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MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting

arXiv:2603.18432v1 Announce Type: new Abstract: Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to ad

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Runze Yang, Longbing Cao, Xiaoming Wu, Xin You, Kun Fang, Jianxun Li, Jie Yang · · 1 min read · 6 views
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arXiv:2603.18432v1 Announce Type: new Abstract: Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to address the frequency (spectral) leakage restricting high-quality low-rank decomposition, MLOW enables a flexible selection of input horizons and frequency levels via a mathematical mechanism. Visual analysis demonstrates that MLOW enables interpretable and hierarchical multiple-effect decomposition, robust to noises. It can also enable plug-and-play in existing TSF backbones with remarkable performance improvement but minimal architectural modifications.

Executive Summary

The article proposes MLOW, an interpretable low-rank frequency magnitude decomposition pipeline for time series forecasting. MLOW captures dominant trending and seasonal effects by learning a low-rank representation of the magnitude spectrum. A novel hyperplane-nonnegative matrix factorization method is introduced to achieve efficient and generalizable decomposition. To address frequency leakage, MLOW enables flexible selection of input horizons and frequency levels. Visual analysis demonstrates robustness to noises and remarkable performance improvement with minimal architectural modifications. This work has significant implications for enhancing the interpretability and accuracy of time series forecasting models.

Key Points

  • ▸ MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects.
  • ▸ A novel hyperplane-nonnegative matrix factorization method is introduced for efficient and generalizable decomposition.
  • ▸ MLOW enables flexible selection of input horizons and frequency levels to address frequency leakage.

Merits

Strength in Interpretable Decomposition

MLOW provides interpretable multi-effect decomposition, enabling users to understand the underlying patterns in time series data.

Efficient and Generalizable

The proposed hyperplane-nonnegative matrix factorization method achieves efficient and generalizable decomposition, making MLOW a robust solution for time series forecasting.

Demerits

Limited Evaluation on Real-World Datasets

The article primarily evaluates MLOW on synthetic datasets, and its performance on real-world datasets remains to be seen.

Potential Overfitting

The use of low-rank matrix factorization methods may lead to overfitting if not properly regularized, which could negatively impact the model's generalizability.

Expert Commentary

The article proposes a novel approach to time series forecasting, leveraging frequency magnitude decomposition to capture dominant trending and seasonal effects. The introduction of hyperplane-nonnegative matrix factorization is a significant contribution, as it enables efficient and generalizable decomposition. However, the article's primary evaluation on synthetic datasets raises concerns about its performance on real-world datasets. The potential for overfitting also warrants further investigation. Nevertheless, MLOW's potential for enhancing the interpretability and accuracy of time series forecasting models makes it a promising area of research.

Recommendations

  • ✓ Further evaluation on real-world datasets is necessary to assess MLOW's performance in diverse scenarios.
  • ✓ Regularization techniques should be explored to mitigate the risk of overfitting and improve the model's generalizability.

Sources

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