Abstract

We study Conformal Prediction (CP) in the practical and challenging regime where labeled training and calibration data observe only a subset of the label space. In this setting, classical Conformal guarantees no longer control marginal risk and naive unseen labels detection methods are either overconservative or uninformative. We introduce CP-POL, a simple operational pipeline that couples Split CP over observed labels with a calibrated novelty test and integrates Prediction-Powered Inference (PPI) for finite sample population estimation. We provide a non-asymptotic theory that (i) proves Le Cam impossibility result: novelty test from features alone is hopeless without structural assumptions, (ii) derives tight finite-sample coverage decompositions that isolate the role of the non-conforming event $s(X)>q$, (iii) gives Dvoretzky-Kiefer-Wolfowitz (DKW)-based conservative estimators and anytime martingale analogues for the novel mass function $\pi_{nov}$, (iv) identifies practically meaningful structural conditions under which strong guarantees for novel region prediction hold, and (v) proves finite-sample PPI bounds that cleanly separate sampling fluctuation, trained model error and novel-mass effects. We validate the theory with reproducible simulations. All bounds are non-asymptotic and designed for immediate use in deployed monitoring pipelines.