  This paper proposes probabilistic conformal prediction (PCP), a predictive
inference algorithm that estimates a target variable by a discontinuous
predictive set. Given inputs, PCP construct the predictive set based on random
samples from an estimated generative model. It is efficient and compatible with
either explicit or implicit conditional generative models. Theoretically, we
show that PCP guarantees correct marginal coverage with finite samples.
Empirically, we study PCP on a variety of simulated and real datasets. Compared
to existing methods for conformal inference, PCP provides sharper predictive
sets.
