Several variants of reweighted risk functionals, such as focal loss, inverse focal loss, and the Area Under the Risk--Coverage Curve (AURC), have been proposed for improving model calibration, yet their theoretical connections to calibration errors remain unclear. In this paper, we revisit a broad class of weighted risk functions commonly used in deep learning and establish a principled connection between calibration error and selective classification. We show that minimizing calibration error is closely linked to the selective classification paradigm and demonstrate that optimizing selective risk in low-confidence region naturally leads to improved calibration. This loss shares a similar reweighting strategy with dual focal loss but offers greater flexibility through the choice of confidence score functions (CSFs). Our approach uses a bin-based cumulative distribution function (CDF) approximation, enabling efficient gradient-based optimization without requiring expensive sorting and achieving $O(nK)$ complexity. Empirical evaluations demonstrate that our method achieves competitive calibration performance across a range of datasets and model architectures.

翻译：诸如Focal Loss、逆Focal Loss以及风险-覆盖曲线下面积（AURC）等加权风险泛函的多种变体已被提出用于改进模型校准，然而它们与校准误差之间的理论联系仍不明确。本文重新审视了深度学习中常用的一类广义加权风险函数，并在校准误差与选择性分类之间建立了原则性的联系。我们证明了最小化校准误差与选择性分类范式紧密相关，并论证了在低置信度区域优化选择性风险会自然地带来校准性能的提升。该损失函数与双重Focal Loss共享类似的加权策略，但通过置信度评分函数（CSF）的选择提供了更大的灵活性。我们的方法采用基于分箱的累积分布函数（CDF）近似，实现了无需昂贵排序的高效梯度优化，并达到了$O(nK)$的复杂度。实证评估表明，我们的方法在多种数据集和模型架构上均取得了具有竞争力的校准性能。