论文标题
一致的多面体代理，用于顶级$ K $分类和变体
Consistent Polyhedral Surrogates for Top-$k$ Classification and Variants
论文作者
论文摘要
Top-$ K $分类是对信息检索，图像分类和其他极端分类设置中广泛使用的多类分类的概括。为此，已经提出了几种类似铰链的（分段线性）替代物，但所有这些都不是不一致的或不一致的。对于提出的凸状替代物（即多面体），我们采用了Finocchiaro等人的最新嵌入框架。 （2019; 2022）确定替代物是一致的预测问题。这些问题都可以解释为顶级$ K $分类的变体，这可能与某些应用程序更好。我们利用此分析来获得对条件标签分布的限制，这些分布在这些分布中，这些拟议的代理人在顶部$ k $中变得一致。有人进一步建议，对于顶部$ k $，每个凸铰链样的替代物都必须不一致。但是，我们使用相同的嵌入框架为此问题提供了第一个一致的多面体代理。
Top-$k$ classification is a generalization of multiclass classification used widely in information retrieval, image classification, and other extreme classification settings. Several hinge-like (piecewise-linear) surrogates have been proposed for the problem, yet all are either non-convex or inconsistent. For the proposed hinge-like surrogates that are convex (i.e., polyhedral), we apply the recent embedding framework of Finocchiaro et al. (2019; 2022) to determine the prediction problem for which the surrogate is consistent. These problems can all be interpreted as variants of top-$k$ classification, which may be better aligned with some applications. We leverage this analysis to derive constraints on the conditional label distributions under which these proposed surrogates become consistent for top-$k$. It has been further suggested that every convex hinge-like surrogate must be inconsistent for top-$k$. Yet, we use the same embedding framework to give the first consistent polyhedral surrogate for this problem.
