## On the Bayes-Optimality of F-Measure Maximizers

*Willem Waegeman, Krzysztof Dembczynski, Arkadiusz Jachnik, Weiwei Cheng, Eyke HÃ¼llermeier*; 15(Nov):3513−3568, 2014.

### Abstract

The F-measure, which has originally been introduced in
information retrieval, is nowadays routinely used as a
performance metric for problems such as binary classification,
multi-label classification, and structured output prediction.
Optimizing this measure is a statistically and computationally
challenging problem, since no closed-form solution exists.
Adopting a decision-theoretic perspective, this article provides
a formal and experimental analysis of different approaches for
maximizing the F-measure. We start with a Bayes-risk analysis of
related loss functions, such as Hamming loss and subset zero-one
loss, showing that optimizing such losses as a surrogate of the
F-measure leads to a high worst-case regret. Subsequently, we
perform a similar type of analysis for F-measure maximizing
algorithms, showing that such algorithms are approximate, while
relying on additional assumptions regarding the statistical
distribution of the binary response variables. Furthermore, we
present a new algorithm which is not only computationally
efficient but also Bayes-optimal, regardless of the underlying
distribution. To this end, the algorithm requires only a
quadratic (with respect to the number of binary responses)
number of parameters of the joint distribution. We illustrate
the practical performance of all analyzed methods by means of
experiments with multi-label classification problems.

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