Conditional dependence via shannon capacity: Axioms, estimators and applications

Weihao Gao, Sreeram Kannan, Sewoong Oh, Pramod Viswanath

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider axiomatically the problem of estimating the strength of a conditional dependence relationship Py/x fr°m a random variables X to a random variable Y. This has applications in determining the strength of a known causal relationship, where the strength depends only on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause). Shannon capacity, appropriately regularized, emerges as a natural measure under these axioms. We examine the problem of calculating Shannon capacity from the observed samples and propose a novel fixed-A: nearest neighbor estimator, and demonstrate its consistency. Finally, we demonstrate an application to single-cell flow- cytometry, where the proposed estimators significantly reduce sample complexity.

Original languageEnglish (US)
Title of host publication33rd International Conference on Machine Learning, ICML 2016
EditorsKilian Q. Weinberger, Maria Florina Balcan
PublisherInternational Machine Learning Society (IMLS)
Pages4057-4066
Number of pages10
ISBN (Electronic)9781510829008
StatePublished - 2016
Event33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
Duration: Jun 19 2016Jun 24 2016

Publication series

Name33rd International Conference on Machine Learning, ICML 2016
Volume6

Other

Other33rd International Conference on Machine Learning, ICML 2016
Country/TerritoryUnited States
CityNew York City
Period6/19/166/24/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Computer Networks and Communications

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