Learning Bayesian networks using the constrained maximum a posteriori probability method

Highlights：

• This paper proposed a frame work based on the inequality constrained optimization model to learn conditional probability table parameters by incorporating expert judgments and Dirichlet priors.

• We further improve the proposed method by developing a constrained Bayesian Dirichlet prior.

• Combined the proposed method, we provide an improved expectation maximum algorithm for learning conditional probability table parameters from incomplete data.

• The contributed algorithm is tested on 13 well-known Bayesian networks, whose parameter number varies from 9 to 1157. The experiments show that the proposed method outperforms most of the existing parameter learning algorithms, especially when training data are extremely scarce.

• A real facial action unit recognition case with incomplete data is conducted. The results show that the proposed method can build a more accurate Bayesian network for recognizing facial action units.

摘要

•This paper proposed a frame work based on the inequality constrained optimization model to learn conditional probability table parameters by incorporating expert judgments and Dirichlet priors.•We further improve the proposed method by developing a constrained Bayesian Dirichlet prior.•Combined the proposed method, we provide an improved expectation maximum algorithm for learning conditional probability table parameters from incomplete data.•The contributed algorithm is tested on 13 well-known Bayesian networks, whose parameter number varies from 9 to 1157. The experiments show that the proposed method outperforms most of the existing parameter learning algorithms, especially when training data are extremely scarce.•A real facial action unit recognition case with incomplete data is conducted. The results show that the proposed method can build a more accurate Bayesian network for recognizing facial action units.