Bayesian Network Structure Learning Method for Continuous Variables Based on k-NN and Max-Min Parents and Children

For Bayesian network structure learning with continuous data, traditional methods typically require data discretization or assume that the data follows a Gaussian distribution. However, the processing method can result in information loss, and real-world data often deviates from the Gaussian assumption, leading to biased outcomes. To address these issues, we propose using the k-nearest neighbor (k-NN) algorithm to estimate mutual information and conditional mutual information for Bayesian network structure learning. The proposed method estimates serve as a new statistical method for conditional independence testing within the Max-Min Parents and Children (MMPC) algorithm. k-NN does not make any assumptions about the distribution of the data, especially as the data does not follow assumptions such as Gaussian distribution. k-NN performs more robustly. We compared the proposed method with traditional Bayesian network learning approaches on publicly available benchmark networks by using continuous data generated from linear structural equation models. Experimental results show that this method has good performance in terms of structural error and is an effective method for learning Bayesian network structures with continuous variables.