Bayesian Network Parameter and Structure
Learning Under Constraints
Based
on our current work in Bayesian Network parameter learning using qualitative
constraints, we have developed software that performs parameter estimation in Bayesian
networks of known structure under various qualitative constraints. The methods and software are very general in
the sense that any constraint on parameters is allowed, which includes a wide
range of ideas discussed in the literature, such as qualitative influences,
synergies, range and ratio constraints as well as the. Besides including constraints on the
estimated model parameters, the software also allows incorporating specific
soft constraints on the prior model parameters such as constraints on the Dirichlet prior.
When all constraints are convex (which is the case for almost all
important constraints defined in the literature), parameter learning is
performed using convex optimization, which ensures to find a global optimum in
polynomial time.
The
parameter learning software can also handle the situation when data is
incomplete. For incomplete data, we
extend the expectation-maximization idea, using our methods developed for
complete data The
expectation step is conducted as usual, but the maximization is treated as a
constrained optimization problem.
Experiments
with both synthetic and real data show that the BN parameter learning accuracy
can be improved significantly with some simple qualitative constraints, and the
improvements are especially significant when training data is either
insufficient, incomplete or unrepresentative.
Besides
the parameter learning software, we also developed software for Bayesian
network structure learning based on our latest ICML paper from data and
expert's knowledge. The software can
efficiently learn the optimal BN structure for up to 100 nodes, much higher
than the 30 nodes achieved by the state of the art BN structure learning
software. A long version of the ICML paper has been accepted by the Journal
of Machine Learning Research.
Both softwares are implemented in Matlab and they are seamlessly integrated with Kevin Murphy’s BNT library so that we can call the functions in the BNT library. The sturcture learning software can be download from the following link . We will soon releasee the constained parametrer learning software. Feel free to contact us if you want to obtain the software immediately.