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. |
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| 15.04.2025 | |
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| 29.04.2025 | |
| Room 3.13, HVP 11 a | |
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last reviewed: March 14, 2025 by Christine Schneider