For smooth functionals of Itô diffusions, the level-K truncated signature achieves minimax-optimal squared L2 error of order K^{-2γ}, and this rate propagates through Signature-OLS, Signature-LASSO, and Signature-Logistic.
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How Fast Do Signatures Learn? Statistical Theory and Applications for Path Regression
For smooth functionals of Itô diffusions, the level-K truncated signature achieves minimax-optimal squared L2 error of order K^{-2γ}, and this rate propagates through Signature-OLS, Signature-LASSO, and Signature-Logistic.