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Generalized bounds for active subspaces

Teixeira Parente, Mario ; Wallin, Jonas LU and Wohlmuth, Barbara (2020) In Electronic Journal of Statistics 14(1). p.917-943
Abstract
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... (More)
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. (Less)
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Electronic Journal of Statistics
volume
14
issue
1
pages
917 - 943
publisher
Institute of Mathematical Statistics
ISSN
1935-7524
language
English
LU publication?
yes
id
7d0d2f3e-3971-4f3c-9ccc-5b0b4185d947
alternative location
https://projecteuclid.org/euclid.ejs/1581995159
date added to LUP
2020-12-10 13:26:24
date last changed
2020-12-10 13:26:24
@article{7d0d2f3e-3971-4f3c-9ccc-5b0b4185d947,
  abstract     = {{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.}},
  author       = {{Teixeira Parente, Mario and Wallin, Jonas and Wohlmuth, Barbara}},
  issn         = {{1935-7524}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{917--943}},
  publisher    = {{Institute of Mathematical Statistics}},
  series       = {{Electronic Journal of Statistics}},
  title        = {{Generalized bounds for active subspaces}},
  url          = {{https://projecteuclid.org/euclid.ejs/1581995159}},
  volume       = {{14}},
  year         = {{2020}},
}