In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores.

翻译：在许多场景中，为评估神经网络预测结果的优劣，人们设计了定制化且加权的分类评分指标。然而，在训练阶段，此类评分的最大化与损失函数的最小化之间存在不一致性。本文建立了一套完整的理论体系，该体系将加权分类度量形式化，进而能够构造出驱动模型优化这些目标度量的损失函数。在详细的理论分析之后，我们证明了该框架将经典代价敏感学习、加权交叉熵损失函数以及数值加权技能评分等成熟方法作为特例加以涵盖。