Generalized Fast Exact Conformalization

Conformal prediction converts nearly any point estimator into a prediction interval under standard assumptions while ensuring valid coverage. However, the extensive computational demands of full conformal prediction are daunting in practice, as it necessitates a comprehensive number of trainings across the entire latent label space. Unfortunately, existing efforts to expedite conformalization often carry strong assumptions and are developed specifically for certain models, or they only offer approximate solution sets. To address this gap, we develop a method for fast exact conformalization of generalized statistical estimation. Our analysis reveals that the structure of the solution path is inherently piecewise smooth, and indicates that utilizing second-order information of difference equations suffices to approximate the entire solution spectrum arbitrarily. We provide a unified view that not only encompasses existing work but also attempts to offer geometric insights.