Learning bayesian network structure using lp relaxations
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Jaakkola_Learning bayesian.pdf
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Author(s)
Jaakkola, Tommi S.
Sontag, David Alexander
Globerson, Amir
Meila, Marina
Date Issued
May 2010
Journal
Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, (AISTATS) 2010
Publisher
Society for Artificial Intelligence and Statistics
Citation
Jaakkola, Tommi, David Sontag, Amir Globerson, and Marina Meila. "Learning Bayesian Network Structure using LP Relaxations." Proceedings of the 13th International Conference
on Arti ficial Intelligence and Statistics (AISTATS) 2010, May 13-15, Chia Laguna Resort, Sardinia, Italy.
Version
Author's final manuscript
Abstract
We propose to solve the combinatorial problem
of finding the highest scoring Bayesian
network structure from data. This structure
learning problem can be viewed as an inference
problem where the variables specify the
choice of parents for each node in the graph.
The key combinatorial difficulty arises from
the global constraint that the graph structure
has to be acyclic. We cast the structure
learning problem as a linear program over
the polytope defined by valid acyclic structures.
In relaxing this problem, we maintain
an outer bound approximation to the polytope
and iteratively tighten it by searching
over a new class of valid constraints. If an
integral solution is found, it is guaranteed
to be the optimal Bayesian network. When
the relaxation is not tight, the fast dual algorithms
we develop remain useful in combination
with a branch and bound method.
Empirical results suggest that the method is
competitive or faster than alternative exact
methods based on dynamic programming.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
http://jmlr.csail.mit.edu/proceedings/papers/v9/jaakkola10a/jaakkola10a.pdf
