MoGU: Mixture-of-Gaussians with Uncertainty-based Gating for Time Series Forecasting

We introduce Mixture-of-Gaussians with Uncertainty-based Gating (MoGU), a novel Mixture-of-Experts (MoE) framework designed for regression tasks. MoGU replaces standard learned gating with an intrinsic routing paradigm where expert-specific uncertainty serves as the native gating signal. By modeling each prediction as a Gaussian distribution, the system utilizes predicted variance to dynamically weight expert contributions. We validate MoGU on multivariate time-series forecasting, a domain defined by high volatility and varying noise patterns. Empirical results across multiple benchmarks, horizon lengths, and backbones demonstrate that MoGU consistently improves forecasting accuracy compared to traditional MoE. Further evaluation via conformal prediction indicates that our approach yields more efficient prediction intervals than existing baselines. These findings highlight MoGU's capacity for providing both competitive performance and reliable, high-fidelity uncertainty quantification. Our code is available at: https://github.com/yolish/moe_unc_tsf