Convex Calibrated Surrogates for the Multi-Label F-Measure
Convex Calibrated Surrogates for the Multi-Label F-Measure
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发表时间：
2020-07
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通讯作者：
Mingyuan Zhang;H. G. Ramaswamy;S. Agarwal
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作者：
Mingyuan Zhang;H. G. Ramaswamy;S. Agarwal
F 度量是一种广泛使用的多标签分类性能度量，其中多个标签可以同时在一个实例中处于活动状态（例如，在图像标记中，多个标签可以在任何图像中处于活动状态）。特别是，F 度量明确地平衡了召回率（预测为活动的活动标签的比例）和精度（预测为活动的标签实际上为活动的比例），这两者对于评估多标签分类器的整体性能都很重要。然而，与大多数离散预测问题一样，直接优化 F 测量在计算上是困难的。在本文中，我们探讨了设计针对 F 度量进行校准的凸代理损失的问题 - 具体来说，它具有最小化代理损失的属性，可以产生（在足够数据的限制下）F 度量的贝叶斯最优多标签分类器。我们证明，当将 s 标签问题视为 2 s × 2 s 损失矩阵时，s 标签问题的 F 度量最多具有 s 2 + 1 的秩，并应用 Ramaswamy 等人的结果。 (2014) 为 F 测量设计一系列凸校准替代项。由此产生的替代风险最小化算法可以被视为将多标签 F 测量学习问题分解为 s 2 + 1 个二元类概率估计问题。我们还为我们的代理提供了定量的遗憾转移界限，这允许将二元问题的任何遗憾保证转移到整体 F 测量问题的遗憾保证，并讨论与 Dembczynski 等人的算法的联系。 （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 × 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.