将多个不确定集合并为一个，通信少且保证覆盖精度。
Data-light Uncertainty Set Merging with Admissibility
- 用合成检验统计量聚合原始不确定集，再通过反演生成合并集。
- 在有限样本下仍保持可靠覆盖率，合并集大小合理。
- 适合分布式场景或不同算法结果融合，尤其通信受限时。
本文提出一种数据轻量的合成、聚合与检验反演（SAT）方法，用于将多个可能相关且来源各异的不确定集合并为单一统一集。该方法仅依赖初始集合及其名义水平，无需额外数据，可灵活适应用户指定的不同覆盖保证输入集。其动机源于在仅知初始集合与控制水平时的集成难题——例如在通信受限条件下整合分布式站点的置信集，或融合不同算法/数据划分产生的合规预测集。SAT通过构造并聚合新型合成检验统计量，再经检验反演获得合并集。方法基于集合估计与假设检验间的对偶性，确保在依赖场景下的可靠覆盖。理论分析证明了SAT在确定性集合合并中的可接受性；理论与实证结果共同验证了其在有限样本下的覆盖有效性及理想的集合规模。
原文摘要 · Abstract (English)
This article introduces a Synthetics, Aggregation, and Test inversion (SAT) approach for merging diverse and potentially dependent uncertainty sets into a single unified set. The procedure is data-light, relying only on initial sets and their nominal levels, and it flexibly adapts to user-specified input sets with possibly varying coverage guarantees. SAT is motivated by the challenge of integrating uncertainty sets when only the initial sets and their control levels are available-for example, when merging confidence sets from distributed sites under communication constraints or combining conformal prediction sets generated by different algorithms or data splits. To address this, SAT constructs and aggregates novel synthetic test statistics, and then derive merged sets through test inversion. Our method leverages the duality between set estimation and hypothesis testing, ensuring reliable coverage in dependent scenarios. A key theoretical contribution is a rigorous analysis of SAT's properties, including its admissibility in the context of deterministic set merging. Both theoretical analyses and empirical results confirm the method's finite-sample coverage validity and desirable set sizes.
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