Learning Bayesian Network Parameters with Domain Knowledge and Insufficient Data
Proceedings of The 3rd International Workshop on Advanced Methodologies for Bayesian Networks, PMLR 73:93-104, 2017.
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 con- straints. Maximum a posteriori (MAP) based methods that use both data and constraints have been studied extensively. Among those methods, the qualitatively maximum a pos- teriori (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 con- straints, which makes the overall QMAP estimation unreliable. To ensure that the QMAP estimation does not violate any given parameter constraint and further improve the learn- ing 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 al- gorithm outperforms most of the existing parameter learning methods when the parameter constraints are correct.