On the Statistical Complexity of Sample Amplification

Abstract

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 ? Axelrod et al. [AGSV20] formalized this question as the sample amplification problem, and gave optimal amplification procedures for discrete distributions and Gaussian location models. However, these procedures and associated lower bounds are tailored to the specific distribution classes, and a general statistical understanding of sample amplification is still largely missing. In this work, we place the sample amplification problem on a firm statistical foundation 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.

Calomplification -- The Power of Generative Calorimeter Models

“…A larger generated sample than the training dataset will then include successively less information per event than the training data, and eventually the information in the generated events will saturate and be dominated by limitations from the network architecture and training. With this pattern in mind [1], we can define an amplification or GANplification factor [2,3] in terms of an effective sample size for a given surrogate model.…”