Conformal Tradeoffs: Guarantees Beyond Coverage

Abstract

Deployed conformal predictors are long-lived decision infrastructure operating over finite operational windows. The real-world question is not only ``Does the true label lie in the prediction set at the target rate?'' (marginal coverage), but ``How often does the system commit versus defer? What error exposure does it induce when it acts? How do these rates trade off?'' Marginal coverage does not determine these deployment-facing quantities: the same calibrated thresholds can yield different operational profiles depending on score geometry. We provide a framework for operational certification and planning beyond coverage with three contributions. (1) Small-Sample Beta Correction (SSBC): we invert the exact finite-sample Beta/rank law for split conformal to map a user request $(α^\star,δ)$ to a calibrated grid point with PAC-style semantics, yielding explicit finite-window coverage guarantees. (2) Calibrate-and-Audit: since no distribution-free pivot exists for rates beyond coverage, we introduce a two-stage design in which an independent audit set produces a reusable region -- label table and certified finite-window envelopes (Binomial/Beta-Binomial) for operational quantities -- commitment frequency, deferral, decisive error exposure, and commit purity -- via linear projection. (3) Geometric characterization: we describe feasibility constraints, regime boundaries (hedging vs.\ rejection), and cost-coherence conditions induced by a fixed conformal partition, explaining why operational rates are coupled and how calibration navigates their trade-offs. The output is an auditable operational menu: for a fixed scoring model, we trace attainable operational profiles across calibration settings and attach finite-window uncertainty envelopes. We demonstrate the approach on Tox21 toxicity prediction (12 endpoints) and aqueous solubility screening using AquaSolDB.