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Jonas Wallin. Photo.

Jonas Wallin

Senior lecturer, Director of third cycle studies, Department of Statistics

Jonas Wallin. Photo.

Generalized bounds for active subspaces

Author

  • Mario Teixeira Parente
  • Jonas Wallin
  • Barbara Wohlmuth

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