Browsing by Author "Dümbgen, Lutz"
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- ItemConfidence sets for the optimal approximating model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Rohde, Angelika; Dümbgen, LutzIn the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the construction of adaptive confidence regions is severely limited (cf. Li, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence sets for the best approximating model in terms of risk. Our construction is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral $chi^2$--distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.
- ItemStatistics meets Machine Learning(Zürich : EMS Publ. House, 2020) Dümbgen, Lutz; Müller, Klaus-Robert; Samworth, RichardTheory and application go hand in hand in most areas of statistics. In a world flooded with huge amounts of data waiting to be analyzed, classified and transformed into useful outputs, the designing of fast, robust and stable algorithms has never been as important as it is today. On the other hand, irrespective of whether the focus is put on estimation, prediction, classification or other purposes, it is equally crucial to provide clear guarantees that such algorithms have strong theoretical guarantees. Many statisticians, independently of their original research interests, have become increasingly aware of the importance of the numerical needs faced in numerous applications including gene expression profiling, health care, pattern and speech recognition, data security, marketing personalization, natural language processing, to name just a few. The goal of this workshop is twofold: (a) exchange knowledge on successful algorithmic approaches and discuss some of the existing challenges, and (b) to bring together researchers in statistics and machine learning with the aim of sharing expertise and exploiting possible differences in points of views to obtain a better understanding of some of the common important problems.