Randomized Signature Layers for Signal Extraction in Time Series Data

Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto, Thomas Hofmann, Josef Teichmann

Keywords: signature, random features, time series, SDE, differential equations, rough path

Abstract:

Time series analysis is a widespread task in Natural Sciences, Social Sciences, and Engineering. A fundamental problem is finding an expressive yet efficient-to-compute representation of the input time series to use as a starting point to perform arbitrary downstream tasks.
In this paper, we build upon recent work using the signature of a path as a feature map and investigate a computationally efficient technique to approximate these features based on linear random projections. We present several theoretical results to justify our approach and empirically validate that our random projections can effectively retrieve the underlying signature of a path.
We show the surprising performance of the proposed random features on several tasks, including (1) mapping the controls of Stochastic Differential Equations to the corresponding solutions and (2) using the random signatures as time series representation for classification tasks. Besides providing a new tool to extract signatures and further validating the high level of expressiveness of such features, we believe our results provide interesting conceptual links between several existing research areas, suggesting new intriguing directions for future investigations.

One-sentence Summary: We show high expressiveness of theoretically grounded random features for times series data