Reproduce “Learning with Expected Signatures: Theory and Applications” on OpenResearch

About this paper

Lorenzo Lucchese, Mikko S. Pakkanen, Almut E. D. Veraart

Researchers at Imperial College London established theoretical consistency and asymptotic normality for empirical expected signature estimators when applied to continuous-time stochastic processes, including those with unbounded variation. They also introduced a novel martingale correction technique, which empirically enhanced predictive accuracy in time series classification and reduced variance in Monte Carlo derivative pricing.

Key insights

• The total error in empirically estimating expected signatures from discrete observations of continuous-time processes can be rigorously analyzed by decoupling in-fill and long-span asymptotic behaviors.
• Specific regularity and dependency conditions on continuous-time stochastic processes are essential for ensuring the accurate approximation of their full signatures from discrete observations.
• Martingale properties can be exploited to create a zero-expectation control variate, effectively reducing the variance of expected signature estimators, even for non-martingale components.

Summary by alphaXiv.