Network Inference With the Lasso.

Area of Science:

• Network analysis
• Statistical inference
• Machine learning

Background:

• Calculating confidence intervals and p-values for network edges quantifies uncertainty.
• Lasso estimation, commonly used for network edge selection, presents challenges in obtaining accurate p-values and confidence intervals due to its discontinuous distribution at zero.
• Assumptions for lasso-based network edge identification may not always align with the data at hand.

Purpose of the Study:

• To review and compare methods for calculating confidence intervals and p-values for network edges.
• To evaluate modified lasso approaches (desparsified/debiased lasso) and non-lasso p-value determination methods.
• To identify optimal methods for network edge selection and uncertainty quantification.

Main Methods:

• Review of three methods: desparsified lasso, debiased lasso, and a hybrid approach using lasso for selection followed by non-lasso p-value calculation.
• Simulation studies comparing these methods with popular Gaussian Graphical Model estimation techniques.
• Evaluation of confidence intervals and p-value accuracy for network edge presence/absence determination.

Main Results:

• The desparsified lasso and its bootstrapped version demonstrated superior performance in simulations.
• These methods effectively address the limitations of standard lasso estimation for uncertainty quantification.
• Comparison with established Gaussian Graphical Model methods highlighted the advantages of the reviewed techniques.

Conclusions:

• The desparsified lasso and its bootstrapped variant are recommended for network edge selection and uncertainty quantification.
• These methods provide reliable confidence intervals and p-values, improving upon standard lasso techniques.
• The findings support the use of desparsified lasso for robust network inference.