Monotone probability distributions over the Boolean cube can be learned with sublinear samples

Ronitt Rubinfeld, Arsen Vasilyan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we give (to our knowledge) the first algorithm that learns an approximation of the distribution in statistical distance using a number of samples that is sublinear in the domain. To do this, we develop a structural lemma describing monotone probability distributions. The structural lemma has further implications to the sample complexity of basic testing tasks for analyzing monotone probability distributions over the Boolean cube: We use it to give nontrivial upper bounds on the tasks of estimating the distance of a monotone distribution to uniform and of estimating the support size of a monotone distribution. In the setting of monotone probability distributions over the Boolean cube, our algorithms are the first to have sample complexity lower than known lower bounds for the same testing tasks on arbitrary (not necessarily monotone) probability distributions. One further consequence of our learning algorithm is an improved sample complexity for the task of testing whether a distribution on the Boolean cube is monotone.

Original languageEnglish
Title of host publication11th Innovations in Theoretical Computer Science Conference, ITCS 2020
EditorsThomas Vidick
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771344
DOIs
StatePublished - Jan 2020
Event11th Innovations in Theoretical Computer Science Conference, ITCS 2020 - Seattle, United States
Duration: 12 Jan 202014 Jan 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume151
ISSN (Print)1868-8969

Conference

Conference11th Innovations in Theoretical Computer Science Conference, ITCS 2020
Country/TerritoryUnited States
CitySeattle
Period12/01/2014/01/20

Funding

FundersFunder number
National Science FoundationCCF-1733808, IIS-1741137, CCF-1650733, CCF-1740751
Directorate for Computer and Information Science and Engineering1733808, 1741137, 1740751
School of Electronic Engineering and Computer Science

    Keywords

    • Estimating support size
    • Learning distributions
    • Monotone probability distributions

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