论文标题
结构化的戒烟问题和洛夫斯铰链
The Structured Abstain Problem and the Lovász Hinge
论文作者
论文摘要
LovászHinge是最近提出的用于结构化二进制分类的凸构代替代物，其中$ k $二进制预测是同时进行的，并且通过子模型集合函数判断错误。尽管在图像细分和相关问题中使用了广泛使用，但其一致性仍然开放。我们解决了这个空旷的问题，表明Lovász铰链对于其所需目标不一致，除非设置功能是模块化的。利用最近的嵌入框架，我们取得了洛瓦斯铰链一致的目标损失。我们称之为结构化的弃用问题的目标使一个人可以在$ k $预测的任何子集上弃权。我们得出了两个链接函数，每个链接函数对于所有子模型集合函数都一致。
The Lovász hinge is a convex surrogate recently proposed for structured binary classification, in which $k$ binary predictions are made simultaneously and the error is judged by a submodular set function. Despite its wide usage in image segmentation and related problems, its consistency has remained open. We resolve this open question, showing that the Lovász hinge is inconsistent for its desired target unless the set function is modular. Leveraging a recent embedding framework, we instead derive the target loss for which the Lovász hinge is consistent. This target, which we call the structured abstain problem, allows one to abstain on any subset of the $k$ predictions. We derive two link functions, each of which are consistent for all submodular set functions simultaneously.
