Causal structure learning for high-dimensional non-stationary time series

Learning the causal structure of high-dimensional non-stationary time series can help in understanding the data generation mechanism, which is a crucial task in machine learning. However, current causal discovery methods for high-dimensional non-stationary time series face several challenges, including the inability to effectively capture non-stationarity, failure to ensure acyclicity of causal graphs, and reliance on subjective threshold definitions, leading to suboptimal algorithm performance. To address these challenges, we introduce a novel Causal Structure Learning model for High-dimensional Non-stationary Time Series (CSL-HNTS). Firstly, this model presents a graph neural network to model the non-stationarity of time series. Secondly, it introduces a novel Directed Acyclic Graph (DAG) sampling method that transforms the space of DAGs into a continuous space, enabling the search for causal graphs within this continuous space to ensure acyclicity. Finally, the model proposes an automatic threshold definition method, without prior knowledge, to convert the weighted adjacency matrix into the Boolean adjacency matrix of the causal graph, thereby avoiding time-consuming postprocessing steps. The proposed approach is validated using simulation datasets and two real datasets, and is benchmarked against current state-of-the-art methods and ablation experiments. The results demonstrate a significant improvement over existing methods, highlighting the efficacy of the proposed model.