Research On Learning Bayesian Networks Structure With Hidden Variables

In the past decades, a great deal of research has focused on learning BayesianNetworks from observation data. It is an important problem that hidden or latentvariables exist in Bayesian Networks. These variables are not observed, yet theirbring together the complex dependencies between the observed variables tosimplify the network structure and network learning, inference and prediction havea major impact. Therefore, the learning of Bayesian Networks model with hiddenvariables become an important research content of this field; the detection ofhidden variables and determine their position in the network are a challengingproblem, but also has important scientific significance and high application value.In this dissert，we explore the problem of new hidden variable in BayesianNetworks. Bayesian network structure learning with hidden variables include twoaspects: first, the number of detect network contains hidden variables; The secondis to determine the local network structure with hidden variables. In view of the twoaspects, carried out in this article are as follows:Firstly,because the number of hidden variables is difficult to be determined, alearning algorithm(S-FAHF) of learing Bayesian network with hidden variables waspresented based on the structural decomposition and factor analysis.The S-FAHFalgorithm basic idea: First of all, the variables sets(Cliques) by Junction Treealgorithm, and the variables in a set have stronger dependence relationships;Second, the factor analysis method is inducted to discriminate the number andlocation of hidden variables for cliques; Finally, the BIC scoring function andLogloss function are used to test validity of hidden variables.Secondly, for using only observational data cann’t accurately determine thecausal relationship between the hidden variables and observational variables, theproposed Intervention learning methods and the S-FAHF algorithm combininglearning Bayesian networks optimal structure with hidden Variables.The basic ideaof this algorithm:find out from the initial network model to learn the local network;then,the hidden variables node is manipulated to occur the intervention data, anduse of the intervention data and observation data experiment; then, according to the change of variable probability distribution to determine the local network structureswith hidden variables; Finally,the logloss function to test the performance of thealgorithm.We evaluate all of our methods on real-life data.The results of experimentshow that S-FAHF algorithm can effectively determine the number and location ofBayesian networks with hidden variables, and logloss will significantly increase.we also demonstrate that models learned with our methods have hidden variablesthat are potential applicability and shed light on the learned domain.