论文标题
关于随机签名作为学习粗糙动态的储层的有效性
On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics
论文作者
论文摘要
许多金融，物理和工程现象都是由由高度不规则（随机）输入驱动的连续时间动力系统建模的。在这种情况下执行时间序列分析的强大工具植根于粗糙的路径理论，并利用所谓的签名变换。该算法具有强大的理论保证，但很难扩展到高维数据。在本文中，我们研究了一种使用Johnson-Lindenstrauss引理获得的新近衍生的随机投影变体，称为随机特征。我们对随机签名方法的有效性提供了深入的实验评估，以便向社区展示该储层的优势。具体而言，我们发现这种方法比模型复杂性，训练时间，准确性，鲁棒性和数据饥饿的截断签名方法和替代深度学习技术更可取。
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.
