Bounded Degree Approximations of Stochastic Networks

Christopher J. Quinn; Ali Pinar; Negar Kiyavash

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arXiv · 1506.04767

Bounded Degree Approximations of Stochastic Networks

Christopher J. Quinn·Ali Pinar·Negar Kiyavash

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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 specified 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.

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Christopher J. Quinn, Ali Pinar, Negar Kiyavash. 2015-06-15. Bounded Degree Approximations of Stochastic Networks. https://arxiv.org/abs/1506.04767

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