可交换性下统计证据的聚合
Aggregation of Statistical Evidence under Exchangeability
浏览论文内容
中文总结 AI 辅助
研究在未知复杂依赖下统计证据的聚合，基于群不变性和排列构造，发展理论及多种聚合版本，其临界值优于确定性校准，能适应未知依赖，还应用于相关领域改进现有方法。
中文摘要 AI 辅助
我们利用群不变性研究在未知且潜在复杂依赖关系下统计证据的聚合。基于将变换后的数据集视为可交换单元的基于排列的构造，我们对每个变换后的数据集跨统计量聚合证据，并在变换间校准所得聚合。我们为此框架发展了有限样本功效和适应性理论，以及对保持有效性的顺序和数据依赖聚合的扩展。对于单批次聚合，我们表明临界值在任意依赖下有效的确定性校准（包括邦费罗尼校正）上均匀改进，同时适应未知依赖结构。我们还引入了允许在证据强时提前拒绝的顺序α花费版本，以及将标准化与校准分离以适应学习到的聚合规则并减少计算的两批次扩展。自适应非参数检验和共形预测的应用说明了这些结果如何改进现有聚合方法。
英文摘要
We study aggregation of statistical evidence under unknown and potentially complex dependence using group-invariance. Building on permutation-based constructions that treat transformed datasets as exchangeable units, we aggregate evidence across statistics for each transformed dataset and calibrate the resulting aggregates across transformations. We develop a finite-sample power and adaptivity theory for this framework, together with extensions to sequential and data-dependent aggregation that preserve validity. For single-batch aggregation, which uses one collection of transformed datasets for both standardization and calibration, we show that the critical values uniformly improve on deterministic calibrations valid under arbitrary dependence, including Bonferroni correction, while adapting to the unknown dependence structure. We also introduce a sequential alpha-spending version that permits early rejection when evidence is strong, and a two-batch extension that separates standardization from calibration to accommodate learned aggregation rules and reduce computation. Applications to adaptive nonparametric testing and conformal prediction illustrate how these results sharpen existing aggregation methods.
发表机构
- University of Cambridge（剑桥大学）
- University College London（伦敦大学学院）
- KAIST（韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。
