Stochastic Algorithms and Nonparametric Statistics

Head:
Vladimir Spokoiny

Coworkers:
Christian Bayer, Oleg Butkovsky, Pavel Dvurechensky, Davit Gogolashvili, Wilfried Kenmoe Nzali, Alexei Kroshnin, Vaios Laschos, László Németh, Luca Pelizzari, Aurela Shehu, Alexandra Suvorikova, Karsten Tabelow, Nikolas Tapia, Sorelle Murielle Toukam Tchoumegne

Secretary:
Christine Schneider

Honorary Members:
Peter Friz

Guests:
Dr. Jörg Polzehl (retired), John G. M. Schoenmakers (retired)

From left to right: Christian Bayer, Oleg Butkovsky, Pavel Dvurechensky, Peter Friz, Davit Gogolashvili, Wilfried Kenmoe Nzali, Alexei Kroshnin, Vaios Laschos, László Németh, Luca Pelizzari, Christine Schneider, John Schoenmakers, Aurela Shehu, Vladimir Spokoiny, Alexandra Suvorikova, Karsten Tabelow, Nikolas Tapia.

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.

A special research focus of the group is on quantitative analysis of stochastic and rough system, continuing the work of a former focus platform on this topic. Furthermore, the group contributes to the development of statistical software, especially in the area of imaging problems in the neurosciences.

Within the framework of the Mathematical Research Data Initiative (MaRDI) at WIAS, the research group plays an important role together with the research group "Partial Differential Equations". The assigned subgroup is part of both research groups and creates essential contributions to the development of an infrastructure for mathematical research data within the NFDI.

