aiqbench analysis
This paper proposes multi-variable conformal prediction, which tunes several prediction-set parameters jointly instead of only a single threshold, so no separate calibration split is needed while finite-sample coverage guarantees are kept. The two variants trade off differently: RemMCP is tractable and generalizes split conformal prediction, while RelMCP handles non-convex problems at higher computational cost. For ML practitioners working on uncertainty quantification, the practical question is whether the reported gains in set size and run-to-run variance hold beyond the ellipsoidal and multi-modal experiments tested.
Multi-Variable Conformal Prediction: Optimizing Prediction Sets using Multiple Calibration Variables
arXiv:2605.12341v2 Announce Type: replace-cross Abstract: Split conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is limited to adjusting a single threshold parameter. Hence, the shape of the prediction sets must be fixed beforehand, typically by fitting it on a reserved part of the calibration data. We introduce multi-variable conformal prediction (MCP), a framework that jointly optimizes and calibrates multiple prediction-set parameters in a single optimization problem, eliminating calibration data split without sacrificing finite-sample coverage guarantees. Building on scenario theory, a principled framework for certifying data-driven decisions, we propose two tractable variants: RemMCP, grounded in constrained optimization with constraint removal, which generalizes split conformal prediction; and RelMCP, based on penalized optimization with constraint relaxation, which also supports non-convex problems, albeit at a higher computational cost. In experiments with ellipsoidal and multi-modal prediction sets, RemMCP and a heuristic, adaptive version of RelMCP consistently meet the target coverage, with lower variance across calibration runs than baselines with calibration data split, and in most settings with smaller or comparable prediction sets.
Abstract:Split conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is limited to adjusting a single threshold parameter. Hence, the shape of the prediction sets must be fixed beforehand, typically by fitting it on a reserved part of the calibration data. We introduce multi-variable conformal prediction (MCP), a framework that jointly optimizes and calibrates multiple prediction-set parameters in a single optimization problem, eliminating calibration data split without sacrificing finite-sample coverage guarantees. Building on scenario theory, a principled framework for certifying data-driven decisions, we propose two tractable variants: RemMCP, grounded in constrained optimization with constraint removal, which generalizes split conformal prediction; and RelMCP, based on penalized optimization with constraint relaxation, which also supports non-convex problems, albeit at a higher computational cost. In experiments with ellipsoidal and multi-modal prediction sets, RemMCP and a heuristic, adaptive version of RelMCP consistently meet the target coverage, with lower variance across calibration runs than baselines with calibration data split, and in most settings with smaller or comparable prediction sets.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2605.12341 [stat.ML]
(or arXiv:2605.12341v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2605.12341 Focus to learn more arXiv-issued DOI via DataCite
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