[2305.10413] On Consistency of Signature Using Lasso

Statistics > Machine Learning arXiv:2305.10413 (stat) [Submitted on 17 May 2023 (v1), last revised 22 Mar 2026 (this version, v5)] Title:On Consistency of Signature Using Lasso Authors:Xin Guo, Binnan Wang, Ruixun Zhang, Chaoyi Zhao View a PDF of the paper titled On Consistency of Signature Using Lasso, by Xin Guo and 3 other authors View PDF Abstract:Signatures are iterated path integrals of continuous and discrete-time processes, and their universal nonlinearity linearizes the problem of feature selection in time series data analysis. This paper studies the consistency of signature using Lasso regression, both theoretically and numerically. We establish conditions under which the Lasso regression is consistent both asymptotically and in finite sample. Furthermore, we show that the Lasso regression is more consistent with the Itô signature for time series and processes that are closer to the Brownian motion and with weaker inter-dimensional correlations, while it is more consistent with the Stratonovich signature for mean-reverting time series and processes. We demonstrate that signature can be applied to learn nonlinear functions and option prices with high accuracy, and the performance depends on properties of the underlying process and the choice of the signature. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST); Applications (stat.AP) Cite as: arXiv:2305.10413 [stat.ML]   (or arXiv:2305.10413v5 [stat.ML] for this version)   h...