Replicable Conformal Prediction

Two analysts who calibrate the same predictive model on independent samples will deploy different prediction sets every time, because the calibration threshold inherits the randomness of the data. Wherever deployments must be audited, cached, or approved across sites, this instability is costly: no one can verify that two calibrations produced the same object. We ask two questions: when can independent calibrations yield the identical classifier, and what must that agreement cost? Perfect agreement is impossible, since a procedure that almost always returns one fixed answer cannot remain valid for every distribution, and exact agreement through shared randomness forces the procedure to ignore its data. Sharing a single random seed and rounding the calibrated threshold up to a coarse shared grid resolves the tension: the deployed classifier becomes identical across analysts with any desired probability, coverage guarantees survive, and the price is a quantified increase in set size and calibration data. Matching lower bounds show that no threshold method can pay less, and the method's one tuning constant vanishes asymptotically. Without any shared seed, a fixed grid still confines all analysts to two adjacent classifiers, and no method does better. Replicability also blocks gaming: selecting the most favorable of many recalibrations barely moves a replicable classifier, while the same selection silently undercovers standard conformal prediction. Experiments on real ImageNet outputs, a four-hospital site split, and four language-model families match the theory, including the measured sample-cost frontier.

Generalized Hierarchical Conformal Prediction

Many prediction problems arise with data collected in groups. In this setting, hierarchical conformal prediction (HCP) (Lee et al., 2026) provides distribution-free prediction sets for a new observation from a previously unseen group under hierarchical exchangeability. In many applications, however, prediction is conducted only after a few observations from the group of interest have already been collected. Standard HCP cannot leverage these observations, as its required symmetry conditions do not hold in this setting. At the same time, the initial sample may still be too small for standard conformal prediction applied within the test group to be informative. We develop predictive inference methods for this setting. Our proposed method, Generalized HCP (GHCP), restores the relevant symmetry needed for conformal inference by assigning the test group a randomly "donated" reference group size. GHCP further leverages the initial test group observations to improve the quality of the nonconformity scores for prediction within that group. To improve efficiency, we introduce a variant that restricts the set of eligible donors. We demonstrate the performance of the proposed method through simulations and an illustration on the American Community Survey dataset.

Robust Bayes-Assisted Conformal Prediction

Bayes-assisted conformal prediction combines the strengths of Bayesian modelling with exact, distribution-free frequentist coverage guarantees. Although conformal validity is preserved even when the Bayesian working model (BWM) is misspecified, the size of the resulting prediction sets can degrade substantially when the prior is poorly aligned with the observed data. We address this limitation by introducing RoBAS (Robust Bayes-Assisted Shrinkage): a Bayes-assisted framework for constructing robust nonconformity scores, with two instantiations: one induced by a heavy-tailed BWM, and a closed-form empirical Bayes shrinkage score. The resulting scores adapt to the quality of the working information encoded in the prior: when this information is reliable, they exploit it to produce efficient prediction sets; when it is weak or inaccurate, they revert to the Distance-To-Average (DTA) score, a robust non-informative baseline. We evaluate the proposed scores on tabular and image regression tasks where the training distribution may differ from the calibration and test distributions, while the calibration and test data themselves remain exchangeable. We find that they are competitive with widely used scores in the absence of such shift, while substantially reducing interval widths in shifted settings.

Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score

Ordinal classification (OC) arises in high-stakes domains such as medicine and finance, where uncertainty quantification must account for the severity of ordinal errors. Conformal prediction (CP) provides distribution-free prediction sets with marginal coverage guarantees; however, its practical effectiveness depends critically on the choice of nonconformity function. We introduce a CP method for ordinal classification based on the ranked probability score (RPS), a proper scoring rule defined over cumulative predictive distributions. Although it reflects ordinal risk quite naturally, it has largely been neglected in conformal ordinal prediction (COP). When used as a measure of nonconformity, RPS yields median-centered contiguous prediction sets by construction. The method is model-agnostic, supports both assessed and grouped ordered categorical outcomes, and permits efficient implementation compared to greedy interval selection procedures. Across multiple ordinal image and tabular datasets, RPS-based CP produces contiguous prediction sets and strikes a favorable balance between prediction set width and the magnitude of ordinal miscoverage relative to existing CP methods.