Data Science Seminar
Date: Friday, 12 September 2025
Time: 2.00 to 3.00 p.m.
Venue: NKN Hall, CMI
Rough Path Theory and the Signature Transform: A New Paradigm for Sequential Data Analysis
Thomas Cass
Imperial College, London, UK.
12-09-25

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Abstract

The Chen-Fliess series lies at the heart of rough path theory, a framework that rigorously defines solutions to nonlinear differential equations driven by highly irregular signals. This series naturally leads to the signature transform, a powerful tool for summarising multimodal, irregularly sampled, and ordered data in a form amenable to computation and learning. Central to this approach is its role in providing a canonical basis for functions on path spaces, enabling principled representations of complex sequential data.

This talk surveys the mathematical foundations of rough paths and the signature transform, highlighting their practical relevance in modern data science. We explore connections to probability theory, including random matrix models, and draw parallels with key concepts in statistical learning such as kernel methods. These links reveal an interplay between abstract mathematics and real-world applications, allowing the signature transform to be used as a versatile and theoretically grounded tool for sequential data analysis.