论文标题
关于多类分类的损失功能和后悔界限
On loss functions and regret bounds for multi-category classification
论文作者
论文摘要
我们在多级设置中开发了新方法，以构建适当的评分规则和铰链式损失，并建立相应的遗憾界限，相对于零零或成本加权的分类损失。我们的损失构建涉及从凹入的熵熵中得出新的反映射，从使用与多分布$ f $ divergence相关的凸差异函数来损失。此外，我们确定了新的多级适当评分规则的新类别，这些规则还恢复并揭示了当前正在使用的各种综合损失之间的有趣关系。我们通过利用相关的广义熵的布雷格曼分歧来建立新的分类对多级适当评分规则的遗憾界限，并在应用程序中为两个特定的适当评分规则提供了简单的有意义的遗憾界限。最后，我们得出了新的类似铰链的凸损失，与相关的铰链样损失相比，凸的扩展更紧密，几何而变得更简单，而非差异的边缘更少，同时达到了类似的遗憾界限。我们还为所有损失造成了与零一损的一般性熵的所有损失的遗憾。
We develop new approaches in multi-class settings for constructing proper scoring rules and hinge-like losses and establishing corresponding regret bounds with respect to the zero-one or cost-weighted classification loss. Our construction of losses involves deriving new inverse mappings from a concave generalized entropy to a loss through the use of a convex dissimilarity function related to the multi-distribution $f$-divergence. Moreover, we identify new classes of multi-class proper scoring rules, which also recover and reveal interesting relationships between various composite losses currently in use. We establish new classification regret bounds in general for multi-class proper scoring rules by exploiting the Bregman divergences of the associated generalized entropies, and, as applications, provide simple meaningful regret bounds for two specific classes of proper scoring rules. Finally, we derive new hinge-like convex losses, which are tighter convex extensions than related hinge-like losses and geometrically simpler with fewer non-differentiable edges, while achieving similar regret bounds. We also establish a general classification regret bound for all losses which induce the same generalized entropy as the zero-one loss.
