Hypersurfaces and their singularities in partial correlation testing
Statistics Theory
2014-11-05 v2 Algebraic Geometry
Statistics Theory
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.
Cite
@article{arxiv.1209.0285,
title = {Hypersurfaces and their singularities in partial correlation testing},
author = {Shaowei Lin and Caroline Uhler and Bernd Sturmfels and Peter Bühlmann},
journal= {arXiv preprint arXiv:1209.0285},
year = {2014}
}