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As an effective tool for knowledge representation and uncertainty reasoning, Bayesian networks (BNs) are widely used in various fields. However, learning the structure of BN is an NP-hard problem. It is impractical to rely solely on the experience and knowledge of domain experts to build BN. Data-driven learning of BN has become a necessity. For the learning of a BN structure with data containing continuous variables, the typical method is to discretize the data or assume that the data follows the Gaussian distribution, and then apply the traditional BN structure learning methods to discover the causal relationship. The discretization inevitably leads to the loss of valuable information of the data. Realworld data sometimes may not follow the Gaussian distribution, which can cause deviation in causality. In this paper, a new constraint-based BN learning method for continuous variables is proposed for BN structure learning. Mutual information and conditional mutual information are derived by a non-parametric kernel density estimation (KDE). The correlation between any two nodes can be determined without assumptions. As new conditional independence tests, they are used in the max-min parents and children (MMPC) algorithm, which is a typical constraint-based method. We compare the proposed method with traditional BN methods using well-known benchmark networks. Synthetic continuous data are generated by linear structural equations. The experimental results show that our method has a good performance. It can be used as an effective BN structure learning method for continuous variables.
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