In large-scale hypothesis testing, computing exact $p$-values or $e$-values is often resource-intensive, creating a need for budget-aware inferential methods. We propose a general framework for active hypothesis testing that leverages inexpensive auxiliary statistics to allocate a global computational budget. For each hypothesis, our data-adaptive procedure probabilistically decides whether to compute the exact test statistic or a transformed proxy, guaranteeing a valid $p$-value or $e$-value while satisfying the budget constraint in expectation. Theoretical guarantees are established for our constructions, showing that the procedure achieves optimality for $e$-values and for $p$-values under independence, and admissibility for $p$-values under general dependence. Empirical results from simulations and two real-world applications, including a large-scale genome-wide association study (GWAS) and a clinical prediction task leveraging large language models (LLM), demonstrate that our framework improves statistical efficiency under fixed resource limits.

翻译：在大规模假设检验中，计算精确的$p$值或$e$值通常需要大量计算资源，因此需要开发预算感知的推断方法。本文提出了一种主动假设检验的通用框架，该框架利用廉价的辅助统计量来分配全局计算预算。对于每个假设，我们的数据自适应过程以概率方式决定是计算精确检验统计量还是转换后的代理统计量，在保证$p$值或$e$值有效性的同时，满足期望上的预算约束。我们为所构建的方法建立了理论保证，证明该过程在$e$值情形下达到最优性，在独立性假设下对$p$值达到最优性，并在一般依赖情形下对$p$值具有可采纳性。通过仿真实验和两个实际应用（包括大规模全基因组关联研究和基于大型语言模型的临床预测任务）的实证结果表明，在固定资源限制下，我们的框架显著提升了统计效率。