TY - JOUR

T1 - Convergence Guarantees for the Good-Turing Estimator

AU - Painsky, Amichai

N1 - Publisher Copyright:
©2022 Painsky.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - Consider a finite sample from an unknown distribution over a countable alphabet. The occupancy probability (OP) refers to the total probability of symbols that appear exactly k times in the sample. Estimating the OP is a basic problem in large alphabet modeling, with a variety of applications in machine learning, statistics and information theory. The Good-Turing (GT) framework is perhaps the most popular OP estimation scheme. Classical results show that the GT estimator converges to the OP, for every k independently. In this work we introduce new exact convergence guarantees for the GT estimator, based on worst-case mean squared error analysis. Our scheme improves upon currently known results. Further, we introduce a novel simultaneous convergence rate, for any desired set of occupancy probabilities. This allows us to quantify the unified performance of OP estimators, and introduce a novel estimation framework with favorable convergence guarantees.

AB - Consider a finite sample from an unknown distribution over a countable alphabet. The occupancy probability (OP) refers to the total probability of symbols that appear exactly k times in the sample. Estimating the OP is a basic problem in large alphabet modeling, with a variety of applications in machine learning, statistics and information theory. The Good-Turing (GT) framework is perhaps the most popular OP estimation scheme. Classical results show that the GT estimator converges to the OP, for every k independently. In this work we introduce new exact convergence guarantees for the GT estimator, based on worst-case mean squared error analysis. Our scheme improves upon currently known results. Further, we introduce a novel simultaneous convergence rate, for any desired set of occupancy probabilities. This allows us to quantify the unified performance of OP estimators, and introduce a novel estimation framework with favorable convergence guarantees.

KW - Good-Turing Estimator

KW - Missing Mass

KW - Natural Language Modeling

KW - Occupancy Probability

UR - http://www.scopus.com/inward/record.url?scp=85142513012&partnerID=8YFLogxK

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AN - SCOPUS:85142513012

SN - 1532-4435

VL - 23

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

M1 - 279

ER -