On the statistical complexity of sample amplification

Abstract

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 $\mathit{n}\mathbf{+}\mathit{m}$ samples which cannot be distinguished from $\mathit{n}\mathbf{+}\mathit{m}$ 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.