Uncertainty quantification in high-dimensional linear models incorporating graphical structures with applications to...

Area of Science:

• Genomics and Bioinformatics
• Statistical Genetics
• High-Dimensional Data Analysis

Background:

• Gene functions in biological networks are often correlated due to functional connectivity.
• Existing variable selection methods incorporate network information but lack uncertainty quantification for individual genes.
• High dimensionality and strong predictor correlations pose challenges in statistical modeling of gene-trait associations.

Purpose of the Study:

• To develop a method for quantifying the uncertainty of individual genes within network-informed variable selection.
• To construct confidence intervals (CIs) and P-values for parameters in high-dimensional linear models with graphical structures.
• To address the limitations of existing methods in handling highly correlated predictors and providing uncertainty estimates.

Main Methods:

• Proposed a graph-constrained desparsified LASSO (GCDL) estimator for high-dimensional linear models.
• Incorporated graphical network information into the LASSO framework to improve variable selection.
• Developed theoretical guarantees for the GCDL estimator, including asymptotic normality and uniform convergence.

Main Results:

• The GCDL estimator demonstrated reduced influence from highly correlated predictors compared to standard desparsified LASSO.
• Theoretical analysis confirmed the asymptotic normality and uniform convergence properties of the GCDL estimator.
• Extensive simulations showed that the GCDL estimator and its derived uniform confidence intervals perform well, even with strong predictor correlations.

Conclusions:

• The proposed GCDL method effectively quantifies gene uncertainty in network-based high-dimensional models.
• The method offers improved accuracy and computational efficiency over existing approaches.
• An R package is available for implementing the GCDL method, facilitating its application in genetic studies.