Jonas Wallin
Senior lecturer, Director of third cycle studies, Department of Statistics
Generalized bounds for active subspaces
Author
Summary, in English
In this article, we consider scenarios in which traditional estimates for the active subspace method based on probabilistic Poincaré inequalities are not valid due to unbounded Poincaré constants. Consequently, we propose a framework that allows to derive generalized estimates in the sense that it enables to control the trade-off between the size of the Poincaré constant and a weaker order of the final error bound. In particular, we investigate independently exponentially distributed random variables in dimension two or larger and give explicit expressions for corresponding Poincaré constants showing their dependence on the dimension of the problem. Finally, we suggest possibilities for future work that aim for extending the class of distributions applicable to the active subspace method as we regard this as an opportunity to enlarge its usability.
Department/s
- Department of Statistics
Publishing year
2020
Language
English
Pages
917-943
Publication/Series
Electronic Journal of Statistics
Volume
14
Issue
1
Document type
Journal article
Publisher
Institute of Mathematical Statistics
Topic
- Probability Theory and Statistics
Status
Published
ISBN/ISSN/Other
- ISSN: 1935-7524