Research On Learning Bayesian Network Structure Based On Evolutionary Algorithms

Bayesian network has been a popular area on the research of AI in recent years.It has great effect on modern expert system, diagnosis system, and decision system. It has been widely used in medical diagnosis,langue understanding,voice identify,data mining etc.Bayesian network integrates graphic and probabiliy,and it indacates the internal relationship among variables, it denotes the joint probability distribution.Modeling the uncertain problem using Bayesian network, we must construct the proper network, then perform the reasoning.It is important to reasoning for the structure and parameters of Bayesian network.So it is important for consturcting the structure. But it is very difficult and time-consuming to construct Bayesian network a difficulty with expert's knowledge, the parameter is hard to confirm, so researcher seek for the some new method.Learning Bayesian network from data has been a popular area for research.Learning Bayesian network includes parameter learning and structure learning.Parameter learning is learning the cpt for each node. When the training data is complete, MLE (Maximum Likelihood Estimation) method and Bayesian method is generally used, the former can't make use of the prior knowledge and the latter can. When training data is incomplete, Gibbs sampling, EM algorithm, grads-ascend method are usually used, the essential is speculating the missing data from observed data, that is, converting the incomplete data to the complete data.But they all convergence to local solution.There are two kinds of method for learning structure of Bayesian network.They are score based method and condition independence test based method.Score based method scores the structure using score function such as MDL and BDe etc.and search the structure which has the highest score.The condition independence test based method carries on condition independence test to find the dependence relationship between variables.Evolutionary Algorithms are applied to Bayesian network learning in recent years.Many researchers use GA,GP,ACO,PSO to learn the Bayesian network. Many researchers pay much attention to the incremental learning of Bayesian network.The incremental learning can not only make use of previous result and reduce the learning time, but also reduce the storage, and adapt with changing environment.But the work in this area is few, and there are a lot of problems to solve.In this paper ,we use (μ,λ) - ES to learn Bayesian network structure incrementally.At present,most incremental learning algorithm can't only use new data and previous learning result,they must keep the old data,so they have large storage.The algorithm in this paper can learn without old data,that is,it doesn't need old data to calculate fitness and learning parameters,and it can learn only with previous learning result and old data.Because the algorithm uses a new Encoding method,it can't create illegal structure,and increases the learning efficiency.Currently ,when most Bayesian network structure learning algorithms search the structure,if they create the structure with cycle,then they don't score and reject it,or give it a low score.they select the next structure and check whether it contains cycle.And this method will create much illegal structure and check whether structure contains cycle,so it has low efficiency. In this paper,we propose a structure learning algorithm,it has small search space.At first,it learn the variables order using ACO,and then it learn the structure using GA in the order. It use an Encoding method,and during evolution it can't create illegal structure.So the search space of the algorithm is the space of variables order plus the space of DAG space given the best order.It has smaller search space than most algorithms,whose search spaces are direct graph space. So the algorithm enhances the learning efficiency.Experiment result shows that the algorithm can learn Bayesian network structure efficiently.As an important method in data mining and machine learning, there are many difficulties to do on Bayesian network learning.It will have wonderfull prospect.