Causal Discovery and Reasoning for Continuous Variables with an Improved Bayesian Network Constructed by Locality Sensitive Hashing and Kernel Density Estimation.

The structure learning of a Bayesian network (BN) is a crucial process that aims to unravel the complex dependencies relationships among variables using a given dataset. This paper proposes a new BN structure learning method for data with continuous attribute values. As a non-parametric distribution-free method, kernel density estimation (KDE) is applied in the conditional independence (CI) test. The skeleton of the BN is constructed utilizing the test based on mutual information and conditional mutual information, delineating potential relational connections between parents and children without imposing any distributional assumptions. In the searching stage of BN structure learning, the causal relationships between variables are achieved by using the conditional entropy scoring function and hill-climbing strategy. To further enhance the computational efficiency of our method, we incorporate a locality sensitive hashing (LSH) function into the KDE process. The method speeds up the calculations of KDE while maintaining the precision of the estimates, leading to a notable decrease in the time required for computing mutual information, conditional mutual information, and conditional entropy. A BN classifier (BNC) is established by using the computationally efficient BN learning method. Our experiments demonstrated that KDE using LSH has greatly improved the speed compared to traditional KDE without losing fitting accuracy. This achievement underscores the effectiveness of our method in balancing speed and accuracy. By giving the benchmark networks, the network structure learning accuracy with the proposed method is superior to other traditional structure learning methods. The BNC also demonstrates better accuracy with stronger interpretability compared to conventional classifiers on public datasets.