Block coordinate descent algorithm improves variable selection and estimation in error-in-variables regression.

Area of Science:

• Statistics
• Biostatistics
• Genomics

Background:

• High-dimensional regression modeling is crucial in medical research.
• Measurement errors in data require specialized error-in-variables methods.
• Existing methods like Convex Conditioned Lasso (CoCoLasso) are computationally intensive.

Purpose of the Study:

• To develop a computationally efficient algorithm for error-in-variables regression in high-dimensional data with partial measurement error.
• To improve upon the performance of existing methods like CoCoLasso and the naive Lasso.
• To enhance the accessibility of error-in-variables adjustments for complex datasets.

Main Methods:

• Developed the Block coordinate Descent Convex Conditioned Lasso (BDCoCoLasso) algorithm.
• Implemented an iterative optimization for uncorrupted and corrupted features to reduce computational cost.
• Utilized a specially calibrated cross-validation error formulation and introduced an optional smoothly clipped absolute deviation penalization.

Main Results:

• BDCoCoLasso successfully handles larger feature sets compared to CoCoLasso.
• The algorithm demonstrates enhanced estimation accuracy and consistency over the naive Lasso, especially with increasing measurement error.
• BDCoCoLasso achieved higher prediction accuracy on UK Biobank data for genetic risk scores.

Conclusions:

• BDCoCoLasso offers a computationally efficient and accurate solution for high-dimensional regression with measurement error.
• The algorithm and accompanying R package make advanced statistical techniques more accessible.
• BDCoCoLasso has significant potential for applications in genomics and personalized medicine.