Learning with Expected Signatures: Theory and Applications
Lorenzo Lucchese, Mikko S. Pakkanen, Almut E. D. Veraart
Abstract
The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This "model-free"' embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML) algorithms for time series and sequential data. The convergence results proved in this paper bridge the gap between the expected signature's empirical discrete-time estimator and its theoretical continuous-time value, allowing for a more complete probabilistic interpretation of expected signature-based ML methods. Moreover, when the data generating process is a martingale, we suggest a simple modification of the expected signature estimator with significantly lower mean squared error and empirically demonstrate how it can be effectively applied to improve predictive performance.
BibTeX
@inproceedings{
lucchese2025learning,
title={Learning with Expected Signatures: Theory and Applications},
author={Lorenzo Lucchese and Mikko S. Pakkanen and Almut E. D. Veraart},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=yDTwamN4LQ}
}