发表机构
New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非自适应条件样本下的分布等价性测试问题，给出了该问题所需查询次数的紧界，证明其复杂度为tildeθ(log n)，明确了该场景下等价性测试的查询复杂度。
AI 中文摘要
我们研究可获取非自适应条件样本的分布测试问题，具体针对等价性测试，即判定两个未知分布是否相等或在总变差距离上相差ε。我们的算法与下界表明，该问题需要且仅需要$\tilde \theta(\frac{\text{log }n}{\text{ε}^2})$次查询。这些结果显示，非自适应条件样本下的均匀性、同一性与等价性测试的复杂度均为$\tilde \theta(\text{log }n)$。
英文摘要
We study distribution testing with access to non-adaptive conditional samples. Specifically, we give tight bounds for equivalence testing, determining whether two unknown distributions are equal to or $\varepsilon$-far from each other in total variation distance. Our algorithm and lower bound show that $\tilde Θ\left(\frac{\log n}{\varepsilon^2}\right)$ queries are necessary and sufficient for this problem. These results demonstrate that the complexity of uniformity, identity, and equivalence testing with non-adaptive conditional samples are all $\tilde Θ(\log n)$.
