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<p>Current metrics for binary classification, like the Area Under the Receiver Operating Characteristic curve (AUC-ROC) or Log Loss, provide a global performance score. However, they do not quantify predictive quality separately for event and non-event classes. This limitation is particularly critical in imbalanced settings like medical diagnostics. To address it, we introduce the U-smile Likelihood Evaluation (LE) method, a substantial extension of the original U-smile framework. The U-smile LE method is based on a new metric called the relative Likelihood Ratio (rLR). This single score measures overall model strength without needing a classification threshold. We decompose this score into two class-specific components: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{rLR}_{1}\)</EquationSource> </InlineEquation> for event class and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{rLR}_{0}\)</EquationSource> </InlineEquation> for non-event class, visualizing them simultaneously in a compact U-shaped plot. We validated the U-smile LE method on synthetic datasets with varying class imbalance and a real-world clinical Heart Disease dataset. In severely imbalanced scenarios (90/10 class distribution), stepwise variable selection guided by U-smile LE outperformed traditional AUC-based selection, improving minority-class detection by 16% in the Area Under the Precision-Recall curve (AUC-PR) and 21% in F1-score. The evolution of U-smile patterns during variable selection provided clear, interpretable insight into class-specific contributions of individual predictors. Demonstrated with both logistic regression and random forest models, U-smile LE offers an explainable, model-agnostic framework for evaluating binary classifiers, especially valuable where class imbalance and interpretability are key concerns.</p>

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Usmile likelihood evaluation provides robust threshold free assessment of binary classification models for balanced and imbalanced datasets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月20日

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  • Barbara Więckowska,
  • Przemysław Guzik

摘要

Current metrics for binary classification, like the Area Under the Receiver Operating Characteristic curve (AUC-ROC) or Log Loss, provide a global performance score. However, they do not quantify predictive quality separately for event and non-event classes. This limitation is particularly critical in imbalanced settings like medical diagnostics. To address it, we introduce the U-smile Likelihood Evaluation (LE) method, a substantial extension of the original U-smile framework. The U-smile LE method is based on a new metric called the relative Likelihood Ratio (rLR). This single score measures overall model strength without needing a classification threshold. We decompose this score into two class-specific components: \(\:{rLR}_{1}\) for event class and \(\:{rLR}_{0}\) for non-event class, visualizing them simultaneously in a compact U-shaped plot. We validated the U-smile LE method on synthetic datasets with varying class imbalance and a real-world clinical Heart Disease dataset. In severely imbalanced scenarios (90/10 class distribution), stepwise variable selection guided by U-smile LE outperformed traditional AUC-based selection, improving minority-class detection by 16% in the Area Under the Precision-Recall curve (AUC-PR) and 21% in F1-score. The evolution of U-smile patterns during variable selection provided clear, interpretable insight into class-specific contributions of individual predictors. Demonstrated with both logistic regression and random forest models, U-smile LE offers an explainable, model-agnostic framework for evaluating binary classifiers, especially valuable where class imbalance and interpretability are key concerns.