Single Trajectory Conformal Prediction
This work addresses the challenge of reliable uncertainty quantification in sequential data for applications like time-series forecasting, though it appears incremental by extending existing conformal prediction methods to correlated settings.
The paper tackles the problem of applying risk-controlling prediction sets (RCPS) to temporally correlated data from unknown stochastic dynamical systems, showing that RCPS achieves performance guarantees similar to i.i.d. settings under asymptotically stationary and contractive dynamics, and characterizes degradation under deviations from these conditions.
We study the performance of risk-controlling prediction sets (RCPS), an empirical risk minimization-based formulation of conformal prediction, with a single trajectory of temporally correlated data from an unknown stochastic dynamical system. First, we use the blocking technique to show that RCPS attains performance guarantees similar to those enjoyed in the iid setting whenever data is generated by asymptotically stationary and contractive dynamics. Next, we use the decoupling technique to characterize the graceful degradation in RCPS guarantees when the data generating process deviates from stationarity and contractivity. We conclude by discussing how these tools could be used toward a unified analysis of online and offline conformal prediction algorithms, which are currently treated with very different tools.