Multi-dimensional Bayesian network classifiers are becoming quite popular for multi-label classification. These models have the advantage of a high expressive power, but may induce a prohibitively high runtime of classification. We argue that the high runtime burden originates from their large treewidth. Thus motivated, we present an algorithm for learning multi-classifiers of small treewidth. Experimental results show that these models have a small runtime of classification, without loosing accuracy compared to unconstrained multi-classifiers.
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