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Data Amplification: A Unified and Competitive Approach to Property Estimation

29 March 2019
Yi Hao
A. Orlitsky
A. Suresh
Yihong Wu
ArXiv (abs)PDFHTML
Abstract

Estimating properties of discrete distributions is a fundamental problem in statistical learning. We design the first unified, linear-time, competitive, property estimator that for a wide class of properties and for all underlying distributions uses just 2n2n2n samples to achieve the performance attained by the empirical estimator with nlog⁡nn\sqrt{\log n}nlogn​ samples. This provides off-the-shelf, distribution-independent, "amplification" of the amount of data available relative to common-practice estimators. We illustrate the estimator's practical advantages by comparing it to existing estimators for a wide variety of properties and distributions. In most cases, its performance with nnn samples is even as good as that of the empirical estimator with nlog⁡nn\log nnlogn samples, and for essentially all properties, its performance is comparable to that of the best existing estimator designed specifically for that property.

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