Communication and Memory Efficient Testing of Discrete Distributions

Ilias Diakonikolas, Themis Gouleakis, Daniel M. Kane, Sankeerth Rao
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:1070-1106, 2019.

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 this Paper

BibTeX
@InProceedings{pmlr-v99-diakonikolas19a, title = {Communication and Memory Efficient Testing of Discrete Distributions}, author = {Diakonikolas, Ilias and Gouleakis, Themis and Kane, Daniel M. and Rao, Sankeerth}, booktitle = {Proceedings of the Thirty-Second Conference on Learning Theory}, pages = {1070--1106}, year = {2019}, editor = {Beygelzimer, Alina and Hsu, Daniel}, volume = {99}, series = {Proceedings of Machine Learning Research}, month = {25--28 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v99/diakonikolas19a/diakonikolas19a.pdf}, url = {https://proceedings.mlr.press/v99/diakonikolas19a.html}, 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.} }
Endnote
%0 Conference Paper %T Communication and Memory Efficient Testing of Discrete Distributions %A Ilias Diakonikolas %A Themis Gouleakis %A Daniel M. Kane %A Sankeerth Rao %B Proceedings of the Thirty-Second Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2019 %E Alina Beygelzimer %E Daniel Hsu %F pmlr-v99-diakonikolas19a %I PMLR %P 1070--1106 %U https://proceedings.mlr.press/v99/diakonikolas19a.html %V 99 %X 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.
APA
Diakonikolas, I., Gouleakis, T., Kane, D.M. & Rao, S.. (2019). Communication and Memory Efficient Testing of Discrete Distributions. Proceedings of the Thirty-Second Conference on Learning Theory, in Proceedings of Machine Learning Research 99:1070-1106 Available from https://proceedings.mlr.press/v99/diakonikolas19a.html.

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