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Learning Bayesian Network Parameters with Domain Knowledge and Insufficient Data

To improve the learning accuracy of parameters in a Bayesian network (BN) from limited data, domain knowledge is often incorporated into the learning process as parameter constraints. Maximum a posteriori (MAP) based methods that use both data and constraints have been studied extensively. Among those methods, the qualitatively maximum a posteriori (QMAP) method exhibits high learning performance. In the QMAP method, when the data are limited, estimation from the data often fails to satisfy all the parameter constraints, which makes the overall QMAP estimation unreliable. To ensure that the QMAP estimation does not violate any given parameter constraint and further improve the learning accuracy, in this paper, we propose a qualitatively maximum a posteriori correction (QMAP-C) estimation algorithm, which regulates QMAP estimation by replacing the data estimation with a further constrained estimation. Experiments show that the proposed algorithm outperforms most of the existing parameter learning methods when the parameter constraints are correct.