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

arXiv:2603.04418v1 Announce Type: new 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-ag

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Zepu Wang (Xuegang), Bowen Liao (Xuegang), Jeff (Xuegang), Ban · · 1 min read · 21 views
#cs.LG #cs.AI #stat.ML

arXiv:2603.04418v1 Announce Type: new 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.

Executive Summary

This article proposes FreST Loss, a novel frequency-enhanced spatio-temporal training objective, to improve the forecasting of graph-structured signals. The proposed method leverages the Joint Fourier Transform to align model predictions with ground truth in a unified spectral domain, effectively decorrelating complex dependencies across space and time. Theoretical analysis demonstrates a reduction in estimation bias, and extensive experiments on six real-world datasets show consistent improvement over state-of-the-art baselines. The method's model-agnostic design and ability to capture holistic spatio-temporal dynamics make it a promising approach for spatio-temporal forecasting. While the article's focus on frequency-domain approaches is timely, its theoretical and empirical contributions warrant further investigation to fully understand the advantages and limitations of FreST Loss.

Key Points

  • ▸ FreST Loss is a novel frequency-enhanced spatio-temporal training objective for graph-structured signal forecasting.
  • ▸ The Joint Fourier Transform is leveraged to align model predictions with ground truth in a unified spectral domain.
  • ▸ Theoretical analysis shows a reduction in estimation bias associated with time-domain training objectives.

Merits

Strength in addressing spatio-temporal dependencies

FreST Loss effectively decorrelates complex dependencies across space and time, making it a promising approach for spatio-temporal forecasting.

Model-agnostic design

The method can be applied to various existing models, making it a versatile solution for spatio-temporal forecasting.

Consistent improvement over state-of-the-art baselines

Extensive experiments on six real-world datasets demonstrate the effectiveness of FreST Loss in capturing holistic spatio-temporal dynamics.

Demerits

Limited evaluation on theoretical bounds

While the article provides theoretical analysis, further investigation is needed to fully understand the advantages and limitations of FreST Loss.

Potential computational complexity

The use of the Joint Fourier Transform may introduce computational complexity, which could be a limitation in large-scale applications.

Expert Commentary

The article makes a significant contribution to the field of spatio-temporal forecasting by proposing a novel frequency-enhanced training objective, FreST Loss. The method's ability to decorrelate complex dependencies across space and time, as well as its model-agnostic design, make it a promising approach for various real-world applications. However, further investigation is needed to fully understand the advantages and limitations of FreST Loss, particularly in terms of its theoretical bounds and potential computational complexity. Additionally, the article's focus on frequency-domain approaches is timely, as recent methods have shown promise in mitigating temporal autocorrelation. Overall, the article provides a valuable contribution to the field and warrants further exploration.

Recommendations

  • ✓ Future research should focus on further investigating the theoretical bounds of FreST Loss and its potential computational complexity.
  • ✓ The method should be applied to other real-world datasets and applications to demonstrate its generalizability and effectiveness.

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