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.

翻译：许多金融、物理及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。在该背景下进行时间序列分析的有力工具源于粗糙路径理论，并利用所谓的签名变换算法。该算法具有坚实的理论保证，但难以扩展至高维数据。本文研究了一种基于Johnson-Lindenstrauss引理推导的随机投影变体——随机签名。我们通过深入实验评估随机签名方法的有效性，旨在向学界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、精度、鲁棒性及数据饥渴程度方面均优于截断签名方法及替代深度学习方法。