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Solving graph compression via optimal transport
Vikas Garg · Tommi Jaakkola

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #54

We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for either directed or undirected graphs, and its dual characterization is cast in terms of distributions over the nodes. The compression pertains to the support of node distributions and makes the problem challenging to solve directly. To this end, we introduce Boolean relaxations and specify conditions under which these relaxations are exact. The relaxations admit algorithms with provably fast convergence. Moreover, we provide an exact O(d log d) algorithm for the subproblem of projecting a d-dimensional vector to transformed simplex constraints. Our method outperforms state-of-the-art compression methods on graph classification.

Author Information

Vikas Garg (MIT)
Tommi Jaakkola (MIT)

Tommi Jaakkola is a professor of Electrical Engineering and Computer Science at MIT. He received an M.Sc. degree in theoretical physics from Helsinki University of Technology, and Ph.D. from MIT in computational neuroscience. Following a Sloan postdoctoral fellowship in computational molecular biology, he joined the MIT faculty in 1998. His research interests include statistical inference, graphical models, and large scale modern estimation problems with predominantly incomplete data.

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