Learning bayesian network structure using lp relaxations
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 difficult...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Society for Artificial Intelligence and Statistics
2011
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| Online Access: | http://hdl.handle.net/1721.1/66317 https://orcid.org/0000-0002-2199-0379 |
| Summary: | 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. |
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