Patch-wise Structural Loss for Time Series Forecasting

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 Squared 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. The data and code are publicly available at: \url{https://github.com/Dilfiraa/PS_Loss}.

Time-series forecasting plays a crucial role in various domains. Most forecasting models are trained using point-wise loss functions, which evaluate errors at each time step independently. However, this approach overlooks the temporal structure of time series data, limiting the model's ability to capture complex patterns.To address this limitation, we propose a new loss function, Patch-wise Structural (PS) loss. Instead of comparing individual time points, PS loss compares short segments (patches) of the predicted and actual series. It measures the similarity between patches using statistical properties including correlation, variance, and mean, which reflect overall trend, fluctuation degree, and value offset, respectively. By incorporating these structural attributes, PS loss encourages models to generate predictions that align more closely with the underlying structure of the true series.This work provides a new perspective on loss function design by integrating patch-wise comparisons and structural information to more effectively capture the intrinsic patterns of time-series data.