Convergence-rate improvement via differential conformal adjustment

Determine whether the differential conformal procedure that selects per-interval endpoint adjustments by minimizing the Euclidean norm of the adjustment vector subject to the calibration coverage constraint—i.e., choosing w = (w_{01},…,w_{1M}) to minimize ||w|| so that the adjusted set \tilde{C}_M = \bigcup_m [\hat{\tau}_{0m} - w_{0m}, \hat{\tau}_{1m} + w_{1m}] achieves calibration coverage P_{\mathcal{I}_2}(s(Y^L_j, Y^U_j; \tilde{C}_M) \le 0) \gtrsim 1 - \alpha—improves the asymptotic convergence rate of the conformal prediction set estimator for interval-censored outcomes compared to the uniform single-quantile endpoint adjustment that shifts all interval endpoints by the same calibration quantile.

Background

The paper constructs conformal prediction sets for interval-censored outcomes and proves finite-sample marginal validity using a score-based split conformal method. In the main construction, all endpoints of the estimated prediction set are adjusted uniformly by the same calibration quantile obtained from a calibration set.

To potentially improve efficiency and convergence, the authors propose in the appendix a differential conformal procedure that adjusts endpoints per interval by solving a minimal Euclidean norm optimization subject to the calibration coverage constraint. They conjecture that this tailored adjustment could yield faster convergence of the conformal prediction set to the oracle prediction set, but they do not provide a proof or rate comparison.