Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecasting

TL;DR

This paper introduces FreST Loss, a novel frequency-domain training objective that enhances spatio-temporal forecasting by jointly modeling space and time, leading to improved accuracy across multiple datasets.

Contribution

The paper proposes FreST Loss, a joint spectral domain training method that captures complex spatio-temporal dependencies more effectively than existing approaches.

Findings

FreST Loss improves forecasting accuracy on six real-world datasets.

The method is model-agnostic and enhances various baseline models.

Theoretical analysis confirms reduced bias in estimation.

Abstract

Standard direct forecasting models typically rely on point-wise objectives such as Mean Squared Error, which fail to capture the complex spatio-temporal dependencies inherent in graph-structured signals. While recent frequency-domain approaches such as FreDF mitigate temporal autocorrelation, they often overlook spatial and cross spatio-temporal interactions. To address this limitation, we propose FreST Loss, a frequency-enhanced spatio-temporal training objective that extends supervision to the joint spatio-temporal spectrum. By leveraging the Joint Fourier Transform (JFT), FreST Loss aligns model predictions with ground truth in a unified spectral domain, effectively decorrelating complex dependencies across both space and time. Theoretical analysis shows that this formulation reduces estimation bias associated with time-domain training objectives. Extensive experiments on six real-world datasets demonstrate that FreST Loss is model-agnostic and consistently improves state-of-the-art baselines by better capturing holistic spatio-temporal dynamics.