论文标题
重新针对Van Rijsbergen的$f_β$度量，用于加权二进制跨境
Reformulating van Rijsbergen's $F_β$ metric for weighted binary cross-entropy
论文作者
论文摘要
绩效指标与基于梯度的损失功能的分离可能并不总是给出最佳结果，并且可能会错过重要的总体信息。本文调查了将性能指标与可区分损失功能合并，以告知培训结果。目的是通过在该性能指标上假设用于动态加权的统计分布来指导模型性能和解释。重点是Van Rijsbergens $F_β$ Metric，这是测量分类性能的流行选择。通过$F_β$的分布假设，可以通过动态惩罚权重建立中间链接与标准二进制跨熵。首先，$f_β$公制是重新重新制定的，以促进假设统计分布，并随附累积密度函数的证据。这些概率在膝盖曲线算法中使用，以找到最佳的$β$或$β_{opt} $。此$β_{opt} $在拟议的加权二进制跨透镜中用作重量或惩罚。与不平衡和平衡类别的基线相比，对公开数据以及基准分析的实验大多会产生更好，可解释的结果。例如，对于具有已知标签错误的IMDB文本数据，显示了$ f_1 $得分的14％提升。结果还揭示了本文中得出的惩罚模型家族与优化中以以召回或精度为中心参数的适用性。这种方法的灵活性可以增强解释。
The separation of performance metrics from gradient based loss functions may not always give optimal results and may miss vital aggregate information. This paper investigates incorporating a performance metric alongside differentiable loss functions to inform training outcomes. The goal is to guide model performance and interpretation by assuming statistical distributions on this performance metric for dynamic weighting. The focus is on van Rijsbergens $F_β$ metric -- a popular choice for gauging classification performance. Through distributional assumptions on the $F_β$, an intermediary link can be established to the standard binary cross-entropy via dynamic penalty weights. First, the $F_β$ metric is reformulated to facilitate assuming statistical distributions with accompanying proofs for the cumulative density function. These probabilities are used within a knee curve algorithm to find an optimal $β$ or $β_{opt}$. This $β_{opt}$ is used as a weight or penalty in the proposed weighted binary cross-entropy. Experimentation on publicly available data along with benchmark analysis mostly yields better and interpretable results as compared to the baseline for both imbalanced and balanced classes. For example, for the IMDB text data with known labeling errors, a 14% boost in $F_1$ score is shown. The results also reveal commonalities between the penalty model families derived in this paper and the suitability of recall-centric or precision-centric parameters used in the optimization. The flexibility of this methodology can enhance interpretation.
