An improved constraint-based Bayesian network learning method using Gaussian kernel probability density estimator

•Use the (conditional) mutual information to calculate the correlation between different variables.•Use the entropy estimation approach of Gaussian kernel probability density estimator.•Do the experiments using the famous Alarm network, verify the improved approach. Bayesian network has powerful expression and reasoning ability of uncertainty knowledge. At present, it is widely used in many fields, such as fault diagnosis, medical diagnosis and prediction, financial analysis and prediction, decision support, etc. How to construct the Bayesian network effectively is an important research problem in the area of data mining. The constraint-based learning algorithm is commonly used for the construction of Bayesian network (BNs), such as Fast Incremental Association (Fast-IAMB) and Max-Min Parents & Children (MMPC), etc. At present, the Chi square test and correlation coefficient are often used to calculate the correlation between variables in these algorithms. But the calculation accuracy of these methods is not high, thus to influence the effectiveness of the constraint-based BNs learning algorithms. On the basis of the entropy estimation approach of Gaussian kernel probability density estimator, this paper uses the (conditional) mutual information to calculate the correlation between different variables and thus to improve the learning accuracy of the constraint-based BNs learning algorithms. The concrete calculation process about the data type of discrete, continuous and mixed has been described separately. Experiment simulations on the Alarm network prove that our algorithm can improve the learning accuracy of the existing three kinds of constraint-based BNs learning algorithms without affecting the learning efficiency. It also has better learning effect when to process the concrete and continuous data with sparsity. The method in this work can be used to learn more accurate Bayesian network, and then served the research of artificial intelligence, expert system decision making, etc.