English

Concentration Bounds for Discrete Distribution Estimation in KL Divergence

Machine Learning 2023-06-14 v2 Discrete Mathematics Information Theory Machine Learning math.IT Probability

Abstract

We study the problem of discrete distribution estimation in KL divergence and provide concentration bounds for the Laplace estimator. We show that the deviation from mean scales as k/n\sqrt{k}/n when nkn \ge k, improving upon the best prior result of k/nk/n. We also establish a matching lower bound that shows that our bounds are tight up to polylogarithmic factors.

Keywords

Cite

@article{arxiv.2302.06869,
  title  = {Concentration Bounds for Discrete Distribution Estimation in KL Divergence},
  author = {Clément L. Canonne and Ziteng Sun and Ananda Theertha Suresh},
  journal= {arXiv preprint arXiv:2302.06869},
  year   = {2023}
}

Comments

Updated discussion of previous work

R2 v1 2026-06-28T08:39:34.389Z