On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics

TL;DR

This paper evaluates Randomized Signatures, a scalable variant of the Signature Transform, demonstrating its advantages over traditional methods in modeling complex dynamical systems with irregular inputs.

Contribution

The study provides an extensive experimental analysis of Randomized Signatures, highlighting its benefits in efficiency, robustness, and accuracy compared to existing approaches.

Findings

Outperforms truncated Signature in various metrics

Reduces training time and model complexity

Shows robustness and data efficiency

Abstract

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.