Lecture notes on rough paths and applications to machine learning
This is an incremental exposition of existing theory and applications for researchers in data science and machine learning.
The notes present the signature transform and rough path theory as applied to machine learning, covering core theory and recent applications like signature-based kernel methods and neural rough differential equations.
These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first principles and then survey some recent popular applications of this approach, including signature-based kernel methods and neural rough differential equations. The notes are based on a course given by the two authors at Imperial College London.