## AbstractWe investigate the problem of classifying data based on the knowledge that the graph of dependencies between class elements is a tree forest. The trees in the forest are collectively interpreted as a taxonomy. That is, we assume that every data instance is labelled with a (possibly empty) set of class labels and, whenever an instance is labelled with a certain label i, then it is also labelled with all the labels on the path from the root of the tree where i occurs down to node i. We also allow for multiple-path labellings, where instances can be tagged with labels belonging to two or more paths in the forest. Given a taxonomy, we learn a hierarchical classifier by fitting the training data with the parameters of a Bayesian network defined on the taxonomy. We show a practical algorithm for learning Bayesian networks of this form. Finally, we show how our approach can be easily extended to a very general Bayesian framework for learning multilabelled data.
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