Data Amplification: A Unified and Competitive Approach to Property Estimation

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.