用超复数模型和频域聚合提升时序预测的效率与精度
Efficient Time Series Forecasting via Hyper-Complex Models and Frequency Aggregation
- 提出基于频域聚合的FIA-Net，用超复数结构融合多个短时傅里叶窗口信息
- 在多个基准上优于现有方法，准确率更高且参数量减少最多3倍
- 适合需要高效长程依赖建模的时序预测场景，如金融、气象
时序预测是统计学与机器学习中的经典问题，核心挑战在于处理长程依赖。近期工作采用短时傅里叶变换（STFT）将序列分块并分别进行傅里叶变换。本文提出频率信息聚合（FIA-Net），基于新型复值MLP架构，在频域聚合相邻窗口信息。为扩大感受野，将一组窗口视为超复数（HC）向量，利用超复数代数统一整合所有STFT窗口信息。超复数MLP骨架显著提升对长时依赖的建模能力，且因运算特性，参数量最多比标准窗口聚合方法少3倍。在多个时序基准测试中，该方法在准确率与效率上均超越现有最优模型。代码已公开于https://anonymous.4open.science/r/research-1803/。
原文摘要 · Abstract (English)
Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier transform (STFT), which partitions the sequence into multiple subsequences and applies a Fourier transform to each separately. We propose the Frequency Information Aggregation (FIA)-Net, which is based on a novel complex-valued MLP architecture that aggregates adjacent window information in the frequency domain. To further increase the receptive field of the FIA-Net, we treat the set of windows as hyper-complex (HC) valued vectors and employ HC algebra to efficiently combine information from all STFT windows altogether. Using the HC-MLP backbone allows for improved handling of sequences with long-term dependence. Furthermore, due to the nature of HC operations, the HC-MLP uses up to three times fewer parameters than the equivalent standard window aggregation method. We evaluate the FIA-Net on various time-series benchmarks and show that the proposed methodologies outperform existing state of the art methods in terms of both accuracy and efficiency. Our code is publicly available on https://anonymous.4open.science/r/research-1803/.
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