Conformal Prediction with Upper and Lower Bound Models
This addresses the challenge of reliable uncertainty quantification in regression for applications like parametric optimization, though it is incremental as it builds on existing conformal prediction frameworks.
The paper tackles the problem of building prediction intervals in regression when only deterministic bounds on the target variable are available, proposing a new conformal prediction method (CPUL-OMLT) that improves coverage in tight regions and shows substantial improvements over baselines on large-scale tasks.
This paper studies a Conformal Prediction (CP) methodology for building prediction intervals in a regression setting, given only deterministic lower and upper bounds on the target variable. It proposes a new CP mechanism (CPUL) that goes beyond post-processing by adopting a model selection approach over multiple nested interval construction methods. Paradoxically, many well-established CP methods, including CPUL, may fail to provide adequate coverage in regions where the bounds are tight. To remedy this limitation, the paper proposes an optimal thresholding mechanism, OMLT, that adjusts CPUL intervals in tight regions with undercoverage. The combined CPUL-OMLT is validated on large-scale learning tasks where the goal is to bound the optimal value of a parametric optimization problem. The experimental results demonstrate substantial improvements over baseline methods across various datasets.