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Title:Conditional dependence via Shannon capacity: axioms, estimators and applications
Author(s):Gao, Weihao
Advisor(s):Viswanath, Pramod; Oh, Sewoong
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Conditional Dependence
Shannon Capacity
Abstract:We consider axiomatically the problem of estimating the strength of a conditional dependence relationship P_{Y|X} from a random variable 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-k 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.
Issue Date:2016-12-01
Rights Information:Copyright 2016 Weihao Gao
Date Available in IDEALS:2017-03-01
Date Deposited:2016-12

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