On the statistical complexity of sample amplification
Brian Axelrod, Shivam Garg, Yanjun Han, Vatsal Sharan, Gregory Valiant
The Annals of Statistics · 2024 · Volume 52 · Issue 6
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 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.
Keywords
62B15, 62C20, Le Cam’s distance, Minimax rate, Sample amplification
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