Leveraging independence in high-dimensional mixed linear regression.

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• High-dimensional data presents challenges for mixed linear regression.
• Existing methods often oversimplify predictor variability and lack synergistic selection.
• The expectation-maximization (EM) algorithm is a common approach for likelihood maximization.

Purpose of the Study:

• To develop an efficient method for estimating regression coefficients and selecting predictors in high-dimensional mixed linear regression.
• To address limitations of existing EM-based procedures by accounting for predictor variability.
• To achieve synergistic variable selection across mixture components.

Main Methods:

• Leveraging the independence between predictors and latent indicator variables for efficient computation.
• Incorporating fast group-penalized EM estimation.
• Establishing non-asymptotic convergence rates for the proposed estimator.

Main Results:

• The proposed method facilitates efficient computation and synergistic variable selection.
• Non-asymptotic convergence rates to true regression parameters are established.
• Demonstrated effectiveness through extensive simulations and real-world data analysis.

Conclusions:

• The novel penalized EM algorithm offers a robust solution for high-dimensional mixed linear regression.
• The method enhances both parameter estimation and variable selection accuracy.
• Applicable to biological data, such as predicting anticancer drug sensitivity.