Multi-Variable Conformal Prediction: Optimizing Prediction Sets using Multiple Calibration Variables
Read the original on arXiv Statistics ML →The paper introduces Multi-Variable Conformal Prediction (MCP), a framework that jointly optimizes and calibrates multiple prediction‑set parameters in a single optimization problem, thereby eliminating the need for a calibration data split while preserving finite‑sample coverage guarantees. Two tractable variants are proposed: RemMCP, which uses constrained optimization with constraint removal and generalizes split conformal prediction, and RelMCP, which employs penalized optimization with constraint relaxation and can handle non‑convex problems. Experiments on ellipsoidal and multi‑modal prediction sets show that both RemMCP and an adaptive version of RelMCP consistently achieve target coverage with lower variance across calibration runs and, in most cases, produce smaller or comparable prediction sets compared to baseline methods.
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