18.12.2023 15:00 Alexander Schell (ETH Zürich):
Functional Analytical Insights into Rough Path Theory and its Expanding Frontiers in Data Science and Machine LearningMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

The theory of rough paths, conceived in the 1990s, has recently evolved significantly beyond its origins in controlled and stochastic differential equations, witnessing a remarkable surge in applications within the realms of data science and machine learning. The central concept behind these advances is the signature transform, a map that captures a multidimensional data stream by sending it to the sequence of its iterated integrals. Intended as an easily accessible invitation to the field, this talk offers a natural functional-analytical perspective on the signature transform and, going beyond theoretical abstraction, gives a brief outlook on how related ideas from rough path theory can be applied to some contemporary challenges within stochastic analysis and statistical machine learning.