Refined Convergence Rates of the Good-Turing Estimator

Amichai Painsky

doi:10.1109/ITW48936.2021.9611389

Refined Convergence Rates of the Good-Turing Estimator

Amichai Painsky^*

^*Corresponding author for this work

Department of Industrial Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Good-Turing (GT) estimator is perhaps the most popular framework for modelling large alphabet distributions. Classical results show that the GT estimator convergences to the occupancy probability, formally defined as the total probability of words that appear exactly k times in the sample. In this work we introduce new convergence guarantees for the GT estimator, based on worst-case MSE analysis. Our results refine and improve upon currently known bounds. Importantly, we introduce a simultaneous convergence rate to the entire collection of occupancy probabilities.

Original language	English
Title of host publication	2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781665403122
DOIs	https://doi.org/10.1109/ITW48936.2021.9611389
State	Published - 2021
Event	2021 IEEE Information Theory Workshop, ITW 2021 - Virtual, Online, Japan Duration: 17 Oct 2021 → 21 Oct 2021

Publication series

Name	2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings

Conference

Conference	2021 IEEE Information Theory Workshop, ITW 2021
Country/Territory	Japan
City	Virtual, Online
Period	17/10/21 → 21/10/21

Access to Document

10.1109/ITW48936.2021.9611389

Cite this

@inproceedings{70eaaa3ba91c41fa9c6471a016823c56,

title = "Refined Convergence Rates of the Good-Turing Estimator",

abstract = "The Good-Turing (GT) estimator is perhaps the most popular framework for modelling large alphabet distributions. Classical results show that the GT estimator convergences to the occupancy probability, formally defined as the total probability of words that appear exactly k times in the sample. In this work we introduce new convergence guarantees for the GT estimator, based on worst-case MSE analysis. Our results refine and improve upon currently known bounds. Importantly, we introduce a simultaneous convergence rate to the entire collection of occupancy probabilities.",

author = "Amichai Painsky",

note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; null ; Conference date: 17-10-2021 Through 21-10-2021",

year = "2021",

doi = "10.1109/ITW48936.2021.9611389",

language = "אנגלית",

series = "2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings",

address = "ארצות הברית",

}

Painsky, A 2021, Refined Convergence Rates of the Good-Turing Estimator. in 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings. 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings, Institute of Electrical and Electronics Engineers Inc., 2021 IEEE Information Theory Workshop, ITW 2021, Virtual, Online, Japan, 17/10/21. https://doi.org/10.1109/ITW48936.2021.9611389

Refined Convergence Rates of the Good-Turing Estimator. / Painsky, Amichai.

2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. (2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Refined Convergence Rates of the Good-Turing Estimator

AU - Painsky, Amichai

PY - 2021

Y1 - 2021

N2 - The Good-Turing (GT) estimator is perhaps the most popular framework for modelling large alphabet distributions. Classical results show that the GT estimator convergences to the occupancy probability, formally defined as the total probability of words that appear exactly k times in the sample. In this work we introduce new convergence guarantees for the GT estimator, based on worst-case MSE analysis. Our results refine and improve upon currently known bounds. Importantly, we introduce a simultaneous convergence rate to the entire collection of occupancy probabilities.

AB - The Good-Turing (GT) estimator is perhaps the most popular framework for modelling large alphabet distributions. Classical results show that the GT estimator convergences to the occupancy probability, formally defined as the total probability of words that appear exactly k times in the sample. In this work we introduce new convergence guarantees for the GT estimator, based on worst-case MSE analysis. Our results refine and improve upon currently known bounds. Importantly, we introduce a simultaneous convergence rate to the entire collection of occupancy probabilities.

UR - http://www.scopus.com/inward/record.url?scp=85123409455&partnerID=8YFLogxK

U2 - 10.1109/ITW48936.2021.9611389

DO - 10.1109/ITW48936.2021.9611389

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85123409455

T3 - 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings

BT - 2021 IEEE Information Theory Workshop, ITW 2021 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 17 October 2021 through 21 October 2021

ER -

Refined Convergence Rates of the Good-Turing Estimator

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this