随机化签名作为学习粗糙动力学储备池的有效性研究
On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics
AI总结：
针对 Signature Transform 难以扩展高维数据的问题，本文实验评估基于 Johnson-Lindenstrauss 引理的 Randomized Signature，证明其在复杂度、训练时间、精度、鲁棒性和数据需求上更具优势。
摘要：
许多金融、物理和工程现象由高度不规则（随机）输入驱动的连续时间动力系统建模。在此背景下，一种用于时间序列分析的强大工具源于粗糙路径理论，并利用所谓的 Signature Transform（签名变换）。该算法具有很强的理论保证，但难以扩展到高维数据。本文研究了一种最近推导的随机投影变体，称为 Randomized Signature（随机化签名），它通过 Johnson-Lindenstrauss 引理获得。我们对 Randomized Signature 方法的有效性进行了深入实验评估，以尝试向社区展示该储备池的优势。具体而言，我们发现该方法在模型复杂度、训练时间、准确性、鲁棒性和数据渴求度方面优于截断 Signature 方法和其他深度学习技术。
英文摘要：
Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory and leverages the so-called Signature Transform. This algorithm enjoys strong theoretical guarantees but is hard to scale to high-dimensional data. In this paper, we study a recently derived random projection variant called Randomized Signature, obtained using the Johnson-Lindenstrauss Lemma. We provide an in-depth experimental evaluation of the effectiveness of the Randomized Signature approach, in an attempt to showcase the advantages of this reservoir to the community. Specifically, we find that this method is preferable to the truncated Signature approach and alternative deep learning techniques in terms of model complexity, training time, accuracy, robustness, and data hungriness.
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