Friday 15:00 - 17:00 in SH 2421 Conference Room (Starting from April 11.)
Contents: This reading group introduces the fundamentals of rough paths and signatures, and studies their edge-cutting applications in different fields, e.g., financial modelling, machine learning, control theory and data science (depending on participants' interests). The first four weeks focus on lectures and an exercise class to build a solid foundation, while the remaining weeks emphasise paper discussions and project development.
Calendar:
Week 1 (April 11.) - Qijin Shi - Introduction, Fundamentals of Signatures (Draft)
Week 2 (April 18.) - Qijin Shi - Supervised Learning with Signatures, Intro to Rough Paths and RP Topology (Draft)(Handout)
Week 3 (April 25.) - Qijin Shi - Rough Integral, Rough Differential Equations and Links to Stochastic Analysis (Draft)(Notes)
Week 4 (May 2.) - Qijin Shi - Consistency between Rough Paths and Controlled Paths and some Exercises (Exercises) (Draft)
Week 5 (May 9.) - No Talk
Week 6 (May 16.) - Ka Lok Lam - The Universal Approximation Theorems for Signatures and Applications
Week 7 (May 23.) - Sam Babichenko -Â Expansion of Stochastic Processes with Signatures and Applications
Week 8 (May 30.) - Botao Jin: Using Signatures to Characterise Stochastic Processes
Week 9 (June 6.) - Haosheng Zhou - GAN: From Wasserstein-GAN to SIG-Wasserstein GAN
Week 10 (June 13.) - Qijin Shi: Controlled Neural Network: Form Neural ODE via Neural SDE to Neural RDE and Neural CDE
References:
Ilya Chevyrev, Andrey Kormilitzin, A Primer on the Signature Method in Machine Learning, 2016
Lajos Gergely Gyurk, Terry Lyons, Mark Kontkowski, and Jonathan Field, Extracting information from the Signature of a Financial Data Stream, 2014
Thomas Cass, Cristopher Salvi, Lecture Notes on Rough Paths and Applications to Machine Learning, 2024
Peter Friz, Martin Hairer, A Course on Rough Paths with an Introduction to Regularity Structures, 2020
Terry Lyons, Andrew Mcleod, Signature Methods in Machine Learning, 2022
Christa Cuchiero, Guido Gazzani, Sara Svaluto-Ferro, Signature-based Models: Theory and Calibration, 2023
Adeline Fermanian, Terry Lyons, James Morrill, Cristopher Salvi, New Directions in the Applications of Rough Path Theory, 2023
Others (to be updated)...
Special thanks to Professor Tomoyuki Ichiba and Professor Ruimeng Hu for offering valuable suggestions on the organisation and contents of this reading group.