Mathematical Sciences Department Financial Math Seminar
Stephen Sturm, WPI
Monday, March 24th
2:00 - 3:00 pm
Title: Path Signatures for Feature Extraction
Abstract: Statistical learning from data streams typically requires a process of feature extraction. Recently path signatures became a popular tool for feature extraction. Based on early work by K. T. Chen in representation theory, the notion of a path signature was rediscovered as fundamental tool in rough analysis and is becoming increasingly popular in machine learning. The strength of this method is that it incorporates naturally path dependence of the data, a drawback (that it shares with many methods in statistical learning) is that it essentially works as a black box.
In this talk I will provide an introduction to the theory of path signatures and their use in statistical learning. Show how results on the perturbation theory of stochastic processes can be used to provide interpretability to features extracted by path signatures. This is based on joint work with Hari P. Krishnan.