A Novel Characterization of the Population Area Under the Risk Coverage Curve (AURC) and Rates of Finite Sample Estimators
This work provides incremental improvements in statistical tools for assessing selective classifiers, which are important for safety-critical applications like medical diagnostics and autonomous driving.
The authors tackled the problem of evaluating selective classifiers by providing a formal statistical formulation of the population Area Under the Risk-Coverage Curve (AURC) and deriving finite sample estimators. They showed that their plug-in estimators are consistent with a convergence rate of O(√(ln(n)/n)) and validated them empirically across multiple datasets and model architectures.
The selective classifier (SC) has been proposed for rank based uncertainty thresholding, which could have applications in safety critical areas such as medical diagnostics, autonomous driving, and the justice system. The Area Under the Risk-Coverage Curve (AURC) has emerged as the foremost evaluation metric for assessing the performance of SC systems. In this work, we present a formal statistical formulation of population AURC, presenting an equivalent expression that can be interpreted as a reweighted risk function. Through Monte Carlo methods, we derive empirical AURC plug-in estimators for finite sample scenarios. The weight estimators associated with these plug-in estimators are shown to be consistent, with low bias and tightly bounded mean squared error (MSE). The plug-in estimators are proven to converge at a rate of $\mathcal{O}(\sqrt{\ln(n)/n})$ demonstrating statistical consistency. We empirically validate the effectiveness of our estimators through experiments across multiple datasets, model architectures, and confidence score functions (CSFs), demonstrating consistency and effectiveness in fine-tuning AURC performance.