The path signature is a powerful tool for solving regression problems on path space, i.e., for computing conditional expectations $\mathbb{E}[Y | X]$ when the random variable $X$ is a stochastic process -- or a time-series. We provide new theoretical convergence guarantees for two different, complementary approaches to regression using signature methods. In the context of global regression, we show that linear functionals of the robust signature are universal in the $L^p$ sense in a wide class of examples. In addition, we present a local regression method based on signature semi-metrics, and show universality as well as rates of convergence.
Based on joint works with Davit Gogolashvili, Luca Pelizzari, and John Schoenmakers.
Please note: The MCF seminar usually takes place on Thursdays from 16:00 to 17:00 in L5. However, for this week, the timing will be changed to 15:00 to 16:00.