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arXiv · 1904.00070

Data Amplification: A Unified and Competitive Approach to Property Estimation

Yi Hao·Alon Orlitsky·Ananda T. Suresh·Yihong Wu
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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 $2n$ samples to achieve the performance attained by the empirical estimator with $n\sqrt{\log n}$ 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 $n$ samples is even as good as that of the empirical estimator with $n\log n$ 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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Yi Hao, Alon Orlitsky, Ananda T. Suresh, Yihong Wu. 2019-03-29. Data Amplification: A Unified and Competitive Approach to Property Estimation. https://arxiv.org/abs/1904.00070

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