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

Understand

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.