Title

"Mean and PGA for time series : the signature method answer!"

Abstract

Multivariate time series (MTS) are ubiquituous in many fields as finance, environment or geosciences... In this talk we shall present a tool which is a analoguous of moments for MTS : the iterated integral signature.

The two main contributions of this talk are related to an extension of mean and PCA to signatures of MTS, based on the lie group properties of the signature space. We illustrate on simulated and real data the effectiveness of our approach, compared to previous versions of PCA.

Bibliography

• 1-I. Chevyrev and A. Kormilitzin  A primer on the signature method in machine learning. arXiv preprint arXiv:1603.03788.
• 2-M. Clausel, J. Diehl, R. Mignot, L. Schmitz, N. Siugara, K. Usevich. The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures. Accepted in SIAM Journal on Applied Algebra and Geometry (2024).
• 3- R. Mignot, M. Clausel, K. Usevich and N. Sugiura, “Principal geodesic analysis for time series encoded with signature features.” Preprint hal-04392568, 2024
• 4- X. Pennec, X. and M. Lorenzi, Beyond Riemannian geometry: The affine connection setting for transformation groups. In Riemannian Geometric Statistics in Medical Image Analysis, pages 169–229. (2020)

Biography

Marianne Clausel (IECL, Université de Lorraine) has been a professor at the Université de Lorraine, affiliated with IECL, since September 2017. She is also an external collaborator of the SiMul team at CRAN. From 2011 to 2017, she was an associate professor in the DAO team at Laboratoire Jean Kuntzmann (Université Grenoble Alpes). Since April 2019, Marianne has been a member of the Scientific Council of the French Machine Learning Society. From February 2022 to September 2023, she was a member of the Scientific Council of INSMI (Institut national des sciences mathématiques et des interactions), which is one of ten CNRS institutes. In 2018-2019, she was a member of the Artificial Intelligence Committee of the French National Agency (CES 23), participating in the selection of ANR projects in this field.  Since March 2018, Marianne has been an associate member of the APTIKAL team at the Grenoble Computer Science Laboratory, working mainly on machine learning and data analysis. She has worked with this group for five years. From September 2017 to August 2021, Marianne Clausel was a member of the AMIES Board of Directors. To this day, she is still involved in interactions with SMEs. From 2015 to 2021: Member of the Jury for the Agrégation Externe de Mathématiques. Marianne was involved in the selection procedures for secondary school mathematics teachers, notably for the “Modeling” oral test. From September 2019 to August 2021, she was also co-responsible, with F. Nicaise, for the “Probability and Statistics” option of the Agrégation Externe (pilot of option A in modeling).