Universal distribution of the empirical coverage in split conformal prediction
This work provides a theoretical foundation for practitioners using split conformal prediction to ensure reliable coverage in applications.
The paper determines the exact universal distribution of empirical coverage in split conformal prediction for finite and infinite batch sizes, establishing a criterion for selecting the minimum calibration sample size based on nominal miscoverage level and calibration sample size.
When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact distribution of its almost sure limit when the batch size goes to infinity. Both distributions are universal, being determined solely by the nominal miscoverage level and the calibration sample size, thereby establishing a criterion for choosing the minimum required calibration sample size in applications.