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Arxiv
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On the Geometry of Receiver Operating Characteristic and Precision-Recall Curves
- The study focuses on the geometry of Receiver Operating Characteristic (ROC) and Precision-Recall (PR) curves in binary classification problems.
- Many commonly used binary classification metrics are found to be functions of a composition function G := F_p ∘ F_n⁻¹.
- G is defined by the class-conditional cumulative distribution functions of classifier scores in positive (F_p(·)) and negative (F_n(·)) classes.
- The geometric perspective aids in selecting operating points, understanding decision thresholds, and comparing classifiers.
- It explains how the shapes and geometry of ROC/PR curves reflect classifier behavior, aiding in building optimized classifiers for specific applications with constraints.
- The study explores conditions for classifier dominance and provides examples showing the impact of class separability and variance on ROC and PR curves.
- A link is derived between the positive-to-negative class leakage function G(·) and the Kullback--Leibler divergence.
- Practical considerations like model calibration, cost-sensitive optimization, and operating point selection under real-world constraints are emphasized.
- This framework enables more informed approaches to classifier deployment and decision-making.
- The study provides objective tools for building classifiers optimized for specific contexts and constraints.
- Analytical and numerical examples are presented to demonstrate the effects of class separability and variance on ROC and PR geometries.
- The study enhances understanding of how ROC/PR curves reflect classifier behavior.
- The insights can help in selecting appropriate decision thresholds for different classifiers.
- The framework aids in comparing classifiers and selecting optimal operating points.
- Explanation is provided on how the geometry of ROC and PR curves influences classifier performance.
- The study bridges the positive-to-negative class leakage function and the Kullback--Leibler divergence, shedding light on classifier behavior.
- The research contributes to enhancing classifier performance for specific applications through a better understanding of the ROC and PR curve geometries.
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