## 2 Related Work
Random forest assigns similar importance to highly correlated features and utilizes a recursive method to remove the least important feature, recalculating the importance in each round, and continuing this process until the least important feature is eliminated. This approach allows for better feature selection by avoiding the simultaneous removal of features based solely on their importance in the initial set. Consequently, when another highly correlated feature is removed, the importance of the remaining features tends to increase, resulting in improved selection of the feature subset space. However, many hybrid algorithms exhibit sensitivity to variations in data distribution. Even when using the same algorithm, changing the training set for feature selection can yield significantly different results. This issue is of significant concern; reproducing the feature subset becomes challenging due to its high time complexity. Recent studies [6] have shown that incorporating causality to assess the relationships between features enhances the interpretability and robustness of the algorithm. The process of learning the structure of a causality graph, also known as learning the structure of a directed acyclic graph (DAG), is a well-known NP-hard problem [17]. Current structure learning algorithms struggle to effectively enforce the acyclic constraint. This limitation arises from the combinatorial nature of the acyclic constraint, where the computational complexity grows exponentially with the number of nodes. Furthermore, even if a directed acyclic graph is obtained that partially satisfies the constraint conditions, it may not be suitable for general-purpose optimization. Presently, structure learning algorithms employ various local heuristic approaches which, although capable of reducing computational complexity, do not guarantee the attainment of a globally optimal structure. Commonly used algorithms encompass branch-cut methods, dynamic programming, A* search, greedy algorithms, and coordinate descent methods [18]. In contrast to these algorithms, the approach employed in this paper utilizes distinct methods to transform the original structural optimization problem into a mathematical optimization problem. Importantly, the solution obtained in this study represents a globally optimal Bayesian network structure for the given data, showcasing significant improvement over traditional heuristic algorithms. Additionally, the employed algorithm does not necessitate researchers to possess an extensive understanding of graph theory, thereby rendering it highly valuable for research and practical applications. The paper [9] compares it with the greedy equivalent search (GES) [19], PC algorithm [20], and LINGAM [21]. The Fast Greedy Search (FGS) by [PERSON] et al. [22] is employed for GES. PC and LINGAM exhibit significantly lower accuracy compared to FGES or NOTEARS. The experiment in the paper [9] demonstrates that, as the number of nodes in the dataset increases, the accuracy of FGS measured by structural Hamming distance (SHD) declines rapidly, whereas NOTEARS exhibits excellent performance. Moreover, this discrepancy is magnified with a higher number of nodes. Furthermore, the paper demonstrates that NOTEARS outperforms for each noise model (Exp, Gauss, and Gumbel), irrespective of the absence of any prior knowledge regarding noise types.