arXiv：cs.LG· Patrick Forr\'e, Lydia Brenner·· 7 小时前AI 评分28
基于模拟的 anytime-valid 假设检验
Anytime-valid simulation-based hypothesis testing
AI 导读
针对仅有模拟样本、无解析密度的场景，研究者构建了 e-test 鞅，用于 $H_0: Q = P_0$ 对 $H_1: Q = P_1$ 的假设检验。该序贯检验具备 anytime-valid 的 type-I 错误保证、近似增长最优性、几何衰减的 type-II 错误界，以及渐近功效为 1。论文以紧凑方式给出了这一 density-free 模拟序贯检验的有效方案。
正文
Abstract:For a given data distribution $(X_t)_{t \in \mathbb{N}} \sim Q$ i.i.d., we investigate the hypothesis testing problem: $H_0: Q = P_0$ vs. $H_1: Q = P_1$, for two different model probability distributions $P_0$ and $P_1$. In contrast to the standard setting, where analytic densities $p_0$ and $p_1$ are given, here, we consider the density-free setting, where we only have access to i.i.d. simulations $(Z^0_t)_{t \in \mathbb{N}} \sim P_0$ and $(Z^1_t)_{t \in \mathbb{N}} \sim P_1$. For this simulation-based hypothesis testing setting, we construct an e-test martingale, resulting in a sequential test with anytime-valid type-I error guarantees, approximate growth optimality, geometrically decaying type-II error bounds, and asymptotic power one. Most ingredients used in our constructions are variants of well known concepts. The value of this paper lies in the compact presentation of an effective, anytime-valid solution for the density-free simulation-based sequential hypothesis testing case.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME) |
| Cite as: | arXiv:2610.08210 [stat.ML] |
| (or arXiv:2610.08210v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08210 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Patrick Forré [view email]
[v1]
Tue, 6 Oct 2026 12:03:25 UTC (28 KB)
来源：arXiv：cs.LG · arxiv.org