SoftMCC：用于类别不平衡下无阈值模型选择的MCC-Brier校准桥梁
SoftMCC: An MCC-Brier Calibration Bridge for Threshold-Free Model Selection under Class Imbalance
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- Sakarya University（萨卡里亚大学）
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中文总结 AI 辅助
SoftMCC是一种用于类别不平衡二分类的无阈值模型选择框架，耦合MCC校准恒等式与共享池选择协议，在18种设置中稳定性排名最优，为校准敏感的MCC家族选择器。
中文摘要 AI 辅助
针对不平衡二分类问题的模型选择常使用马修斯相关系数（MCC），但阈值化会使验证排名依赖于所选阈值。SoftMCC是一种基于已建立的概率值混淆计数的训练后MCC验证框架，耦合了MCC特定的校准恒等式与感知平局的共享池选择协议。其核心得分是协方差归一化的概率-标签关联，对于硬预测会精确退化为MCC，且具有皮尔逊界。在完美总体校准下，它等于具有相同候选排序的Brier技能得分；在该范围之外，其差距并不能标识校准误差。在包含12次安全分组重复的18种设置中，SoftMCC取得了最佳稳定性平均排名（2.31）和最高的平均平局校正肯德尔W值（0.659），弗里德曼检验显示结果具有显著性（p=0.007）；内梅尼分析将其与AUPRC和MCC@0.5区分开，而14个源族敏感性分析仅保留了后者。所选模型效用未显示出优势：6个预设比较中有3个的平均测试-MCC差异为负，仅F1@best通过霍尔姆校正（p=0.014），数据集水平测试不显著（p=0.117）。标签置换将平均W降至0.092；温度缩放会改变SoftMCC排名（平均斯皮尔曼相关系数为0.851），而基于排名和阈值优化的指标保持不变。SoftMCC是一种对校准敏感的MCC家族选择器，具有有界的稳定性和效用证据。
英文摘要
Model selection for imbalanced binary classification often uses the Matthews correlation coefficient (MCC), but thresholding makes validation rankings threshold-dependent. SoftMCC is a post-training MCC validation framework on established probability-valued confusion counts, coupling an MCC-specific calibrated identity with a tie-aware, shared-pool selection protocol. Its core score is a covariance-normalized probability-label association, reduces exactly to MCC for hard predictions, and is Pearson-bounded. Under perfect population calibration it equals the Brier skill score with identical candidate ordering; outside that regime the gap does not identify calibration error. Across 18 settings with 12 duplicate-safe grouped repeats, SoftMCC attains the best stability mean rank (2.31) and highest mean tie-corrected Kendall's W (0.659), with a significant Friedman test (p=0.007); Nemenyi analysis separates it from AUPRC and MCC@0.5, while 14-source-family sensitivity retains only the latter. Selected-model utility shows no advantage. Three of six prespecified comparisons have negative mean test-MCC differences, only F1@best survives Holm correction (p=0.014), and the dataset-level test is not significant (p=0.117). Label permutation lowers mean W to 0.092; temperature scaling shifts SoftMCC rankings (mean Spearman 0.851) whereas rank-based and threshold-optimized metrics remain invariant. SoftMCC is a calibration-sensitive MCC-family selector with bounded stability and utility evidence.
