Sequential Algorithms for Testing Closeness of Distributions - Archive ouverte HAL Access content directly
Conference Papers Year : 2021

Sequential Algorithms for Testing Closeness of Distributions

Abstract

What advantage do sequential procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions D1 and D2 on {1,…,n} are equal or ϵ-far, we give several answers to this question. We show that for a small alphabet size n, there is a sequential algorithm that outperforms any batch algorithm by a factor of at least 4 in terms sample complexity. For a general alphabet size n, we give a sequential algorithm that uses no more samples than its batch counterpart, and possibly fewer if the actual distance TV(D1,D2) between D1 and D2 is larger than ϵ. As a corollary, letting ϵ go to 0, we obtain a sequential algorithm for testing closeness when no a priori bound on TV(D1,D2) is given that has a sample complexity O ̃(n^{2/3}/TV(D1,D2)^{4/3}): this improves over the O ̃(n/logn/TV(D1,D2)^2) tester of Daskalakis and Kawase [2017] and is optimal up to multiplicative constants. We also establish limitations of sequential algorithms for the problem of testing identity and closeness: they can improve the worst case number of samples by at most a constant factor.
Fichier principal
Vignette du fichier
NeurIPS-2021-sequential-algorithms-for-testing-closeness-of-distributions-Paper.pdf (574.98 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03481048 , version 1 (06-12-2022)

Identifiers

  • HAL Id : hal-03481048 , version 1

Cite

Omar Fawzi, Nicolas Flammarion, Aurélien Garivier, Aadil Oufkir. Sequential Algorithms for Testing Closeness of Distributions. NeurIPS 2021, Dec 2021, Virtual, France. ⟨hal-03481048⟩
61 View
10 Download

Share

Gmail Facebook Twitter LinkedIn More