Multi-label classification problems require each instance to be assigned a subset of auddefined set of labels. This problem is equivalent to finding a multi-valued decision functionudthat predicts a vector of binary classes. In this paper we study the decision boundaries ofudtwo widely used approaches for building multi-label classifiers, when Bayesian networkaugmentedudnaive Bayes classifiers are used as base models: Binary relevance methodudand chain classifiers. In particular extending previous single-label results to multi-labeludchain classifiers, we find polynomial expressions for the multi-valued decision functionsudassociated with these methods. We prove upper boundings on the expressive power ofudboth methods and we prove that chain classifiers provide a more expressive model thanudthe binary relevance method.
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