论文标题
关于样品扩增的统计复杂性
On the Statistical Complexity of Sample Amplification
论文作者
论文摘要
``示例放大''问题正式提出了以下问题：给定$ n $ i.i.d.从未知分布$ p $中得出的样品，什么时候可以生产较大的$ n+m $样品，这些样本无法与$ n+m $ i.i.d.从$ p $抽取样本？在这项工作中，我们通过得出通常适用的放大程序，下限技术和连接到现有统计概念来为此问题提供牢固的统计基础。我们的技术适用于包括指数家族在内的大量分布，并在样本扩增和分配学习之间建立了严格的联系。
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.
