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.

该研究论文使用决策论和贝叶斯风险分析方法，提出了一种在二值分类、多标签分类和结构化输出预测等问题中，优化 F-measure 评价指标的方法，并提出了一个新的算法，它不仅计算效率高，而且在任何分布下都是贝叶斯最优的。

F-度量最大化算法的贝叶斯最优性探讨