Learning with expected signatures: theory and applications
File(s)
Published version
Author(s)
Lucchese, Lorenzo
Pakkanen, Mikko S
Veraart, Almut ED
Type
Conference Paper
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.
Date Issued
2025-07-13
Date Acceptance
2025-05-01
Citation
Proceedings of Machine Learning Research, 2025, 267, pp.40995-41055
ISSN
2640-3498
Publisher
MLResearchPress
Start Page
40995
End Page
41055
Journal / Book Title
Proceedings of Machine Learning Research
Volume
267
Copyright Statement
Copyright © 2025 by the author(s).
Identifier
https://proceedings.mlr.press/v267/lucchese25a.html
Source
The 42nd International Conference on Machine Learning (ICML 2025)
Subjects
stat.ML
stat.ML
cs.LG
math.PR
math.ST
stat.TH
Publication Status
Published
Start Date
2025-07-13
Finish Date
2025-07-19
Coverage Spatial
Vancouver, Canada