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Title: Bounded-Degree Approximations of Stochastic Networks

Abstract

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.

Authors:
ORCiD logo; ;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1427284
Report Number(s):
SAND-2015-5116J
Journal ID: ISSN 2332-7804; 594636
DOE Contract Number:
AC04-94AL85000
Resource Type:
Journal Article
Resource Relation:
Journal Name: IEEE Transactions on Molecular, Biological and Multi-Scale Communications; Journal Volume: 3; Journal Issue: 2; Related Information: Early version
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Quinn, Christopher J., Pinar, Ali, and Kiyavash, Negar. Bounded-Degree Approximations of Stochastic Networks. United States: N. p., 2017. Web. doi:10.1109/TMBMC.2017.2686387.
Quinn, Christopher J., Pinar, Ali, & Kiyavash, Negar. Bounded-Degree Approximations of Stochastic Networks. United States. doi:10.1109/TMBMC.2017.2686387.
Quinn, Christopher J., Pinar, Ali, and Kiyavash, Negar. Thu . "Bounded-Degree Approximations of Stochastic Networks". United States. doi:10.1109/TMBMC.2017.2686387. https://www.osti.gov/servlets/purl/1427284.
@article{osti_1427284,
title = {Bounded-Degree Approximations of Stochastic Networks},
author = {Quinn, Christopher J. and Pinar, Ali and Kiyavash, Negar},
abstractNote = {We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.},
doi = {10.1109/TMBMC.2017.2686387},
journal = {IEEE Transactions on Molecular, Biological and Multi-Scale Communications},
number = 2,
volume = 3,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
}