Stochastic Algorithms and Nonparametric Statistics

Head:
Vladimir Spokoiny

Coworkers:
Valeriy Avanesov, Christian Bayer, Franz Besold, Simon Breneis, Oleg Butkovsky, Darina Dvinskikh, Pavel Dvurechensky, Alexander Gasnikov, Jörg Polzehl, Sebastian Riedel, John G. M. Schoenmakers, Alexandra Suvorikova, Karsten Tabelow, Nikolas Tapia

Secretary:
Christine Schneider

Honorary Members:
Peter Friz

The research group Stochastic Algorithms and Nonparametric Statistics focuses on two areas of mathematical research, Statistical data analysis and Stochastic modeling, optimization, and algorithms. The projects within the group are related to timely applications mainly in economics, financial engineering, life sciences, and medical imaging. These projects contribute in particular to the main application areas Optimization and control in technology and economy and Quantitative biomedicine of the WIAS.

Specifically, the mathematical research within the group concentrates on the

• modeling of complex systems using methods from nonparametric statistics,
• statistical learning,
• risk assessment,
• valuation in financial markets using efficient stochastic algorithms and
• various tools from classical, stochastic, and rough path analysis.

The research group hosts the focus plattform Quantitative analysis of stochastic and rough systems. Furthermore, the group contributes to the development of statistical software, especially in the area of imaging problems in the neurosciences.

Highlights

• The article "Statistical inference for Bures-Wasserstein barycenters" by A. Kroshnin, V. Spokoiny, A. Suvorikova will appear at "The Annals ofApplied Probability ". (WIAS-Preprint 2788)
• The paper "Self-concordant analysis of Frank-Wolfe algorithms" by M. Staudigl, P. Dvurechensky, S. Shtern, K. Safin, and P. Ostroukhov was accepted for International Conference on Machine Learning 2020.
• On May 12, 2020 Kirill Efimov successfully defended his dissertation "Adaptive nonparametric clustering" at Humboldt-Universität zu Berlin (supervisor Vladimir Spokoiny).
• A paper "Generalized couplings and ergodic rates for SPDEs and other Markov models" (authors: Oleg Butkovsky, Alexei Kulik and Michael Scheutzow) appeared in the journal "The Annals of Applied Probability" Volume 30, Number 1 (2020), 1-39.
• A paper "Strong existence and uniqueness for stable stochastic differential equations with distributional drift" (authors: Siva Athreya, Oleg Butkovsky, and Leonid Mytnik) appeared in the journal "The Annals of Probability" Volume 48, Number 1 (2020), 178-210.
• The monograph "Magnetic Resonance Brain Imaging with R" by Jörg Polzehl and Karsten Tabelow was published by Springer.
• Christian Bayer obtained his habilitation from Technical University Berlin.
• The Research Unit 2402 Rough paths, stochastic partial differential equeations and related topics was approved to be funded for another period. The research group contributes with the project "Numerical analysis of rough PDEs" (PIs: Christian Bayer, John Schoenmakers)
• Martin Redmann and Paolo Pigato received junior professorships in Halle and Rome, respectively.