Problem
Research questions and friction points this paper is trying to address.
Generative Conformal Prediction
Sample Efficiency
Uncertainty Sets
Adaptive Sample Allocation
Coverage
Sample-Efficient Generative Conformal Prediction
🤖 AI Summary
This study addresses the limitation of fixed sampling budgets in generative conformal prediction, which often causes under-coverage for complex distributions and sample wastage for simple ones. To this end, this work proposes CASA, a method that establishes the first theoretical framework for marginal sample value. By quantifying this marginal value to adaptively allocate sampling budgets, CASA minimizes prediction sets while satisfying coverage constraints. Theoretically, we prove that adaptive allocation outperforms fixed-count strategies, effectively mitigating radius inflation caused by mode omission. Empirical evaluations on both synthetic and real-world tasks demonstrate that CASA significantly reduces prediction set sizes and improves conditional coverage. Furthermore, the proposed approach is orthogonal and complementary to existing radius-adaptive methods.
📝 Abstract
Generative conformal prediction builds uncertainty sets from samples of a conditional generator, which are efficient only when the samples represent the response distribution well. This can require many samples, each of which can be costly, as in large diffusion models and scientific simulators, so the sampling budget must be used efficiently. Existing methods draw the same number of samples at every input, wasting samples where the response distribution is simple and undersampling where it is complex, which inflates sets and leaves those inputs under-covered. We propose CASA (Conformal Adaptive Sample Allocation), which characterizes the marginal value of an additional sample and allocates samples across inputs to minimize the expected set size subject to marginal coverage and an average sampling budget. Theoretical analysis shows that adaptive allocation yields smaller sets than a fixed count at the same budget: a missed mode forces a radius that spans the gap between modes, and even oracle radius cannot compensate for it. On synthetic and real tasks, CASA produces substantially smaller sets at the same budget, often improves conditional coverage, and complements existing radius-adaptive methods.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Generative Conformal Prediction
Adaptive Sample Allocation
Sample Efficiency
Uncertainty Quantification
Marginal Coverage
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