Automorphism groups of Gaussian Bayesian networks

Draisma, Jan; Zwiernik, Piotr (2017). Automorphism groups of Gaussian Bayesian networks. Bernoulli, 23(2), pp. 1102-1129. International Statistical Institute 10.3150/15-BEJ771

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In this paper, we extend earlier work on groups acting on Gaussian graphical models to Gaussian Bayesian networks and more general Gaussian models defined by chain graphs with no induced subgraphs of the form i→j−k. We fully characterise the maximal group of linear transformations which stabilises a given model and we provide basic statistical applications of this result. This includes equivariant estimation, maximal invariants for hypothesis testing and robustness. In our proof, we derive simple necessary and sufficient conditions on vanishing subminors of the concentration matrix in the model. The computation of the group requires finding the essential graph. However, by applying Stúdeny’s theory of imsets, we show that computations for DAGs can be performed efficiently without building the essential graph.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Draisma, Jan

Subjects:

500 Science > 510 Mathematics

ISSN:

1350-7265

Publisher:

International Statistical Institute

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 10:56

Last Modified:

17 Apr 2018 10:56

Publisher DOI:

10.3150/15-BEJ771

BORIS DOI:

10.7892/boris.109146

URI:

https://boris.unibe.ch/id/eprint/109146

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