## 6 Conclusions  
In view of the natural advantages of causal inference in revealing the essential laws of things, a heuristic causal inference method for identifying the key factors influencing complex systems is proposed. On the basis of acquiring the causal network among variables by using observational data, the direct cause and indirect cause of the target variable are defined, and the global causal pathway, local causal pathway, and average causal pathway length from the cause variable to the target variable are defined. By referring to the analysis approach for a complex network, the causal pathway contribution degree is proposed to replace the causal effect of the cause variable on the target variable. Based on this, heuristic causal inference is carried out, which helps to quickly identify the key factors influencing the system from the perspective of causality.  
Simulation experiments are carried out on the SECOM dataset, and a causal network consisting of 347 nodes and 493 edges is obtained. Taking product quality test results as the target variable, the key influencing factors are identified. Based on the modelling analysis process and the experimental results of our research, the following conclusions can be drawn:  
(1) It is feasible to analyse complex systems via causal science, and the causal network that drives the generation of a system monitoring dataset can be obtained by combining the traditional causal discovery method with domain prior knowledge.  
(2) The heuristic causal inference method proposed in this paper addresses the problem that it is difficult to identify key influencing factors in complex systems. The core index of heuristic causal inference, the causal path contribution degree, can scientifically reflect the causal impact of cause variables on the target variable and can be quantitatively calculated with low computational complexity.  
(3) Compared with the method based on experimental simulation and DEMATEL, our proposed method has certain advantages. First, our proposed method does not need to establish a system simulation model, so it has better applicability. In general, it is expensive or impossible to build simulation models for complex systems with multiple factors. In addition, the proposed method combines the theories and techniques of network science and causal science and is based on the scientific analysis of data generated by complex systems, avoiding the influence of experts' subjective factors, such as the DEMATEL method, on the analysis results to have a higher degree of availability.  
Since the proposed model combines the theory of causal inference and complex networks, it can be used to analyse complex systems and problems in different forms in practical applications, such as the analysis of the causes of major diseases and the analysis of the key factors affecting education. Since we made only a preliminary exploration, we can continue to conduct in-depth integration studies of complex networks and causal inference in the future, including considering causal factors in network topology analysis and studying robustness and evolution rules in causal networks.  
J.W.: conceptualization, writing--original draft, writing--reviewing and editing, methodology, validation, formal analysis. Y.L.: supervision, writing--reviewing and editing. D.L.: supervision, data procession, formal analysis. W.Z.: supervision, writing--editing. J.H.: supervision, writing--editing. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The dataset and code generated during the current study are not publicly available because the data and code also form part of the ongoing study, but they can be obtained from the corresponding authors according to reasonable requirements.  
The authors thank all reviewers who helped to improve this manuscript.  
The authors declare no conflict of interest.