RI-Loss: 一种可学习的残差引导损失用于时间序列预测
RI-Loss: A Learnable Residual-Informed Loss for Time Series Forecasting
AI总结：
RI-Loss通过建模残差序列与随机时间序列的依赖关系，提升时间序列预测的鲁棒性和噪声感知能力。
摘要：
时间序列预测依赖于从历史数据中预测未来值，但大多数最先进的方法，包括基于Transformer和多层感知机的模型，都使用均方误差（MSE）进行优化，这有两个根本性缺点：其点误差计算无法捕捉时间关系，且不考虑数据中固有的噪声。为克服这些限制，我们引入了残差引导损失（RI-Loss），一种基于希尔伯特-施瓦茨独立准则（HSIC）的新目标函数。RI-Loss通过强制残差序列与随机时间序列之间的依赖关系，显式建模噪声结构，从而实现更稳健、噪声感知的表示。理论上，我们推导了第一个非渐近的HSIC界，具有显式的双样本复杂度项，通过伯恩斯坦型集中不等式和拉多复杂度分析，实现最优收敛率。这为RI-Loss优化提供了严格的保证，同时精确量化了核空间交互。实验上，跨八个现实世界基准和五个领先预测模型的实验显示了预测性能的提升，验证了我们方法的有效性。代码已公开在：https://github.com/shang-xl/RI-Loss。
英文摘要：
Time series forecasting relies on predicting future values from historical data, yet most state-of-the-art approaches-including transformer and multilayer perceptron-based models-optimize using Mean Squared Error (MSE), which has two fundamental weaknesses: its point-wise error computation fails to capture temporal relationships, and it does not account for inherent noise in the data. To overcome these limitations, we introduce the Residual-Informed Loss (RI-Loss), a novel objective function based on the Hilbert-Schmidt Independence Criterion (HSIC). RI-Loss explicitly models noise structure by enforcing dependence between the residual sequence and a random time series, enabling more robust, noise-aware representations. Theoretically, we derive the first non-asymptotic HSIC bound with explicit double-sample complexity terms, achieving optimal convergence rates through Bernstein-type concentration inequalities and Rademacher complexity analysis. This provides rigorous guarantees for RI-Loss optimization while precisely quantifying kernel space interactions. Empirically, experiments across eight real-world benchmarks and five leading forecasting models demonstrate improvements in predictive performance, validating the effectiveness of our approach. The code is publicly available at: https://github.com/shang-xl/RI-Loss.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
