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Asymmetric Likelihood-Free Hypothesis Testing

Gunjan Kumar, Yash Pote, Jonathan Scarlett · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29798 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

在低分布式假设数据测试(LFHT)中,从两个未知分布式 $P,Q$ 和 $[n]$ 进行分离假设测试(P,Q)\geq\varepsilon$),从第三个分布式 $D\in\{P,Q}$ 进行样本测试(LFHT),目标是确定 $D=P$ 或 $D=Q$. 我们研究非对称的假设测试,在那里样本预算 $s_P$ 和 $s_Q$ 对于 $P$ 和 $Q$ 可能有所不同,并特征可行的三倍 $(s_P,Q,Q,D) 是否升至逻辑因素。我们确立了不等式的分布式假设测试,在这种不等式的预算可以给出一个已知的

Machine translation (Meta M2M100); the English original follows.

Abstract

In likelihood-free hypothesis testing (LFHT), given samples from two unknown distributions $P,Q$ on $[n]$ with $\mathrm{d_{TV}}(P,Q)\geq\varepsilon$, and from a third distribution $D\in\{P,Q\}$, the goal is to identify whether $D=P$ or $D=Q$. We study asymmetric likelihood-free hypothesis testing, where the sample budgets $s_P$ and $s_Q$ for $P$ and $Q$ may differ, and characterize the feasible triples $(s_P,s_Q,s_D)$ up to logarithmic factors. We establish that unequal reference budgets can give a polynomial saving. For instance, for constant separation, $n$ samples from $P$ and $n^{3/4}$ from $Q$ allow testing with $\widetilde O(n^{1/4})$ samples from $D$, whereas both existing baselines---symmetric LFHT and unequal-sample closeness testing---require $Ω(\sqrt n)$ samples from $D$. We further apply our results to non-adaptive distribution 2-clustering, where the sample allocation among $k$ distributions must be fixed before observing any data. We obtain matching upper and lower bounds for this problem up to logarithmic factors in terms of the domain size, number of distributions, smaller cluster size, and separation, both with one cluster distribution known and with both unknown. Comparing with known bounds for adaptive sample allocation gives a worst-case adaptivity gap of $\widetildeΘ(k^{1/4})$.

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Topics: Mathematics, Closeness, Matching (statistics), Logarithm, Sample (material), Statistical hypothesis testing

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