# Frequency-aligned loss and spectral filtering improve long-range influenza forecasting

## TL;DR

This paper introduces a new method for improving long-term influenza forecasts by using frequency-aware techniques to reduce errors and enhance accuracy.

## Contribution

The paper introduces a novel frequency-aligned loss and spectral filtering approach for long-range influenza forecasting.

## Key findings

- The proposed model reduces MSE by 6–15% and MAE by 2–20% at 24-week horizons compared to six baselines.
- Joint time-frequency supervision and dual static-dynamic filtering are essential for peak performance.

## Abstract

Long-horizon forecasts of seasonal influenza remain limited by (i) rapid error growth beyond a few weeks, (ii) entanglement of persistent seasonal cycles with transient outbreaks, and (iii) training objectives that ignore strong autocorrelation in future incidence labels.

We introduce a frequency-aware pipeline that couples a Spectral Adaptive Filtering Network with a Frequency-Aligned Direct Loss. The backbone first isolates stable global spectral bands and then builds window-specific cross-covariate filters to capture transient events; this convex loss function simultaneously supervises prediction results in both the time domain and the approximated decorrelated frequency domain, effectively reducing bias caused by autocorrelation without sacrificing point accuracy.

On 49 US states (2010–2020), 10 HHS and 9 Census regions (2002–2020), the proposed model lowers MSE by 6–15% and MAE by 2–20% at 24-week horizons vs. six recent baselines while maintaining interpretable band-pass responses that match annual and semi-annual epidemiological periodicities. Ablation and sensitivity analyses confirm that joint time-frequency supervision and dual static-dynamic filtering are both required for peak performance.

Explicit spectral decomposition coupled with autocorrelation-aware training offers a principled route to stable, interpretable long-range influenza forecasting; the modular objective can be plugged into alternative architectures to gain similar error reductions.