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Selective Inference for Sparse Graphs via Neighborhood Selection.

Yiling Huang1, Snigdha Panigrahi1, Walter Dempsey2

  • 1Department of Statistics, University of Michigan.

Electronic Journal of Statistics
|November 24, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new selective inference method for Gaussian graphical models, enhancing the replicability of graph estimates by providing uncertainty estimates for precision matrices. The method improves statistical power and accuracy in network analysis.

Keywords:
Covariance selectionGaussian graphical modelsNetwork analysisPenalized regressionPost-selection inferenceSelective inference

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Area of Science:

  • Statistics
  • Machine Learning
  • Network Analysis

Background:

  • Neighborhood selection estimates sparse precision matrices for graphical models.
  • Point estimates lack uncertainty, hindering replicability, especially in psychology.
  • Gaussian graphical models are widely used but require robust uncertainty quantification.

Purpose of the Study:

  • To introduce a selective inference method for Gaussian graphical models.
  • To provide uncertainty estimates for selected edges in precision matrices.
  • To improve the replicability and accuracy of graph structure estimation.

Main Methods:

  • Developed a selective inference technique for Gaussian graphical models.
  • Incorporated exact adjustments for edge selection within the Wishart density.
  • Utilized externally added randomization variables for computational efficiency.

Main Results:

  • The proposed method provides valid selective inferences with exact adjustments.
  • Demonstrated higher statistical power compared to existing methods.
  • Showcased improved estimation accuracy in simulations and a real-world health study.

Conclusions:

  • The selective inference method enhances the reliability of graphical model selection.
  • Offers a practical solution for addressing the replicability crisis in network analysis.
  • Validates the approach through simulations and a mobile health trial application.