ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2210.06728
53
0

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

13 October 2022
Moses Charikar
Zhihao Jiang
Kirankumar Shiragur
Aaron Sidford
ArXiv (abs)PDFHTML
Abstract

We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given nnn independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for estimating various symmetric properties when the estimation error ϵ≫n−1/3\epsilon \gg n^{-1/3}ϵ≫n−1/3. This result improves upon the previous best accuracy threshold of ϵ≫n−1/4\epsilon \gg n^{-1/4}ϵ≫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 111-Lipschitz property when ϵ≪n−1/3\epsilon \ll n^{-1/3}ϵ≪n−1/3.

View on arXiv
Comments on this paper