We introduce Rolling Conformal Prediction (rolling-CP), a distribution-free predictive inference method for the setting of sequential model training.
Specifically, given a data stream $(X_1,Y_1),(X_2,Y_2),\dots$, at each time $n$ the trained model may depend on the observed history $\{(X_i,Y_i)\}_{i
Rolling-CP first calibrates each incoming observation against the current predictor and then rolls it into future training. In this way, we avoid the need for data splitting.
Remarkably, although the models at times $n=1,2,\dots$ may have entirely different properties and accuracy levels, for exchangeable data it is nonetheless possible to establish a guarantee of marginal coverage, with a familiar universal factor-two guarantee (a worst case guarantee of $1-2α$ coverage, as compared to the target level $1-α$), without any assumptions of stability or any restrictions on the model training process.
For i.i.d. data streams, we further prove high-probability training-conditional validity uniformly over time; under stability conditions, coverage guarantees sharpen towards $1-α$.
Numerical experiments on sequential regression, multiclass SGD, and one-pass neural-network training further demonstrate the practical effectiveness of rolling-CP.