## 3 Proposed Method
### Technical Framework  
The essence of identifying the key influencing factors is to clarify the complex and nonlinear relationship among the factors in the complex system. With the support of an observation dataset, we adopt the methods of causal discovery and heuristic causal inference to solve the above problem. The overall technical framework of the research is shown in Figure 1.  
Figure 1: Technical framework for research.  
The framework includes three key parts: causal network learning, heuristic causal inference, and identification of key influencing factors, which are further divided into seven steps. The first step is to obtain the original data, which is the basis of our research. We require the original data to conform to the general characteristics of complex systems; that is, the dataset consists of enough interrelated and interacting variables, and one of them can be regarded as the target of the system. The second step is to obtain experimental data. We pre-process the original data based on specific research ideas, including missing value processing, outlier value processing, and sampling processing, to form usable experimental data. In this process, we can eliminate some variables that are clearly irrelevant to the research content by combining prior knowledge. Step 3 is partially directed causal network learning, which mainly uses the FCI algorithm [37; 38] to generate the initial causal network and combines prior knowledge and causal orientation rules to synchronously complete step 4, that is, global causal network construction. The fifth step is the construction of the adjacent local causal network of the target. The so-called adjacent local causal network refers to the target variable as the centre. Within a given order, it searches the causal variables connected with it, and the causal network composed of them is the adjacent local causal network of the target variable. We set that the order of an adjacent local causal network with a maximum causal pathway distance of \(k\) (\(k\geq 1\)) between the cause variable and the target variable is k. By referring to the concepts of \"path\" and \"distance\" in complex networks, the direct cause, indirect cause, and causal pathway length are defined, and the adjacent local causal network of the target variable is obtained via graph search. Step 6 is the calculation of the causal pathway contribution degree. The causal pathway contribution degree reflects the potential impact of cause variables (direct causes/indirect causes) on the target variable from the perspective of causal network topology analysis. It is used to comprehensively consider the number of causal pathways pointing to the target variable using cause variables and the distance of causal pathways from cause variables to the target. For its formal definition, see Definition 7 in Section 3.3. Based on defining the global causal pathway, local causal pathway, and average causal pathway's length, we establish a heuristic causal effect calculation model to achieve an approximate calculation of causal effects among variables in the system. Step 7 is based on the calculated causal pathway contribution degree; the key influencing factors of the target are finally identified.  
In the above research, steps 1-4 correspond to the completion of causal network learning, and steps 5-7 correspond to the completion of heuristic causal inference and identification of key influencing factors.