Hypersurfaces and their singularities in partial correlation testing
Lin S, Uhler C, Sturmfels B, Bühlmann P. 2014. Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. 14(5), 1079–1116.
Download (ext.)
Journal Article
| Published
| English
Scopus indexed
Author
Lin, Shaowei;
Uhler, CarolineISTA 
;
Sturmfels, Bernd;
Bühlmann, Peter
;
Sturmfels, Bernd;
Bühlmann, PeterDepartment
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.
Publishing Year
Date Published
2014-10-10
Journal Title
Foundations of Computational Mathematics
Publisher
Springer
Acknowledgement
This work was supported in part by the US National Science Foundation (DMS-0968882) and the Defense Advanced Research Projects Agency (DARPA) Deep Learning program (FA8650-10-C-7020).
Volume
14
Issue
5
Page
1079 - 1116
IST-REx-ID
Cite this
Lin S, Uhler C, Sturmfels B, Bühlmann P. Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. 2014;14(5):1079-1116. doi:10.1007/s10208-014-9205-0
Lin, S., Uhler, C., Sturmfels, B., & Bühlmann, P. (2014). Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9205-0
Lin, Shaowei, Caroline Uhler, Bernd Sturmfels, and Peter Bühlmann. “Hypersurfaces and Their Singularities in Partial Correlation Testing.” Foundations of Computational Mathematics. Springer, 2014. https://doi.org/10.1007/s10208-014-9205-0.
S. Lin, C. Uhler, B. Sturmfels, and P. Bühlmann, “Hypersurfaces and their singularities in partial correlation testing,” Foundations of Computational Mathematics, vol. 14, no. 5. Springer, pp. 1079–1116, 2014.
Lin S, Uhler C, Sturmfels B, Bühlmann P. 2014. Hypersurfaces and their singularities in partial correlation testing. Foundations of Computational Mathematics. 14(5), 1079–1116.
Lin, Shaowei, et al. “Hypersurfaces and Their Singularities in Partial Correlation Testing.” Foundations of Computational Mathematics, vol. 14, no. 5, Springer, 2014, pp. 1079–116, doi:10.1007/s10208-014-9205-0.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Link(s) to Main File(s)
Access Level
Open Access
Google Scholar