A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions
; Proceedings of the 34th International Conference on Machine Learning, PMLR 70:11-21, 2017.
Symmetric distribution properties such as support size, support coverage, entropy, and proximity to uniformity, arise in many applications. Recently, researchers applied different estimators and analysis tools to derive asymptotically sample-optimal approximations for each of these properties. We show that a single, simple, plug-in estimator—profile maximum likelihood (PML)—is sample competitive for all symmetric properties, and in particular is asymptotically sample-optimal for all the above properties.