Communication and Memory Efficient Testing of Discrete Distributions
Abstract
We study distribution testing with communication and memory constraints in the following computational models: (1) The {\em one-pass streaming model} where the goal is to minimize the sample complexity of the protocol subject to a memory constraint, and (2) A {\em distributed model} where the data samples reside at multiple machines and the goal is to minimize the communication cost of the protocol. In both these models, we provide efficient algorithms for uniformity/identity testing (goodness of fit) and closeness testing (two sample testing). Moreover, we show nearly-tight lower bounds on (1) the sample complexity of any one-pass streaming tester for uniformity, subject to the memory constraint, and (2) the communication cost of any uniformity testing protocol, in a restricted `one-pass' model of communication.
Cite
@article{arxiv.1906.04709,
title = {Communication and Memory Efficient Testing of Discrete Distributions},
author = {Ilias Diakonikolas and Themis Gouleakis and Daniel M. Kane and Sankeerth Rao},
journal= {arXiv preprint arXiv:1906.04709},
year = {2019}
}
Comments
Full version of COLT 2019 paper