Signature transforms are iterated path integrals of continuous and
discrete-time time series data, and their universal nonlinearity linearizes the
problem of feature selection. This paper revisits the consistency issue of
Lasso regression for the signature transform, both theoretically and
numerically. Our study shows that, for processes and time series that are
closer to Brownian motion or random walk with weaker inter-dimensional
correlations, the Lasso regression is more consistent for their signatures
defined by It\^o integrals; for mean reverting processes and time series, their
signatures defined by Stratonovich integrals have more consistency in the Lasso
regression. Our findings highlight the importance of choosing appropriate
definitions of signatures and stochastic models in statistical inference and
machine learning.

本文研究了在 Lasso 回归中使用 signature transforms 的一致性问题，指出对于具有较弱跨维关联的过程和时间序列，其由 Itô 积分定义的 Signature 变换更一致，而对于均值回归过程和时间序列，其由 Stratonovich 积分定义的 Signature 变换更一致，突显了在统计推断和机器学习中选择合适的签名和随机模型的重要性。