EI-Loss: Enhancing infectious disease forecasting via HSIC-guided signal-noise separation

Accurate forecasting of infectious disease dynamics is critical for public health preparedness, yet conventional deep learning models rely on generic loss functions (MSE/MAE) that fail to disentangle true transmission dynamics from systematic surveillance distortions and ignore epidemiological temporal structure. We propose Epidemic-Informed Loss (EI-Loss), which enhances predictive performance by incorporating a Hilbert-Schmidt Independence Criterion (HSIC) regularizer. By maximizing dependence between model residuals and surrogate noise, EI-Loss extracts robust transmission signals while delegating unpredictable variation to stochastic residuals. Theoretically, we derive the first finite-sample generalization bound for HSIC in epidemic forecasting, proving MSE-trained models systematically underestimate true error proportionally to their capacity to fit reporting noise. Across three diverse influenza datasets and multiple models, EI-Loss achieves state-of-the-art performance with average MSE reductions of 11.2-15.8% and MAE improvements of 10.9-15.1%, with gains accelerating to 19.6% at 60-week horizons.