非对称树距离损失下的贝叶斯最优层次分类
Bayes-optimal Hierarchical Classification over Asymmetric Tree-Distance Loss
摘要：
层次分类是一种有监督的多类分类问题，它是在按层次结构组织的类标签集合上进行的。在这份报告中，我们研究的工作Ramaswamy等。在对称树距离损失上的分层分类。我们扩展了非对称树距离损失的层次分类算法的一致性。我们设计了一个$\mathcal{O}(nk\log{}n)$算法来寻找贝叶斯最优分类的k元树作为一个层次。我们表明，在合理的假设下，非对称损失函数，贝叶斯最优分类在这种非对称损失可以找到$\mathcal{O}(k\log{}n)$。我们利用这一洞察力，并试图扩展Ova级联算法\citet{ramaswamy2015convex}的分层分类的不对称损失。
英文摘要：
Hierarchical classification is supervised multi-class classification problem over the set of class labels organized according to a hierarchy. In this report, we study the work by Ramaswamy et. al. on hierarchical classification over symmetric tree distance loss. We extend the consistency of hierarchical classification algorithm over asymmetric tree distance loss. We design a $\mathcal{O}(nk\log{}n)$ algorithm to find Bayes optimal classification for a k-ary tree as a hierarchy. We show that under reasonable assumptions over asymmetric loss function, the Bayes optimal classification over this asymmetric loss can be found in $\mathcal{O}(k\log{}n)$. We exploit this insight and attempt to extend the Ova-Cascade algorithm \citet{ramaswamy2015convex} for hierarchical classification over the asymmetric loss.
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