are defined, and $${\hbox {ABC-Miner}+_2}$$ABC-Miner+2, in which the two types of dependency relationships in the Markov blanket classifier are discovered in a single integrated process. Empirical evaluations on 33 UCI benchmark datasets show that our extended algorithms outperform the original version in terms of predictive accuracy, model size and computational time. Moreover, they have shown a very competitive performance against other well-known classification algorithms in the literature.