OGC-MoE: Online Granger-Causal Mixture-of-Experts for High-Dimensional Nonstationary Time Series

Causal discovery in high-dimensional multivariate time series is challenging because the number of candidate relations grows rapidly, while nonstationarity may cause the underlying causal mechanisms to evolve over time. Existing methods often assume a single stable graph or estimate local graphs independently, limiting the reuse of historical knowledge and producing unstable estimates from short windows. We propose Online Granger-Causal Mixture-of-Experts (OGC-MoE), an online graph-level mixture-of-experts framework for causal discovery in high-dimensional nonstationary time series. OGC-MoE maintains a library of causal experts, each pairing a graph-conditioned temporal predictor with a sparse Granger-causal graph. For each incoming window, the model evaluates historical experts using prediction and causal-residual information, refines their routing weights, and combines the selected graphs to represent either a single historical mechanism or a recombination of multiple mechanisms. When the mixture is insufficient, sparse local adaptation is applied to moderate deviations, whereas a window identified as a genuinely unseen state is used directly to construct a new expert. Experiments on synthetic benchmarks and real-world financial data demonstrate the strong and robust causal discovery performance of OGC-MoE.