Highlights

• Two works were presented at the "International Conference on Machine Learning 2024":
  • Barrier Algorithms for Constrained Non-Convex Optimization, authored by Pavel Dvurechensky and Mathias Staudigl.
  • High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise, authored by Eduard Gorbunov, Abdurakhmon Sadiev, Marina Danilova, Samuel Horvath, Gauthier Gidel, Pavel Dvurechensky, Alexander Gasnikov, and Peter Richtarik.
• Egor Gladin successfully defended his PhD thesis entitled ”Cutting plane methods and dual problems" on August 20, 2024. He was supervised by Prof. Dr. V. Spokoiny
• The article "Robust multiple stopping ? A duality approach" by Roger J. A. Laeven, John G. M. Schoenmakers, Nikolaus Schweizer, Mitja Stadje was published online in Mathematics of Operations Research on May 15, 2024.
• On April 9, 2024 Simon Breneis defended his PhD thesis with predicate summa cum laude.
• The book "Rough volatility" edited by Christian Bayer, Peter K. Friz, Masaaki Fukasawa, Jim Gatheral, Antoine Jacquier, and Mathieu Rosenbaum appeared in the SIAM series Financial Mathematics in 2023.
• The article "Generalized iterated-sums signatures" by J. Diehl, K. Ebrahimi-Fard, N. Tapia appeared in the Journal of Algebra in 2023.
• The article "Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation" by S. Athreya, O. Butkovsky, K. Lê, L. Mytnik appeared in Communications on Pure and Applied Mathematics in 2024.
• The article "Optimal rate of convergence for approximations of SPDEs with non-regular drift" by O. Butkovsky, K. Dareiotis, M. Gerencsé appeared in the SIAM Journal on Numerical Analysis in 2023.
• The 19th Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis will take place June 24th-26th 2024 at WIAS.
• The project "Linguistic Meaning and Bayesian Modelling" together with ZAS and university of Tübingen is funded bei Leibniz Association April 1st, 2024 until March 31st, 2027 (V. Spokoiny and K. Tabelow).
• P. Dvurechensky, M. Liero (RG1), G. Steidl (TU Berlin), and J.-J. Zhu (WG DDOC) organized a Workshop on Optimal Transport: from Theory to Applications (https://sites.google.com/view/ot-berlin-2024/) that received a very positive feedback from the participants.
• The article "Analysis of Kernel Mirror Prox for Measure Optimization" by P. Dvurechensky and J.-J. Zhu (WG DDOC) has been accepted to "International Conference on Artificial Intelligence and Statistics 2024".
• The article "Hessian barrier algorithms for non-convex conic optimization" by P. Dvurechensky and M. Staudigl appeared online in "Mathematical Programming" (DOI 10.1007/s10107-024-02062-7).
• On November 20, 2023 Pavel Dvurechensky defended his Habilitation at the Humboldt University of Berlin.
• The article "High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance" by A. Sadiev, M. Danilova, E. Gorbunov, S. Horvath, G. Gidel, P. Dvurechensky, A. Gasnikov, and P. Richtarik was presented at "International Conference on Machine Learning 2023".
• The second revised and extended Edition of the Springer monograph Magnetic Resonance Brain Imaging: Modeling and Data Analysis with R by J. Polzehl and K. Tabelow appeared in 2023
• The paper "Optimal stopping with signatures" by CH. Bayer, P. Hager, S. Riedel, J.G.M. Schoenmakers appeared in the journal "The Annals of Applied Probability" Volume 33(1): 238-273 (DOI:10.1214/22-AAP1814 )
• The new MATH+-project AA4-13 "Equilibria for Distributed Multi-Modal Energy Systems under Uncertainty" (PIs: M. Hintermüller, C. Geiersbach, P. Dvurechensky, A. Kannan (HU Berlin)) was approved to be funded.
• The article "Decentralized Local Stochastic Extra-Gradient for Variational Inequalities" by A. Beznosikov, P. Dvurechensky, A. Koloskova, V. Samokhin, S. U Stich, and A. Gasnikov has been accepted to "Conference on Neural Information Processing Systems 2022".
• The article "Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noise " by E. Gorbunov, M. Danilova, D. Dobre, P. Dvurechensky, A. Gasnikov, G. Gidel has been accepted to "Conference on Neural Information Processing Systems 2022".
• The article "The power of first-order smooth optimization for black-box non-smooth problems" by A. Gasnikov, A. Novitskii, V. Novitskii, F. Abdukhakimov, D. Kamzolov, A. Beznosikov, M. Takac, P. Dvurechenskii, and B. Gu was presented at "International Conference on Machine Learning 2022".
• P. Dvurechensky, B. Schmitzer, and G. Steidl organized a mini-symposium on " Multimarginal Optimal Transport" at the SIAM 2022 Conference on Imaging Science (IS22).
• Pavel Dvurechensky gave an invited talk "Accelerated Alternating Minimization Methods with Application to Optimal Transport" at the One World Optimization Seminar ( https://owos.univie.ac.at/ ).
• Within the framework of the Mathematical Research Data Initiative (MaRDI), one position each was acquired in the area of "Statistics and Machine Learning" and "Cooperation with Other Disciplines", respectively.
• The MATH+ Board awarded Prof. Peter Friz with the "MATH+ Distinguished Fellowship " This includes a research grant and featured research activities by MATH+. Congratulations!
• The article "Solving optimal stopping problems via randomization and empirical dual optimization" by D. Belomestny, Ch. Bender and J.G.M. Schoenmakers appeared online in "Mathematics of Operations Research" .
• The new MATH+-project EF1-22 "Bayesian optimization and inference for deep networks" (PIs: V. Spokoiny, C. Schillings (HU Berlin)) was approved to be funded.
• The article "An accelerated method for derivative-free smooth stochastic convex optimization" by E. Gorbunov, P. Dvurechensky and A. Gasnikov appeared in "SIAM Journal on Optimization" (DOI 10.1137/19M1259225).
• The article "Generalized self-concordant analysis of Frank-Wolfe algorithms" by P. Dvurechensky, K. Safin, S. Shtern, and M. Staudigl appeared in "Mathematical Programming" (DOI 10.1007/s10107-022-01771-1).
• The new MATH+-project AA4-9 "Volatile electricity markets and battery storage: A model based approach for optimal control" (PIs: Ch. Bayer, D. Kreher (HU Berlin) und M. Landstorfer) was approved to be funded.
• MATH+-project AA4-2 "Optimal control in energy markets using rough analysis and deep networks" (PIs: Ch. Bayer, P. Friz, J. Schoenmakers and V. Spokoiny) was approved to be funded until March 31, 2025.
• On August 18, 2021 Darina Dvinskikh defended her PhD thesis with predicate summa cum laude.
• The article "Approximation of SDEs: A stochastic sewing approach" by O. Butkovsky, K. Dareiotis, M. Gerencser appeared in the journal "Probability theory and related fields" Volume 181.4, 2021: 975-1034. (DOI: https://doi.org/10.1007/s00440-021-01080-2 )
• The paper "Statistical inference for Bures-Wasserstein barycenters" by A. Kroshnin, V. Spokoiny, A. Suvorikova appeared in the journal "The Annals of Probability" Volume 31(3): 1264-1298. (DOI: 10.1214/20-AAP1618)