Stochastic Fractal Search for Bayesian Network Structure Learning Under Soft/Hard Constraints

A Bayesian network (BN) is an uncertainty processing model that simulates human cognitive thinking on the basis of probability theory and graph theory. Its network topology is a directed acyclic graph (DAG) that can be manually constructed through expert knowledge or automatically generated through data learning. However, the acquisition of expert knowledge faces problems such as excessively high labor costs, limited expert experience, and the inability to solve large-scale and highly complex DAGs. Moreover, the current data learning methods also face the problems of low computational efficiency or decreased accuracy when dealing with large-scale and highly complex DAGs. Therefore, we consider mining fragmented knowledge from the data to alleviate the bottleneck problem of expert knowledge acquisition. This generated fragmented knowledge can compensate for the limitations of data learning methods. In our work, we propose a new binary stochastic fractal search (SFS) algorithm to learn DAGs. Moreover, a new feature selection (FS) method is proposed to mine fragmented knowledge. This fragmented prior knowledge serves as a soft constraint, and the acquired expert knowledge serves as a hard constraint. The combination of the two serves as guidance and constraints to enhance the performance of the proposed SFS algorithm. Extensive experimental analysis reveals that our proposed method is more robust and accurate than other algorithms.