On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics
This work addresses a scalability bottleneck for researchers and practitioners in fields like finance and physics dealing with irregular time series data, offering an incremental improvement over existing methods.
The paper tackled the challenge of scaling the Signature Transform for analyzing rough dynamics in finance, physics, and engineering by evaluating Randomized Signatures, finding it outperforms truncated signatures and deep learning in model complexity, training time, accuracy, robustness, and data efficiency.
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.