Weston-Watkins Hinge Loss and Ordered Partitions
Weston-Watkins Hinge Loss and Ordered Partitions
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发表时间：
2020-06
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通讯作者：
Yutong Wang;C. Scott
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作者：
Yutong Wang;C. Scott
支持向量机（SVM）的多类扩展已经以各种方式制定。最近对9种此类公式进行的经验比较[Dobalan等人，2016]建议采用韦斯顿和沃特金斯（WW）提出的变体，尽管事实上没有根据0-1损失校准WW铰链损失。在这项工作中，我们引入了一种新的离散损失函数的多类分类，有序分区损失，并证明了相对于此损失的WW-hinge损失校准。我们还认为，有序分区损失是最大的离散损失满足这一属性的信息。最后，我们应用我们的理论来证明Dopelan等人的经验观察，即WW-SVM即使在大规模标签噪声下也能很好地工作，这对多类SVM来说是一个挑战。
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.