Rough paths, signature and statistical learning

schedule le lundi 06 mai 2019 de 17h00 à 18h00

Organisé par : A. Lefebvre, N. Meyer, O. Safsafi, T. Touati

Intervenant : Adeline Fermanian (LPSM)
Lieu : Jussieu, salle Paul Levy 16-26 - 209

Sujet : Rough paths, signature and statistical learning.

Résumé :

Modern applications of statistics and machine learning have lead to a tremendous amount of temporal data. Think for example of quantitative finance, signals from medical devices or handwriting trajecto- ries. Such data flows are traditionally considered as realizations of sampled stochastic processes. In order to use classical learning algorithms, it is necessary to represent these processes as vectors of fi- nite dimension. We will be interested in the signature transformation of a multidimensional data flow, which encodes geometric properties of its associated process. The signature dates back from the 60s when Chen (1965) noticed that a path can be represented by its iterated integrals and it has been at the center of Lyons’ rough paths theory in the 90s. The signature transformation combined with a learning algorithm has achieved state of the art results for several applications, see e.g. Yang (2017), which raises the issue of its statistical properties. Therefore, we review the main properties of the signature and we investigate its applications in statistical learning. We will look more closely at the representation of data as a path and its consequences on prediction accuracy.