Empirical Optimal Risk to Quantify Model Trustworthiness for Failure Detection

Failure detection (FD) in AI systems is a crucial safeguard for the deployment for safety-critical tasks. The common evaluation method of FD performance is the Risk-coverage (RC) curve, which reveals the trade-off between the data coverage rate and the performance on accepted data. One common way to quantify the RC curve by calculating the area under the RC curve. However, this metric does not inform on how suited any method is for FD, or what the optimal coverage rate should be. As FD aims to achieve higher performance with fewer data discarded, evaluating with partial coverage excluding the most uncertain samples is more intuitive and meaningful than full coverage. In addition, there is an optimal point in the coverage where the model could achieve ideal performance theoretically. We propose the Excess Area Under the Optimal RC Curve (E-AUoptRC), with the area in coverage from the optimal point to the full coverage. Further, the model performance at this optimal point can represent both model learning ability and calibration. We propose it as the Trust Index (TI), a complementary evaluation metric to the overall model accuracy. We report extensive experiments on three benchmark image datasets with ten variants of transformer and CNN models. Our results show that our proposed methods can better reflect the model trustworthiness than existing evaluation metrics. We further observe that the model with high overall accuracy does not always yield the high TI, which indicates the necessity of the proposed Trust Index as a complementary metric to the model overall accuracy. The code are available at \url{https://github.com/AoShuang92/optimal_risk}.