MDK-MoE: Multi-view Decomposed Kalman Mixture of Experts Framework for Non-stationary Time Series Forecasting

Non-stationary time series forecasting (NTSF) requires modeling evolving trends and seasonal patterns. Although linear decomposition operators (e.g., FFT) help isolate these patterns, they often introduce operator-dependent biases and idiosyncratic noise. To address this issue, we propose a novel Multi-view Decomposed Kalman Mixture of Experts (MDK-MoE) framework, which \textit{improves forecasting by strategically integrating multiple complementary, yet biased, linear decompositions}. Specifically, a Multi-view Decomposition (MVD) extracts frequency components from three complementary views. To mitigate view-specific noise, a Maximizing Mutual Information (MMI) enhances cross-view consistency, maximizes task-relevant information across diverse views, and suppresses view-dependent task-irrelevant information. To address the conflicts inherent in multi-source observations, the efficient Kalman MoE adaptively fuses distinct multi-view features. Instead of adopting traditional $O(d^3)$ covariance inversion, our learnable Kalman gain design enhances numerical stability and enables reliable state estimation under non-stationary scenarios. Extensive experiments on 13 real-world datasets demonstrate that MDK-MoE consistently achieves state-of-the-art performance.