ON THE STATISTICAL COMPLEXITY OF SAMPLE AMPLIFICATION

• 成果类型: Article
• 署名作者: Axelrod, Brian; Garg, Shivam; Han, Yanjun; Sharan, Vatsal; Valiant, Gregory
• 署名单位: Stanford University; Microsoft; New York University; New York University; University of Southern California
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2444
• 发表日期: 2024
• 页码: 2767-2790
• 关键词: gaussian white-noise; Nonparametric Regression; asymptotic equivalence; DENSITY-ESTIMATION

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.