Predicting the directed acyclic graph based on feature extraction

Directed acyclic graphs (DAGs) are important tools for causal discovery. However, the existing methods mainly focus on estimating DAGs from observed cross-sectional or time series data, and less attention is given to the prediction of DAGs. We introduce a novel DAG prediction method that transforms the DAG prediction problem into a matrix prediction problem. This approach obtains causal order and conditional independence information by extracting the demixing matrices and correlation coefficient matrices at different time points and predicts future DAGs by modeling these matrices. This method provides a versatile framework that can be adapted to include a range of time series forecasting techniques according to specific needs. Numerical simulations demonstrate the effectiveness of the proposed method in terms of predicting both feature matrices and the final DAG. A real-world application involving financial market data successfully predicts risk spillover relationship changes. The flexibility of the method and its ability to forecast the future relationships between variables have significant implications for fields such as economics, management, and social sciences.