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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.01423 |
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| _version_ | 1866910111322079232 |
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| author | Kuang, Qi Gang, Bowen Xia, Yin |
| author_facet | Kuang, Qi Gang, Bowen Xia, Yin |
| contents | 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 exact budget constraint. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Active Hypothesis Testing under Computational Budgets with Applications to GWAS and LLM Kuang, Qi Gang, Bowen Xia, Yin Methodology 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 exact budget constraint. 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. |
| title | Active Hypothesis Testing under Computational Budgets with Applications to GWAS and LLM |
| topic | Methodology |
| url | https://arxiv.org/abs/2512.01423 |