Conditional Dependence via Shannon Capacity: Axioms, Estimators and Applications

Weihao Gao, Sreeram Kannan, Sewoong Oh, Pramod Viswanath
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2780-2789, 2016.

Abstract

We consider axiomatically the problem of estimating the strength of a conditional dependence relationship P_Y|X from 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-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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-gaob16, title = {Conditional Dependence via Shannon Capacity: Axioms, Estimators and Applications}, author = {Gao, Weihao and Kannan, Sreeram and Oh, Sewoong and Viswanath, Pramod}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {2780--2789}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/gaob16.pdf}, url = {https://proceedings.mlr.press/v48/gaob16.html}, abstract = {We consider axiomatically the problem of estimating the strength of a conditional dependence relationship P_Y|X from 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-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.} }
Endnote
%0 Conference Paper %T Conditional Dependence via Shannon Capacity: Axioms, Estimators and Applications %A Weihao Gao %A Sreeram Kannan %A Sewoong Oh %A Pramod Viswanath %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-gaob16 %I PMLR %P 2780--2789 %U https://proceedings.mlr.press/v48/gaob16.html %V 48 %X We consider axiomatically the problem of estimating the strength of a conditional dependence relationship P_Y|X from 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-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.
RIS
TY - CPAPER TI - Conditional Dependence via Shannon Capacity: Axioms, Estimators and Applications AU - Weihao Gao AU - Sreeram Kannan AU - Sewoong Oh AU - Pramod Viswanath BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-gaob16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 2780 EP - 2789 L1 - http://proceedings.mlr.press/v48/gaob16.pdf UR - https://proceedings.mlr.press/v48/gaob16.html AB - We consider axiomatically the problem of estimating the strength of a conditional dependence relationship P_Y|X from 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-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. ER -
APA
Gao, W., Kannan, S., Oh, S. & Viswanath, P.. (2016). Conditional Dependence via Shannon Capacity: Axioms, Estimators and Applications. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:2780-2789 Available from https://proceedings.mlr.press/v48/gaob16.html.

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