论样本扩增的统计复杂度
On the Statistical Complexity of Sample Amplification
AI总结：
本文研究样本扩增问题的统计复杂度，推导了通用扩增流程与下界技术，建立了其与现有统计概念及分布学习的关联，技术可应用于指数族等大类分布。
摘要：
“样本扩增”问题将如下问题形式化：给定从未知分布$P$中抽取的$n$个独立同分布（i.i.d.）样本，何时能够生成规模更大的$n+m$个样本，且这些样本无法与从$P$中抽取的$n+m$个独立同分布样本区分开？本文通过推导通用的扩增流程、下界技术，以及该问题与现有统计概念的关联，为其奠定了坚实的统计基础。我们的技术适用于包括指数族在内的一大类分布，并建立了样本扩增与分布学习之间的严格联系。
英文摘要：
The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$ i.i.d. samples drawn from $P$? In this work, we provide a firm statistical foundation for this problem by deriving generally applicable amplification procedures, lower bound techniques and connections to existing statistical notions. Our techniques apply to a large class of distributions including the exponential family, and establish a rigorous connection between sample amplification and distribution learning.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
