A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1121, 2017.
Abstract
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 sampleoptimal approximations for each of these properties. We show that a single, simple, plugin estimator—profile maximum likelihood (PML)—is sample competitive for all symmetric properties, and in particular is asymptotically sampleoptimal for all the above properties.
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