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arXiv · 2210.06728

On the Efficient Implementation of High Accuracy Optimality of Profile Maximum Likelihood

Moses Charikar·Zhihao Jiang·Kirankumar Shiragur·Aaron Sidford
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Abstract

We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given $n$ independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for estimating various symmetric properties when the estimation error $\epsilon \gg n^{-1/3}$. This result improves upon the previous best accuracy threshold of $\epsilon \gg n^{-1/4}$ achievable by polynomial time computable PML-based universal estimators [ACSS21, ACSS20]. Our estimator reaches a theoretical limit for universal symmetric property estimation as [Han21] shows that a broad class of universal estimators (containing many well known approaches including ours) cannot be sample optimal for every $1$-Lipschitz property when $\epsilon \ll n^{-1/3}$.

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Moses Charikar, Zhihao Jiang, Kirankumar Shiragur, Aaron Sidford. 2022-10-13. On the Efficient Implementation of High Accuracy Optimality of Profile Maximum Likelihood. https://arxiv.org/abs/2210.06728

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