Project B01
Statistical learning from path observations

Project description

Statistics and machine learning are now successfully applied to extremely complex and high-dimensional problems, often with data having a natural path-like structure, such as time series. This project aims to explore the statistical properties of the theory of rough paths and compare it with other methods. We will use path signatures as feature maps in learning, incorporating them into standard classification methods and analyzing the data with algebraic and geometric methods. The goal is to create explainable classifiers with theoretical guarantees for practical applications. 

Principal Investigators

Carlos Améndola (TU Berlin)

Christian Bayer (WIAS) 

Markus Reiß (HU Berlin)

Project members

Gabriel Riffo (TU Berlin)

Nikolas Tapia (WIAS & HU Berlin)

Publications

• Améndola, C., Galuppi, F., Ríos Ortiz, Á.D., Santarsiero, P., Seynnaeve, T., 2025. Decomposing tensor spaces via path signatures. Journal of Pure and Applied Algebra 229, 107807. https://doi.org/10.1016/j.jpaa.2024.107807 (A04, B01)

Preprints

• Shmelev, D., Ebrahimi-Fard, K., Tapia, N., Salvi, C., 2025. Explicit and Effectively Symmetric Runge-Kutta Methods. https://arxiv.org/abs/2507.21006

• Berglund, N., Klose, T., Tapia, N., 2025. Perturbative renormalisation of the Φ⁴₄₋ε model via generalized Wick maps. https://doi.org/10.48550/arXiv.2507.03820

• Beda, J., dos Reis, G., Tapia, N., 2025. An introduction to tensors for path signatures. https://doi.org/10.48550/ARXIV.2502.15703

• Chevyrev, I., Diehl, J., Ebrahimi-Fard, K., Tapia, N., 2024. A multiplicative surface signature through its Magnus expansion. https://doi.org/10.48550/ARXIV.2406.16856 

• Bayer, C., Redmann, M., 2024. Dimension reduction for path signatures. https://doi.org/10.48550/ARXIV.2412.14723 (B01, B03)