Hypersurfaces and their singularities in partial correlation testing

DOI10.1007/s10208-014-9205-0zbMath1308.62110arXiv1209.0285OpenAlexW2143143687MaRDI QIDQ486682

Bernd Sturmfels, Shaowei Lin, Caroline Uhler, Peter Bühlmann

Publication date: 16 January 2015

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0285

zbMATH Keywords

resolution of singularitiescausal inferenceGaussian graphical modelalgebraic statisticsreal log canonical thresholdsingular learning theory

Mathematics Subject Classification ID

Measures of association (correlation, canonical correlation, etc.) (62H20) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Computational aspects of algebraic surfaces (14Q10)

Related Items (5)

Unnamed Item ⋮ Geometry of the faithfulness assumption in causal inference ⋮ Partial correlation hypersurfaces in Gaussian graphical models ⋮ A review of Gaussian Markov models for conditional independence ⋮ A uniformly consistent estimator of causal effects under the \(k\)-triangle-faithfulness assumption

Uses Software

• Macaulay2
• SINGULAR
• pcalg

Cites Work

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• Geometry of the faithfulness assumption in causal inference
• Oscillatory integral decay, sublevel set growth, and the Newton polyhedron
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Adjustments and their Consequences-Collapsibility Analysis using Graphical Models
• Algebraic Geometry and Statistical Learning Theory
• Lectures on Resolution of Singularities (AM-166)
• The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
• Level Sets and NonGaussian Integrals of Positively Homogeneous Functions

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