Generative Conformal Prediction with Optimized Coverage Allocation

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 Optimized Ranking and Coverage Allocation (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.