URegina Topology and Geometry Seminar: Darrick Lee

Abstract: Functional data such as time series and images are ubiquitous in applications and are equipped with natural concatenation operations. For machine learning applications, it is often helpful to build structured representations of such data which preserve the underlying algebraic structure, and satisfy universality (allows us to approximate functions) and characteristicness (allows us to characterize probability measures). By viewing such data as paths and surfaces, we discuss how (higher) parallel transport can be used to provide such representations, and discuss their universal and characteristic properties. Based on joint work with Harald Oberhauser (Oxford).