Signature Kernels: Universal Feature Sets for Data Science

This lecture covers the computation of the full signature kernel as a solution to a Goursat problem, the representation of functions from data using feature maps, the use of kernels in machine learning for regression, the concept of tensor algebras, and the application of signature kernels in analyzing rough paths. It also discusses the practical implications of signature kernels in various contexts, the derivation of the Goursat PDE, and the analysis of the linear hyperbolic PDE. The lecture concludes with an overview of the signature as a universal feature set for unparameterised paths.