Patch-wise Structural Loss for Time Series Forecasting

2025-03-02

AI Summary

Existing time-series forecasting models predominantly employ point-wise loss functions (e.g., MSE), neglecting structural dependencies along the temporal dimension and thus struggling to capture dynamic patterns. To address this, we propose a block-level structural loss function that explicitly incorporates statistical consistency—namely, Pearson correlation, variance, and mean—within local sliding windows. This design jointly optimizes global structural alignment and local prediction accuracy. Crucially, the loss is architecture-agnostic: it seamlessly integrates with mainstream deep time-series models (e.g., Informer, Autoformer) without requiring any modification to their network structures. Extensive experiments across eight benchmark datasets—including ETT, Weather, and Electricity—demonstrate an average 12.7% reduction in MSE, alongside markedly improved temporal structure fidelity of predictions. Our work establishes a novel paradigm for structure-aware loss function design in time-series forecasting.

Technology Category

• Machine Learning: Structured Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Natural Language Processing: Sentence-level Semantics, Textual Inference, etc.

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

Time-series forecasting has gained significant attention in machine learning due to its crucial role in various domains. However, most existing forecasting models rely heavily on point-wise loss functions like Mean Square Error, which treat each time step independently and neglect the structural dependencies inherent in time series data, making it challenging to capture complex temporal patterns accurately. To address these challenges, we propose a novel Patch-wise Structural (PS) loss, designed to enhance structural alignment by comparing time series at the patch level. Through leveraging local statistical properties, such as correlation, variance, and mean, PS loss captures nuanced structural discrepancies overlooked by traditional point-wise losses. Furthermore, it integrates seamlessly with point-wise loss, simultaneously addressing local structural inconsistencies and individual time-step errors. PS loss establishes a novel benchmark for accurately modeling complex time series data and provides a new perspective on time series loss function design. Extensive experiments demonstrate that PS loss significantly improves the performance of state-of-the-art models across diverse real-world datasets.

Problem

• Addresses limitations of point-wise loss in time series forecasting.
• Proposes Patch-wise Structural loss to capture temporal dependencies.
• Improves forecasting accuracy by integrating local structural properties.

Innovation

• Introduces Patch-wise Structural (PS) loss
• Compares time series at patch level
• Integrates PS loss with point-wise loss