# Optimizing the F-Measure in Multi-Label Classification: Plug-in Rule Approach versus Structured Loss Minimization

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Krzysztof Dembczynski,
Arkadiusz Jachnik,
Wojciech Kotlowski,
Willem Waegeman,
Eyke Huellermeier
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Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1130-1138, 2013.

#### Abstract

We compare the plug-in rule approach for optimizing the F-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-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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