Single Trajectory Conformal Prediction

Brian Lee, Nikolai Matni

Abstract: We study the performance of risk-controlling prediction sets (RCPS), an empirical risk minimization-based formulation of conformal prediction, on a single trajectory of data from an unknown stochastic process. Our analysis characterizes the graceful degradation in RCPS performance as data becomes nearly arbitrarily dependent and nonstationary, subject only to a mild requirement that the underlying process is causal. By specializing this analysis, we find that RCPS attains guarantees comparable to those enjoyed on independent and identically distributed data whenever data is generated by an asymptotically stationary and mixing process. We then relate these conditions to system-theoretic properties like contractivity.