Bernoulli

  • Bernoulli
  • Volume 23, Number 2 (2017), 1102-1129.

Automorphism groups of Gaussian Bayesian networks

Jan Draisma and Piotr Zwiernik

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Abstract

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 $i\to j-k$. 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.

Article information

Source
Bernoulli, Volume 23, Number 2 (2017), 1102-1129.

Dates
Received: January 2015
Revised: September 2015
First available in Project Euclid: 4 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1486177394

Digital Object Identifier
doi:10.3150/15-BEJ771

Mathematical Reviews number (MathSciNet)
MR3606761

Zentralblatt MATH identifier
1381.62223

Keywords
chain graphs Gaussian graphical models group action equivariant estimator invariant test transformation family

Citation

Draisma, Jan; Zwiernik, Piotr. Automorphism groups of Gaussian Bayesian networks. Bernoulli 23 (2017), no. 2, 1102--1129. doi:10.3150/15-BEJ771. https://projecteuclid.org/euclid.bj/1486177394


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