Revising the Parameters of Bayesian Network with Multi-Father Nodes from Small Data Set

Bayesian networks are graphical representations of dependency relationships between variables. They are intuitive representations of knowledge and are akin to human reasoning paradigms. They are powerful tools to deal with uncertainties, and have been extensively used to the representation and reasoning of uncertain knowledge. In the past decades, they have been successfully applied in medical diagnoses, software intelligence, finance risk analysis, DNA functional analysis, Web mining and so on; and have become a rapidly growing field of research. Bayesian network learning is the foundation of its application. It includes structure learning and parameters learning. Research on parameters learning of Bayesian network with multi-father nodes from small data sets is important and challenging. Due to the insufficiency of information, many parameters of multi-father nodes can not be directly estimated. It is the key problem how these parameters can be effectively learned. In this paper, an effective and applied method of learning Bayesian network parameters with multi-father nodes from small data set is developed. Firstly, a small data set is extended by using bootstrap sampling. Then, Gibbs sampling is combined with maximum likelihood tree and Bayesian network respectively. Finally, the parameters of multi-father nodes are learned by revising a part of extended data in a certain proportion iteratively. Experimental results show that this method can efficiently learn a majority of parameters of multi-father nodes.