Research Group "Stochastic Algorithms and Nonparametric Statistics"
Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Summer Semester 2025
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| 01.04.2025 | Prof. Dr. Vladimir Spokoiny | Estimation and inference for deep neuronal network: Blessing of dimension Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like nonlinear least squares estimation go back to Gauss and Legendre. Recent developments in statistics and machine learning like Deep Neuronal Networks (DNN) or nonlinear PDE stimulate new research in this direction which has to address the important issues and challenges of statistical inference such as huge complexity and parameter dimension of the model, limited sample size, lack of convexity and identifiability, among many others. Classical results of nonparametric statistics in terms of rate of convergence do not really address the mentioned issues. This paper offers a general approach to studying a nonlinear regression problem based on the notion of effective dimension. Despite generality, all the presented bounds are nearly sharp and the classical asymptotic results can be obtained as simple corollaries. In applications to DNN, the proposed approach helps to rigorously address the mentioned issues of overparametrization, non-convex optimization, and lack of identifiability. |
| 08.04.2025 | |
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| 15.04.2025 | |
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| 22.04.2025 | |
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| 29.04.2025 | |
| Room 3.13, HVP 11 a | |
| 06.05.2025 | |
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| 13.05.2025 | |
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| 20.05.2025 | |
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| 27.05.2025 | |
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| 03.06.2025 | Josha Dekker (University of Amsterdam) |
| Optimal decision-making with randomly arriving decision moments Control problems with randomly arriving control moments occur naturally. Financial situations in which control moments may arrive randomly are e.g., asset-liquidity spirals or optimal hedging in illiquid markets. We develop methods and algorithms to analyze such problems in a continuous time finite horizon setting, under mild conditions on the arrival process of control moments. Operating on the random timescale implied by the control moments, we obtain a discrete time, infinite-horizon problem. This problem may be solved accordingly or suitably truncated to a finite-horizon problem. We develop a stochastic primal-dual simulation-and-regression algorithm that does not require knowledge of the transition probabilities, as these may not be readily available for such problems. To this end, we present a corresponding dual representation result. We then apply our methods to several examples, where we explore in particular the effect of randomly arriving rebalancing moments on the optimal control. Joint work with Roger J.A. Laeven, John G.M. Schoenmakers and Michel H. Vellekoop. |
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| 10.06.2025 | Prof. Dr. Peter Friz (TU & WIAS Berlin) |
| Rough filtering | |
| 17.06.2025 | Dr. Alexey Kroshnin (WIAS Berlin) |
| Optimal rates of uniform approximation of additive time functionals of diffusion processes
We consider the uniform discrete approximation error of an additive time functional $int_0^1 f(X_t) d t$ of a d-dimensional Itô, diffusion $(X_t)_t$. We obtain bounds on the expected error for Hölder functions as the number of discretization points grows. Notably, there are two regimes in the one-dimensional case, depending on the Hölder exponent, but only one in higher dimensions. Furthermore, on the example of Brownian motion, we show that these bounds are tight. Based on a joint work with Oleg Butkovsky and Antoine Grenier. |
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| 24.06.2025 | Sorelle Murielle Toukam (WIAS Berlin) |
| Expected signature of diffusion processes |
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| 01.07.2025 | Dr. Helena Kremp (TU & WIAS Berlin) |
| Overcoming the order barrier for approximations of nonlinear SPDEs with additive space-time white noise |
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| 08.07.2025 | |
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| 15.07.2025 | |
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| 22.07.2025 | Dr. Ben Robinson (Universität Klagenfurt) |
| Bicausal optimal transport between the laws of SDEs |
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| 29.07.2025 | |
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| 05.08.2025 | Prof. Dr. Young-Heon Kim (University of British Columbia) |
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| 12.08.2025 | |
| 19.08.2025 | |
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| 26.08.2025 | |
| 02.09.2025 | |
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| 09.09.2025 | |
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| 16.09.2025 | |
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| 23.09.2025 | |
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| 30.09.2025 | |
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| 07.10.2025 | |
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last reviewed: June 12, 2025 by Christine Schneider