改进的平衡分类：基于理论的损失函数
Improved Balanced Classification with Theoretically Grounded Loss Functions
AI总结：
本文提出两种改进的平衡分类损失函数，通过理论分析和实验验证，证明其在类别不平衡场景下具有更强的理论保证和更好的性能表现。
摘要：
平衡损失是处理类别不平衡的多类分类中广泛采用的目标。通过赋予所有类别相等的重要性，无论其频率如何，它促进了公平性，并确保少数类不被忽视。然而，直接最小化平衡分类损失通常是不可行的，这使得设计有效的替代损失函数成为核心问题。本文介绍了并研究了两种先进的替代损失家族：广义对数调整（GLA）损失函数和广义类感知加权（GCA）损失。GLA损失扩展了对数调整损失，即根据类别先验调整logits，到更广泛的交叉熵损失家族。GCA损失扩展了标准的类加权损失，即通过类频率逆向缩放损失，通过引入类依赖的置信度边缘并扩展到一般的交叉熵家族。我们对这两种损失家族的相容性进行了全面的理论分析。我们证明GLA损失是贝叶斯一致的，但仅在完全（即无界）的假设集中是H一致的。此外，它们的H一致性界限与最小类概率成反比，至少以1/p_min的速度增长。相比之下，GCA损失在任何有界或完全的假设集中都是H一致的，其H一致性界限以1/sqrt(p_min)的速度增长，提供了在不平衡设置中更强的理论保证。我们报告了实验结果，显示在经验上，具有校准的类依赖置信度边缘的GCA损失和GLA损失在很大程度上优于传统的类加权损失以及LA损失。GLA通常在常规基准测试中略胜一筹，而GCA在高度不平衡的设置中略占优势。
英文摘要：
The balanced loss is a widely adopted objective for multi-class classification under class imbalance. By assigning equal importance to all classes, regardless of their frequency, it promotes fairness and ensures that minority classes are not overlooked. However, directly minimizing the balanced classification loss is typically intractable, which makes the design of effective surrogate losses a central question. This paper introduces and studies two advanced surrogate loss families: Generalized Logit-Adjusted (GLA) loss functions and Generalized Class-Aware weighted (GCA) losses. GLA losses generalize Logit-Adjusted losses, which shift logits based on class priors, to the broader general cross-entropy loss family. GCA loss functions extend the standard class-weighted losses, which scale losses inversely by class frequency, by incorporating class-dependent confidence margins and extending them to the general cross-entropy family. We present a comprehensive theoretical analysis of consistency for both loss families. We show that GLA losses are Bayes-consistent, but only $H$-consistent for complete (i.e., unbounded) hypothesis sets. Moreover, their $H$-consistency bounds depend inversely on the minimum class probability, scaling at least as $1/\mathsf p_{\min}$. In contrast, GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p_{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings. We report the results of experiments demonstrating that, empirically, both the GCA losses with calibrated class-dependent confidence margins and GLA losses can greatly outperform straightforward class-weighted losses as well as the LA losses. GLA generally performs slightly better in common benchmarks, whereas GCA exhibits a slight edge in highly imbalanced settings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
