How Fast Do Signatures Learn? Statistical Theory and Applications for Path Regression
路径签名学习有多快?路径回归的统计理论与应用
Many prediction and decision-making problems in operations research involve path-valued covariates -- data that evolve over time -- for which path signatures have become a canonical feature representation. Their use is justified by a universal approximation theorem, but this is an existence result: it guarantees that a finite-level signature can approximate any continuous path functional, without quantifying how fast the approximation error decreases as the truncation level…