论文标题
韦斯顿 - 沃特金斯铰链损失和有序分区
Weston-Watkins Hinge Loss and Ordered Partitions
论文作者
论文摘要
支持向量机（SVM）的多类扩展已经以多种方式制定。最近对九种此类制剂的经验比较[Doǧan等。 [2016年]建议韦斯顿和沃特金斯（WW）提出的变体，尽管事实上WW-Hinge损失没有相对于0-1的损失进行校准。在这项工作中，我们引入了多类分类，有序分区损失的新型离散损失函数，并证明了有关此损失的WW-HINGE损失。我们还认为，在满足该财产的离散损失中，有序分区损失在最大程度上有用。最后，我们运用理论来证明Doǧan等人的经验观察是合理的。即使在大量标签噪声下，WW-SVM也可以很好地工作，这是多类SVM的具有挑战性的环境。
Multiclass extensions of the support vector machine (SVM) have been formulated in a variety of ways. A recent empirical comparison of nine such formulations [Doǧan et al. 2016] recommends the variant proposed by Weston and Watkins (WW), despite the fact that the WW-hinge loss is not calibrated with respect to the 0-1 loss. In this work we introduce a novel discrete loss function for multiclass classification, the ordered partition loss, and prove that the WW-hinge loss is calibrated with respect to this loss. We also argue that the ordered partition loss is maximally informative among discrete losses satisfying this property. Finally, we apply our theory to justify the empirical observation made by Doǧan et al. that the WW-SVM can work well even under massive label noise, a challenging setting for multiclass SVMs.
