Cutting plane algorithms for variational inference in graphical models
Name
191958182-MIT.pdf
Description
Full printable version
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487.13 KB
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90897f6de6195ed04241ce4f9e0645ba
Author(s)
Sontag, David Alexander
Advisor(s)
Tommi S. Jaakkola.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concave upper bound on the entropy, this gives a new variational inference algorithm for probabilistic inference in discrete Markov Random Fields (MRFs). Valid constraints are derived for the marginal polytope through a series of projections onto the cut polytope. Projecting onto a larger model gives an efficient separation algorithm for a large class of valid inequalities arising from each of the original projections. As a result, we obtain tighter upper bounds on the logpartition function than possible with previous variational inference algorithms. We also show empirically that our approximations of the marginals are significantly more accurate. This algorithm can also be applied to the problem of finding the Maximum a Posteriori assignment in a MRF, which corresponds to a linear program over the marginal polytope. One of the main contributions of the thesis is to bring together two seemingly different fields, polyhedral combinatorics and probabilistic inference, showing how certain results in either field can carry over to the other.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (leaves 65-66).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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