Selective Inference for Sparse Graphs via Neighborhood Selection

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.