Research Of Consensus Bayesian Networks And Its Application

The combination of Bayesian network has been researched for several years. And in thispaper, we proposed a novel Bayesian network combination algorithm. We have carefullystudied the properties of probabilities and our combination algorithm is based on it. Due toprobabilistic independence, Conditional Probability Tables (CPTs) can be extended, thencorresponding nodes’ CPTs can be changed into a same form and the aggregation function canbe applied to aggregate the conditional probabilities in the corresponding positions in thecorresponding CPTs of the Bayesian networks. The time complexity and space complexity ofthis process is very small. Next, we proposed a new method to determine whether twovariables are dependent or not. We proved that whether two variables are dependent or not canbe determined by judging the conditional probability of the two variables changes or not whenthe value of one node changes. And then we can use the variance to determine whether theconditional probability changes or not. Some nodes’ CPTs were extended before thecombination of Bayesian networks, so they may have bogus parents after combination, thenwe can use this method to find them, delete the bogus edges and simplify the CPTs. After thatwe presents a new probability aggregation function. Then we introduced an algorithm tocombine Bayesian networks which defined over the same variable set and have a same priororder.Based on the research of the equivalence classes of Bayesian networks, we present amethod to change a Bayesian network into another Bayesian network which is equivalentwith it by reversing some directed edges. With this method, we can change the Bayesiannetworks that with a different prior order into that with the same prior order. Next, weintroduced a method to extended the Bayesian networks waiting to be combined into theBayesian networks that defined over the same variable set. With this two method, any twoBayesian networks can be combined.After that, we introduced two improtant application of the Bayesian networkcombination algorithm. In the Bayesian network structure learning integrating expertknowledge, we can view the expert knowledge as a small Bayesian network, and we cancombine it with the Bayesian network that learned from the dataset to construct the consensusBayesian network. Secend, we proposed that using the consensus Bayesian Bayesian networkfor modeling the genes’regulatory pathway, the Bayesian network combination algorithm canimprove the accuacy of the sturcture learning.