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Partial correlation graphical LASSO
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Carter, Jack Storror, Rossell, David and Smith, Jim Q. (2023) Partial correlation graphical LASSO. Scandinavian Journal of Statistics, 51 (1). pp. 32-63. doi:10.1111/sjos.12675 ISSN 0303-6898.
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Official URL: http://dx.doi.org/10.1111/sjos.12675
Abstract
Standard likelihood penalties to learn Gaussian graphical models are based on regularizing the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit sample variances. We show that such standardization can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood,
and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an
penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference.
Item Type: | Journal Article | ||||||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Asymptotic efficiencies (Statistics), Gaussian processes , Bayesian statistical decision theory, Mathematical statistics, Linear models (Statistics), Matrices | ||||||||||||||||||||||||
Journal or Publication Title: | Scandinavian Journal of Statistics | ||||||||||||||||||||||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||||||||||||||||||
ISSN: | 0303-6898 | ||||||||||||||||||||||||
Official Date: | March 2023 | ||||||||||||||||||||||||
Dates: |
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Volume: | 51 | ||||||||||||||||||||||||
Number: | 1 | ||||||||||||||||||||||||
Page Range: | pp. 32-63 | ||||||||||||||||||||||||
DOI: | 10.1111/sjos.12675 | ||||||||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||||||||
Date of first compliant deposit: | 18 October 2023 | ||||||||||||||||||||||||
Date of first compliant Open Access: | 20 October 2023 | ||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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