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# Bayesian Network Classifiers Under the Ensemble Perspective

*Proceedings of the Ninth International Conference on Probabilistic Graphical Models*, PMLR 72:1-12, 2018.

#### Abstract

Augmented naive Bayesian classifiers relax the original independence assumption by allowing additional dependencies in the model. This strategy leads to parametrized learners that can produce a wide spectrum of models of increasing complexity. Expressiveness and efficiency can be controlled to adjust a trade-off specific to the problem at hand. Recent studies have transposed this finding to the domain of bias and variance, demonstrating that inducing complex multivariate probability distributions produces low-bias/high-variance classifiers that are especially suitable for large data domains. Frameworks like A$k$DE avoid structural learning and reduce variance by averaging a full family of constrained models, at the expense of increasing its spatial and computational complexity. Model selection is then required and performed using Information Theory techniques. We present a new approach to reduce model space from the point of view of ensemble classifiers, where we study the individual contribution to error for each model and how model selection affects this via the aggregation process. We perform a thorough experimentation to analyse bias stability and variance reduction and compare the results within the context of other popular ensemble models such as Random Forest, leading to a discussion on the effectiveness of the previous approaches. The conclusions support new strategies to design more consistent ensemble Bayesian network classifiers which we explore at the end of the paper.