NDLI: Hypersurfaces and Their Singularities in Partial Correlation Testing

Content Provider	Springer Nature Link
Author	Uhler, Caroline Sturmfels, Bernd Bühlmann, Peter Lin, Shaowei
Copyright Year	2014
Abstract	An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC algorithm and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow ties, tripartite graphs, and complete graphs.
Ending Page	1116
Page Count	38
Starting Page	1079
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	5
Volume Number	14
Language	English
Publisher	Springer US
Publisher Date	2014-05-30
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Causal inference Economics general Algebraic statistics Linear and Multilinear Algebras, Matrix Theory Singular learning theory Resolution of singularities Measures of association (correlation, canonical correlation, etc.) Numerical Analysis Real log canonical threshold Computer Science Gaussian graphical model Characterization and structure theory Applications of Mathematics Math Applications in Computer Science Surfaces, hypersurfaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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