Skip to yearly menu bar Skip to main content


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

Moses Charikar · Zhihao Jiang · Kirankumar Shiragur · Aaron Sidford

Hall J (level 1) #817

Keywords: [ profile maximum likelihood ] [ symmetric property estimation ] [ property estimation ]

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 \cite{ACSS20, ACSS20b}. Our estimator reaches a theoretical limit for universal symmetric property estimation as \cite{Han20} 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 $\epsilon \ll n^{-1/3}$.

Chat is not available.