  Uncertainty quantification and false selection error rate (FSR) control are
crucial in many high-consequence scenarios, so we need models with good
interpretability. This article introduces the optimality function for the
binary classification problem in selective classification. We prove the
optimality of this function in oracle situations and provide a data-driven
method under the condition of exchangeability. We demonstrate it can control
global FSR with the finite sample assumption and successfully extend the above
situation from binary to multi-class classification. Furthermore, we
demonstrate that FSR can still be controlled without exchangeability,
ultimately completing the proof using the martingale method.
