结构性弃权问题与Lovász铰链
The Structured Abstain Problem and the Lovász Hinge
摘要：
Lovász铰链是最近提出的一种用于结构化二元分类的凸代理，其中同时进行$k$二元预测，并通过子模集函数判断错误。尽管它在图像分割和相关问题中得到了广泛的应用，但它的一致性仍然是开放的。我们解决了这个悬而未决的问题，表明Lovász铰链是不一致的，其所需的目标，除非设置功能是模块化的。利用最近的嵌入框架，我们反而推导出Lovász铰链一致的目标损失。这个目标，我们称之为结构化弃权问题，允许人们对$k$预测的任何子集弃权。我们得到了两个链接函数，其中每一个是一致的所有子模集函数的同时。
英文摘要：
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.
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