A Novel Characterization of the Population Area Under the Risk Coverage Curve (AURC) and Rates of Finite Sample Estimators

TL;DR

This paper introduces a new statistical framework for the population AURC metric in selective classifiers, along with consistent finite-sample estimators validated through extensive experiments.

Contribution

It provides a formal statistical formulation of population AURC and develops consistent, low-bias estimators with proven convergence rates for finite samples.

Findings

Estimators are statistically consistent with low bias.

Convergence rate of estimators is $oxed{ ext{O}(rac{ ext{sqrt}( ext{ln}(n))}{n})}$.

Empirical validation across multiple datasets confirms estimator effectiveness.

Abstract

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.