论文标题
凸面校准了多标签F量的替代物
Convex Calibrated Surrogates for the Multi-Label F-Measure
论文作者
论文摘要
F-Measure是一种用于多标签分类的广泛使用的性能度量，其中可以同时在实例中活跃多个标签（例如，在图像标签中，在任何图像中都可以活跃多个标签）。特别是，F量表明确平衡了召回率（预计为有效的活动标签的一部分）和精度（预测为有效的标签的部分是如此），这两者对于评估多标签分类器的整体性能都很重要。然而，与大多数离散的预测问题一样，直接优化F量的F-Measure在计算上很难。在本文中，我们探讨了设计凸替代损失的问题，这些替代损失是为F量表进行了校准的 - 特别是，这些属性可以最大程度地减少替代损失产量的产量（在足够数据的限制中）贝叶斯最佳多标签分类器的F量。我们表明，当被视为$ 2^s \ times 2^s $损失矩阵时，$ s $ label问题的F量表最多具有$ s^2+1 $，并应用了Ramaswamy等人的结果。 （2014年）设计一个凸家的家族，校准了替代物以进行F量。由此产生的替代风险最小化算法可以看作是将多标签F量度学习问题分解为$ S^2+1 $二进制类别概率估计问题。我们还为我们的代理人提供了定量的遗憾转移，这允许对二进制问题进行任何遗憾保证，以遗憾地保证整体F量级问题，并与Dembczynski等人的算法进行讨论。 （2013）。我们的实验证实了我们的理论发现。
The F-measure is a widely used performance measure for multi-label classification, where multiple labels can be active in an instance simultaneously (e.g. in image tagging, multiple tags can be active in any image). In particular, the F-measure explicitly balances recall (fraction of active labels predicted to be active) and precision (fraction of labels predicted to be active that are actually so), both of which are important in evaluating the overall performance of a multi-label classifier. As with most discrete prediction problems, however, directly optimizing the F-measure is computationally hard. In this paper, we explore the question of designing convex surrogate losses that are calibrated for the F-measure -- specifically, that have the property that minimizing the surrogate loss yields (in the limit of sufficient data) a Bayes optimal multi-label classifier for the F-measure. We show that the F-measure for an $s$-label problem, when viewed as a $2^s \times 2^s$ loss matrix, has rank at most $s^2+1$, and apply a result of Ramaswamy et al. (2014) to design a family of convex calibrated surrogates for the F-measure. The resulting surrogate risk minimization algorithms can be viewed as decomposing the multi-label F-measure learning problem into $s^2+1$ binary class probability estimation problems. We also provide a quantitative regret transfer bound for our surrogates, which allows any regret guarantees for the binary problems to be transferred to regret guarantees for the overall F-measure problem, and discuss a connection with the algorithm of Dembczynski et al. (2013). Our experiments confirm our theoretical findings.
