# On the Statistical Complexity of Sample Amplification

arXiv: https://arxiv.org/abs/2201.04315 · HTML: https://mlsanity.com/paper/2201.04315/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 12 Jan 2022.

## Builds on (most cited first, 5 of 5)

- [Data Augmentation Generative Adversarial Networks](https://mlsanity.com/paper/1711.04340/) (2017)
- [GAN-based Synthetic Medical Image Augmentation for increased CNN Performance in Liver Lesion Classification](https://mlsanity.com/paper/1803.01229/) (2018)
- [Reducibility and Statistical-Computational Gaps from Secret Leakage](https://mlsanity.com/paper/2005.08099/) (2020)
- [Optimal Average-Case Reductions to Sparse PCA: From Weak Assumptions to Strong Hardness](https://mlsanity.com/paper/1902.07380/) (2019)
- [Sample Amplification: Increasing Dataset Size even when Learning is Impossible](https://mlsanity.com/paper/1904.12053/) (2019)

## Built on by (most cited first, 3 of 3)

- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Differentially Private Sampling from Distributions](https://mlsanity.com/paper/2211.08193/) (2022)
- [Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model](https://mlsanity.com/paper/2610.00424/) (2026)

## Abstract (arXiv)

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.