Concentration Bounds for Discrete Distribution Estimation in KL Divergence

02/14/2023

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by   Clément L. Canonne, et al.

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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 when n ≥ k, improving upon the best prior result of k/n. We also establish a matching lower bound that shows that our bounds are tight up to polylogarithmic factors.