Robust directed tree approximations for networks of stochastic processes

Christopher J. Quinn; Jalal Etesami; Negar Kiyavash; Todd P. Coleman

doi:10.1109/ISIT.2013.6620627

Robust directed tree approximations for networks of stochastic processes

Christopher J. Quinn, Jalal Etesami, Negar Kiyavash, Todd P. Coleman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

We develop low-complexity algorithms to robustly identify the best directed tree approximation for a network of stochastic processes in the finite-sample regime. Directed information is used to quantify influence between stochastic processes and identify the best directed tree approximation in terms of Kullback-Leibler (KL) divergence. We provide finite-sample complexity bounds for confidence intervals of directed information estimates. We use these confidence intervals to develop a minimax framework to identify the best directed tree that is robust to point estimation errors. We provide algorithms for this minimax calculation and describe the relationships between exactness and complexity.

Original language	English
Title of host publication	2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages	2254-2258
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2013.6620627
State	Published - 2013
Externally published	Yes
Event	2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey Duration: 7 Jul 2013 → 12 Jul 2013

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Conference

Conference	2013 IEEE International Symposium on Information Theory, ISIT 2013
Country/Territory	Turkey
City	Istanbul
Period	7/07/13 → 12/07/13

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10.1109/ISIT.2013.6620627

Cite this

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title = "Robust directed tree approximations for networks of stochastic processes",

abstract = "We develop low-complexity algorithms to robustly identify the best directed tree approximation for a network of stochastic processes in the finite-sample regime. Directed information is used to quantify influence between stochastic processes and identify the best directed tree approximation in terms of Kullback-Leibler (KL) divergence. We provide finite-sample complexity bounds for confidence intervals of directed information estimates. We use these confidence intervals to develop a minimax framework to identify the best directed tree that is robust to point estimation errors. We provide algorithms for this minimax calculation and describe the relationships between exactness and complexity.",

author = "Quinn, {Christopher J.} and Jalal Etesami and Negar Kiyavash and Coleman, {Todd P.}",

year = "2013",

doi = "10.1109/ISIT.2013.6620627",

language = "English",

isbn = "9781479904464",

series = "IEEE International Symposium on Information Theory - Proceedings",

pages = "2254--2258",

booktitle = "2013 IEEE International Symposium on Information Theory, ISIT 2013",

note = "2013 IEEE International Symposium on Information Theory, ISIT 2013 ; Conference date: 07-07-2013 Through 12-07-2013",

}

Quinn, CJ, Etesami, J, Kiyavash, N & Coleman, TP 2013, Robust directed tree approximations for networks of stochastic processes. in 2013 IEEE International Symposium on Information Theory, ISIT 2013., 6620627, IEEE International Symposium on Information Theory - Proceedings, pp. 2254-2258, 2013 IEEE International Symposium on Information Theory, ISIT 2013, Istanbul, Turkey, 7/07/13. https://doi.org/10.1109/ISIT.2013.6620627

Robust directed tree approximations for networks of stochastic processes. / Quinn, Christopher J.; Etesami, Jalal; Kiyavash, Negar et al.
2013 IEEE International Symposium on Information Theory, ISIT 2013. 2013. p. 2254-2258 6620627 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Kiyavash, Negar

AU - Coleman, Todd P.

PY - 2013

Y1 - 2013

N2 - We develop low-complexity algorithms to robustly identify the best directed tree approximation for a network of stochastic processes in the finite-sample regime. Directed information is used to quantify influence between stochastic processes and identify the best directed tree approximation in terms of Kullback-Leibler (KL) divergence. We provide finite-sample complexity bounds for confidence intervals of directed information estimates. We use these confidence intervals to develop a minimax framework to identify the best directed tree that is robust to point estimation errors. We provide algorithms for this minimax calculation and describe the relationships between exactness and complexity.

AB - We develop low-complexity algorithms to robustly identify the best directed tree approximation for a network of stochastic processes in the finite-sample regime. Directed information is used to quantify influence between stochastic processes and identify the best directed tree approximation in terms of Kullback-Leibler (KL) divergence. We provide finite-sample complexity bounds for confidence intervals of directed information estimates. We use these confidence intervals to develop a minimax framework to identify the best directed tree that is robust to point estimation errors. We provide algorithms for this minimax calculation and describe the relationships between exactness and complexity.

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ER -

Robust directed tree approximations for networks of stochastic processes

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