Our interest lies in random projections of high dimensional objects, e.g., random vectors and sets. Such objects arise in a variety of contexts. In the statistics and machine learning literature, projections onto random lower-dimensional subspaces are employed for dimension reduction, clustering, regression, and topic discovery in the setting of high-dimensional data. We focus on projections of random vectors selected according to some probability measure on the n-dimensional lp-ball. More precisely, we study probabilistic limit theorems such as a central limit theorem, or a moderate and a large deviation principle for the volume of random projections of general lp-balls.
| Principal Investigator(s) at the University | Prof. Dr. Joscha Prochno (Lehrstuhl für Funktionalanalysis) |
|---|---|
| Project period | 01.10.2023 - 30.09.2026 |
| Source of funding |
DFG - Deutsche Forschungsgemeinschaft > DFG - Sachbeihilfe
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| Projektnummer | 516672205 |
| Themenfelder | Mathematik |
