English

Partial correlation hypersurfaces in Gaussian graphical models

Statistics Theory 2018-09-25 v2 Algebraic Geometry Combinatorics Statistics Theory

Abstract

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-B\"uhlmann.

Keywords

Cite

@article{arxiv.1806.00320,
  title  = {Partial correlation hypersurfaces in Gaussian graphical models},
  author = {Jan Draisma},
  journal= {arXiv preprint arXiv:1806.00320},
  year   = {2018}
}

Comments

9 pages, 5 figures, added Example 13, some minor further edits

R2 v1 2026-06-23T02:16:03.212Z