Title: Generative Conformal Prediction with Optimized Coverage Allocation
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Conformal Prediction, Uncertainty Quantification, Generative Model

Abstract: Conformal prediction provides model-agnostic uncertainty quantification with guaranteed coverage, but conventional methods often yield overly conservative uncertainty sets, particularly in multimodal or heterogeneous settings. This inefficiency arises from two sources: (i) limited expressiveness of the predictive model and (ii) simplistic nonconformity scores design. Most existing approaches advance only one of these axes, leaving the other underexplored. We propose *generative conformal prediction with* ***O**ptimized* ***R**anking and **C**overage **A**llocation (ORCA)*, a three-stage framework that advances both aspects jointly. ORCA leverages generative models to capture the full conditional distribution and introduces a rank-dependent optimization procedure that adaptively allocates coverage for efficiency while maintaining validity. We cast this coverage allocation as an optimization problem, derive an exact mixed-integer linear programming formulation, and show that the solution converges asymptotically to the oracle density-level set. Across synthetic, semi-synthetic, and real datasets, ORCA produces substantially more efficient uncertainty sets than state-of-the-art baselines, demonstrating robust gains in scenarios where conventional conformal prediction methods fail.