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Partial correlation hypersurfaces in Gaussian graphical models
Draisma, Jan1
1 Universität Bern Mathematisches Institut Sidlerstrasse 5 3012 Bern (Switzerland) and Eindhoven University of Technology Department of Mathematics and Computer Science P.O. Box 513 5600 MB Eindhoven (The Netherlands)
Algebraic Combinatorics, Volume 2 (2019) no. 3, pp. 439-446.

We derive a combinatorial sufficient condition for a partial correlation hypersurface in the parameter space of a directed Gaussian graphical model to be nonsingular, and speculate on whether this condition can be used in algorithms for learning the graph. Since the condition is fulfilled in the case of a complete DAG on any number of vertices, the result implies an affirmative answer to a question raised by Lin–Uhler–Sturmfels–Bühlmann.

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Accepted:
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DOI: 10.5802/alco.44
Classification: 62H05, 62H20
Keywords: partial correlation, Gaussian graphical models, trek separation

Draisma, Jan 1

1 Universität Bern Mathematisches Institut Sidlerstrasse 5 3012 Bern (Switzerland) and Eindhoven University of Technology Department of Mathematics and Computer Science P.O. Box 513 5600 MB Eindhoven (The Netherlands)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Draisma, Jan. Partial correlation hypersurfaces in Gaussian graphical models. Algebraic Combinatorics, Volume 2 (2019) no. 3, pp. 439-446. doi : 10.5802/alco.44. https://alco.centre-mersenne.org/articles/10.5802/alco.44/

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