We compare the plug-in rule approach for optimizing the F_β-measure in multi-label classification with an approach based on structured loss minimization, such as the structured support vector machine (SSVM). Whereas the former derives an optimal prediction from a probabilistic model in a separate inference step, the latter seeks to optimize the F_β-measure directly during the training phase. We introduce a novel plug-in rule algorithm that estimates all parameters required for a Bayes-optimal prediction via a set of multinomial regression models, and we compare this algorithm with SSVMs in terms of computational complexity and statistical consistency. As a main theoretical result, we show that our plug-in rule algorithm is consistent, whereas the SSVM approaches are not. Finally, we present results of a large experimental study showing the benefits of the introduced algorithm.
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