Conformal Prediction Through the Lens of Hypothesis Testing: Universality, Impossibility, and Optimality
The connections between conformal prediction and permutation tests are already widely-known in the literature. Some authors motivate conformal prediction by saying that it computes a permutation p-value for the hypothesis $H_0 : Y_{n+1} = y$, and then inverts this to form a prediction set for $Y_{n+1}$ (i.e., accepts a...