Asymptotics for conformal inference

Understand

Conformal inference is a versatile tool for building prediction sets in regression or classification.

• We study the false coverage proportion (FCP) in a simultaneous inference setting with a calibration sample of $n$ points and a test sample of $m$ points.
• We identify the exact, distribution-free, asymptotic distribution of the FCP when both $n$ and $m$ tend to infinity.
• This shows in particular that FCP control can be achieved by using the well-known Kolmogorov distribution, and puts forward that the asymptotic variance is decreasing in the ratio $n/m$.