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The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error probability $\delta$.
Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator
Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz · 1956
Earlier work this paper cites.
The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
Pascal Massart · 1990
Earlier work this paper cites.
Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
Cited alongside, same era.
A Survey on Distribution Testing: Your Data is Big. But is it Blue?
Clément L. Canonne · 2015
Cited alongside, same era.
On learning distributions from their samples
Sudeep Kamath, Alon Orlitsky, Dheeraj Pichapati, and Ananda Theertha Suresh · 2015
Later among the works it cites.
Multinomial concentration in relative entropy at the ratio of alphabet and sample sizes
Rohit Agrawal · 2019
Later among the works it cites.
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