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Learning Bayesian network parameters from small data sets
Guo Z., Gao X., Ren H., Yang Y., Di R., Chen D. International Journal of Approximate Reasoning91  22-35,2017.Type:Article
Date Reviewed: Mar 12 2018

Bayesian networks (BNs) represent a powerful statistical tool for uncertainty analysis with applications in many areas, for example, medical diagnosis. Since data is often not sufficiently available to accurately learn the parameters of a BN by the traditional maximum likelihood (ML) method, extra domain knowledge in the form of linear parameter constraints is provided, giving rise to additional virtual data samples; from these, the qualitative maximum a posteriori (QMAP) algorithm can estimate better network parameters. Since QMAP, however, abstracts the constraints to a single numerical constant, the derived estimation may fail to satisfy all constraints and thus cannot be necessarily trusted.

This paper extends QMAP to further constrained QMAP (FC-QMAP), which checks whether the estimation derived by QMAP violates any given parameter constraints and in this case computes a new estimation by applying convex optimization (as, for example, implemented in the MATLAB software) to the original constraint set. The paper demonstrates via a medical example from cancer diagnosis how FC-QMAP may produce a correct result where both ML and QMAP fail. An extensive experimental section benchmarks the accuracy and efficiency of the approach in comparison with various other algorithms, demonstrating, for example, that FC-QMAP takes typically only about two to three times more time than QMAP.

While the paper does not present any great new theoretical insights, it nicely demonstrates that the “brute-force” approach of convex optimization is in this application context practically feasible. Further work will focus on the inclusion of non-convex parameter constraints and improving the efficiency of the method.

Reviewer:  Wolfgang Schreiner Review #: CR145909 (1806-0338)
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