Data Amplification: A Unified and Competitive Approach to Property Estimation

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Yi Hao, Alon Orlitsky, Ananda Theertha Suresh, Yihong Wu


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.